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diff --git a/slib_5.html b/slib_5.html deleted file mode 100644 index b3ef4b8..0000000 --- a/slib_5.html +++ /dev/null @@ -1,6100 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" - "http://www.w3.org/TR/html40/loose.dtd"> -<HTML> -<!-- Created on January, 10 2005 by texi2html 1.66 --> -<!-- -Written by: Lionel Cons <Lionel.Cons@cern.ch> (original author) - Karl Berry <karl@freefriends.org> - Olaf Bachmann <obachman@mathematik.uni-kl.de> - and many others. -Maintained by: Many creative people <dev@texi2html.cvshome.org> -Send bugs and suggestions to <users@texi2html.cvshome.org> - ---> -<HEAD> -<TITLE>SLIB: Mathematical Packages</TITLE> - -<META NAME="description" CONTENT="SLIB: Mathematical Packages"> -<META NAME="keywords" CONTENT="SLIB: Mathematical Packages"> -<META NAME="resource-type" CONTENT="document"> -<META NAME="distribution" CONTENT="global"> -<META NAME="Generator" CONTENT="texi2html 1.66"> - -</HEAD> - -<BODY LANG="en" BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#0000FF" VLINK="#800080" ALINK="#FF0000"> - -<A NAME="SEC88"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_4.html#SEC87"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC89"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_4.html#SEC45"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H1> 5. Mathematical Packages </H1> -<!--docid::SEC88::--> -<P> - -<TABLE BORDER="0" CELLSPACING="0"> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC89">5.1 Bit-Twiddling</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'logical</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC95">5.2 Modular Arithmetic</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'modular</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC96">5.3 Prime Numbers</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'factor</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC97">5.4 Random Numbers</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'random</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC100">5.5 Fast Fourier Transform</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'fft</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC101">5.6 Cyclic Checksum</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'crc</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC102">5.7 Graphing</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC112">5.8 Solid Modeling</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">VRML97</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC118">5.9 Color</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC134">5.10 Root Finding</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'root</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC135">5.11 Minimizing</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'minimize</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC136">5.12 Commutative Rings</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'commutative-ring</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC139">5.15 Matrix Algebra</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'determinant</TD></TR> -</TABLE> -<P> - -<A NAME="Bit-Twiddling"></A> -<HR SIZE="6"> -<A NAME="SEC89"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC90"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.1 Bit-Twiddling </H2> -<!--docid::SEC89::--> -<P> - -<CODE>(require 'logical)</CODE> -<A NAME="IDX476"></A> -</P> -<P> - -The bit-twiddling functions are made available through the use of the -<CODE>logical</CODE> package. <CODE>logical</CODE> is loaded by inserting -<CODE>(require 'logical)</CODE> before the code that uses these -<A NAME="IDX477"></A> -functions. These functions behave as though operating on integers -in two's-complement representation. -</P> -<P> - -<HR SIZE="6"> -<A NAME="SEC90"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC89"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC91"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.1.1 Bitwise Operations </H3> -<!--docid::SEC90::--> -<P> - -<A NAME="IDX478"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logand</B> <I>n1 n1</I> -<DD>Returns the integer which is the bit-wise AND of the two integer -arguments. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (logand #b1100 #b1010) 2) - => "1000" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX479"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logior</B> <I>n1 n2</I> -<DD>Returns the integer which is the bit-wise OR of the two integer -arguments. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (logior #b1100 #b1010) 2) - => "1110" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX480"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logxor</B> <I>n1 n2</I> -<DD>Returns the integer which is the bit-wise XOR of the two integer -arguments. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (logxor #b1100 #b1010) 2) - => "110" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX481"></A> -</P> -<DL> -<DT><U>Function:</U> <B>lognot</B> <I>n</I> -<DD>Returns the integer which is the 2s-complement of the integer argument. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (lognot #b10000000) 2) - => "-10000001" -(number->string (lognot #b0) 2) - => "-1" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX482"></A> -</P> -<DL> -<DT><U>Function:</U> <B>bitwise-if</B> <I>mask n0 n1</I> -<DD>Returns an integer composed of some bits from integer <VAR>n0</VAR> and some -from integer <VAR>n1</VAR>. A bit of the result is taken from <VAR>n0</VAR> if the -corresponding bit of integer <VAR>mask</VAR> is 1 and from <VAR>n1</VAR> if that bit -of <VAR>mask</VAR> is 0. -</DL> -<P> - -<A NAME="IDX483"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logtest</B> <I>j k</I> -<DD><TABLE><tr><td> </td><td class=example><pre>(logtest j k) == (not (zero? (logand j k))) - -(logtest #b0100 #b1011) => #f -(logtest #b0100 #b0111) => #t -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX484"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logcount</B> <I>n</I> -<DD>Returns the number of bits in integer <VAR>n</VAR>. If integer is positive, -the 1-bits in its binary representation are counted. If negative, the -0-bits in its two's-complement binary representation are counted. If 0, -0 is returned. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(logcount #b10101010) - => 4 -(logcount 0) - => 0 -(logcount -2) - => 1 -</pre></td></tr></table></DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC91"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC90"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC92"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.1.2 Bit Within Word </H3> -<!--docid::SEC91::--> -<P> - -<A NAME="IDX485"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logbit?</B> <I>index j</I> -<DD><TABLE><tr><td> </td><td class=example><pre>(logbit? index j) == (logtest (integer-expt 2 index) j) - -(logbit? 0 #b1101) => #t -(logbit? 1 #b1101) => #f -(logbit? 2 #b1101) => #t -(logbit? 3 #b1101) => #t -(logbit? 4 #b1101) => #f -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX486"></A> -</P> -<DL> -<DT><U>Function:</U> <B>copy-bit</B> <I>index from bit</I> -<DD>Returns an integer the same as <VAR>from</VAR> except in the <VAR>index</VAR>th bit, -which is 1 if <VAR>bit</VAR> is <CODE>#t</CODE> and 0 if <VAR>bit</VAR> is <CODE>#f</CODE>. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (copy-bit 0 0 #t) 2) => "1" -(number->string (copy-bit 2 0 #t) 2) => "100" -(number->string (copy-bit 2 #b1111 #f) 2) => "1011" -</pre></td></tr></table></DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC92"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC91"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC93"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.1.3 Fields of Bits </H3> -<!--docid::SEC92::--> -<P> - -<A NAME="IDX487"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logical:ones</B> <I>n</I> -<DD>Returns the smallest non-negative integer having <VAR>n</VAR> binary ones. -</DL> -<P> - -<A NAME="IDX488"></A> -</P> -<DL> -<DT><U>Function:</U> <B>bit-field</B> <I>n start end</I> -<DD>Returns the integer composed of the <VAR>start</VAR> (inclusive) through -<VAR>end</VAR> (exclusive) bits of <VAR>n</VAR>. The <VAR>start</VAR>th bit becomes -the 0-th bit in the result. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (bit-field #b1101101010 0 4) 2) - => "1010" -(number->string (bit-field #b1101101010 4 9) 2) - => "10110" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX489"></A> -</P> -<DL> -<DT><U>Function:</U> <B>copy-bit-field</B> <I>to start end from</I> -<DD>Returns an integer the same as <VAR>to</VAR> except possibly in the -<VAR>start</VAR> (inclusive) through <VAR>end</VAR> (exclusive) bits, which are -the same as those of <VAR>from</VAR>. The 0-th bit of <VAR>from</VAR> becomes the -<VAR>start</VAR>th bit of the result. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (copy-bit-field #b1101101010 0 4 0) 2) - => "1101100000" -(number->string (copy-bit-field #b1101101010 0 4 -1) 2) - => "1101101111" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX490"></A> -</P> -<DL> -<DT><U>Function:</U> <B>ash</B> <I>n count</I> -<DD>Returns an integer equivalent to -<CODE>(inexact->exact (floor (* <VAR>n</VAR> (expt 2 <VAR>count</VAR>))))</CODE>. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (ash #b1 3) 2) - => "1000" -(number->string (ash #b1010 -1) 2) - => "101" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX491"></A> -</P> -<DL> -<DT><U>Function:</U> <B>integer-length</B> <I>n</I> -<DD>Returns the number of bits neccessary to represent <VAR>n</VAR>. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(integer-length #b10101010) - => 8 -(integer-length 0) - => 0 -(integer-length #b1111) - => 4 -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX492"></A> -</P> -<DL> -<DT><U>Function:</U> <B>integer-expt</B> <I>n k</I> -<DD>Returns <VAR>n</VAR> raised to the non-negative integer exponent <VAR>k</VAR>. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(integer-expt 2 5) - => 32 -(integer-expt -3 3) - => -27 -</pre></td></tr></table></DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC93"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC92"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC94"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.1.4 Bit order and Lamination </H3> -<!--docid::SEC93::--> -<P> - -<A NAME="IDX493"></A> -</P> -<DL> -<DT><U>Function:</U> <B>logical:rotate</B> <I>k count len</I> -<DD>Returns the low-order <VAR>len</VAR> bits of <VAR>k</VAR> cyclically permuted -<VAR>count</VAR> bits towards high-order. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(number->string (logical:rotate #b0100 3 4) 2) -=> "10" -(number->string (logical:rotate #b0100 -1 4) 2) -=> "10" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX494"></A> -</P> -<DL> -<DT><U>Function:</U> <B>bit-reverse</B> <I>k n</I> -<DD>Returns the low-order <VAR>k</VAR> bits of <VAR>n</VAR> with the bit order -reversed. The low-order bit of <VAR>n</VAR> is the high order bit of the -returned value. -<P> - -<TABLE><tr><td> </td><td class=example><pre>(number->string (bit-reverse 8 #xa7) 16) - => "e5" -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX495"></A> -</P> -<DL> -<DT><U>Function:</U> <B>integer->list</B> <I>k len</I> -<DD><A NAME="IDX496"></A> -<DT><U>Function:</U> <B>integer->list</B> <I>k</I> -<DD><CODE>integer->list</CODE> returns a list of <VAR>len</VAR> booleans corresponding -to each bit of the given integer. #t is coded for each 1; #f for 0. -The <VAR>len</VAR> argument defaults to <CODE>(integer-length <VAR>k</VAR>)</CODE>. -<P> - -<A NAME="IDX497"></A> -<DT><U>Function:</U> <B>list->integer</B> <I>list</I> -<DD><CODE>list->integer</CODE> returns an integer formed from the booleans in the -list <VAR>list</VAR>, which must be a list of booleans. A 1 bit is coded for -each #t; a 0 bit for #f. -</P> -<P> - -<CODE>integer->list</CODE> and <CODE>list->integer</CODE> are inverses so far as -<CODE>equal?</CODE> is concerned. -</P> -</DL> -<P> - -<A NAME="IDX498"></A> -</P> -<DL> -<DT><U>Function:</U> <B>booleans->integer</B> <I>bool1 <small>...</small></I> -<DD>Returns the integer coded by the <VAR>bool1</VAR> <small>...</small> arguments. -</DL> -<P> - -<A NAME="IDX499"></A> -</P> -<DL> -<DT><U>Function:</U> <B>bitwise:laminate</B> <I>k1 <small>...</small></I> -<DD>Returns an integer composed of the bits of <VAR>k1</VAR> <small>...</small> interlaced -in argument order. Given <VAR>k1</VAR>, <small>...</small> <VAR>kn</VAR>, the n low-order -bits of the returned value will be the lowest-order bit of each -argument. -<P> - -<A NAME="IDX500"></A> -<DT><U>Function:</U> <B>bitwise:delaminate</B> <I>count k</I> -<DD>Returns a list of <VAR>count</VAR> integers comprised of every <VAR>count</VAR>h -bit of the integer <VAR>k</VAR>. -</P> -<P> - -For any non-negative integers <VAR>k</VAR> and <VAR>count</VAR>: -<TABLE><tr><td> </td><td class=example><pre>(eqv? k (bitwise:laminate (bitwise:delaminate count k))) -</pre></td></tr></table></DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC94"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC93"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC95"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.1.5 Gray code </H3> -<!--docid::SEC94::--> -<P> - -<A NAME="IDX501"></A> -A <EM>Gray code</EM> is an ordering of non-negative integers in which -exactly one bit differs between each pair of successive elements. There -are multiple Gray codings. An n-bit Gray code corresponds to a -Hamiltonian cycle on an n-dimensional hypercube. -</P> -<P> - -Gray codes find use communicating incrementally changing values between -asynchronous agents. De-laminated Gray codes comprise the coordinates -of Peano-Hilbert space-filling curves. -</P> -<P> - -<A NAME="IDX502"></A> -</P> -<DL> -<DT><U>Function:</U> <B>integer->gray-code</B> <I>k</I> -<DD>Converts <VAR>k</VAR> to a Gray code of the same <CODE>integer-length</CODE> as -<VAR>k</VAR>. -<P> - -<A NAME="IDX503"></A> -<DT><U>Function:</U> <B>gray-code->integer</B> <I>k</I> -<DD>Converts the Gray code <VAR>k</VAR> to an integer of the same -<CODE>integer-length</CODE> as <VAR>k</VAR>. -</P> -<P> - -For any non-negative integer <VAR>k</VAR>, -<TABLE><tr><td> </td><td class=example><pre>(eqv? k (gray-code->integer (integer->gray-code k))) -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX504"></A> -</P> -<DL> -<DT><U>Function:</U> <B>=</B> <I>k1 k2</I> -<DD><A NAME="IDX505"></A> -<DT><U>Function:</U> <B>gray-code<?</B> <I>k1 k2</I> -<DD><A NAME="IDX506"></A> -<DT><U>Function:</U> <B>gray-code>?</B> <I>k1 k2</I> -<DD><A NAME="IDX507"></A> -<DT><U>Function:</U> <B>gray-code<=?</B> <I>k1 k2</I> -<DD><A NAME="IDX508"></A> -<DT><U>Function:</U> <B>gray-code>=?</B> <I>k1 k2</I> -<DD>These procedures return #t if their Gray code arguments are -(respectively): equal, monotonically increasing, monotonically -decreasing, monotonically nondecreasing, or monotonically nonincreasing. -<P> - -For any non-negative integers <VAR>k1</VAR> and <VAR>k2</VAR>, the Gray code -predicate of <CODE>(integer->gray-code k1)</CODE> and -<CODE>(integer->gray-code k2)</CODE> will return the same value as the -corresponding predicate of <VAR>k1</VAR> and <VAR>k2</VAR>. -</P> -</DL> -<P> - -<A NAME="Modular Arithmetic"></A> -<HR SIZE="6"> -<A NAME="SEC95"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC94"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC96"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.2 Modular Arithmetic </H2> -<!--docid::SEC95::--> -<P> - -<CODE>(require 'modular)</CODE> -<A NAME="IDX509"></A> -</P> -<P> - -<A NAME="IDX510"></A> -</P> -<DL> -<DT><U>Function:</U> <B>mod</B> <I>x1 x2</I> -<DD><A NAME="IDX511"></A> -<DT><U>Function:</U> <B>rem</B> <I>x1 x2</I> -<DD><P> - -These procedures implement the Common-Lisp functions of the same names. -The real number <VAR>x2</VAR> must be non-zero. -<CODE>mod</CODE> returns <CODE>(- <VAR>x1</VAR> (* <VAR>x2</VAR> (floor (/ <VAR>x1</VAR> <VAR>x2</VAR>))))</CODE>. -<CODE>rem</CODE> returns <CODE>(- <VAR>x1</VAR> (* <VAR>x2</VAR> (truncate (/ <VAR>x1</VAR> <VAR>x2</VAR>))))</CODE>. -</P> -<P> - -If <VAR>x1</VAR> and <VAR>x2</VAR> are integers, then <CODE>mod</CODE> behaves like -<CODE>modulo</CODE> and <CODE>rem</CODE> behaves like <CODE>remainder</CODE>. -</P> -<P> - -<TABLE><tr><td> </td><td class=display><pre style="font-family: serif"><TT>(mod -90 360) => 270 -(rem -90 180) => -90 - -(mod 540 360) => 180 -(rem 540 360) => 180 - -(mod (* 5/2 pi) (* 2 pi)) => 1.5707963267948965 -(rem (* -5/2 pi) (* 2 pi)) => -1.5707963267948965 -</TT> -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX512"></A> -</P> -<DL> -<DT><U>Function:</U> <B>extended-euclid</B> <I>n1 n2</I> -<DD><P> - -Returns a list of 3 integers <CODE>(d x y)</CODE> such that d = gcd(<VAR>n1</VAR>, -<VAR>n2</VAR>) = <VAR>n1</VAR> * x + <VAR>n2</VAR> * y. -</P> -</DL> -<P> - -<A NAME="IDX513"></A> -</P> -<DL> -<DT><U>Function:</U> <B>symmetric:modulus</B> <I>n</I> -<DD><P> - -Returns <CODE>(quotient (+ -1 n) -2)</CODE> for positive odd integer <VAR>n</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX514"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modulus->integer</B> <I>modulus</I> -<DD><P> - -Returns the non-negative integer characteristic of the ring formed when -<VAR>modulus</VAR> is used with <CODE>modular:</CODE> procedures. -</P> -</DL> -<P> - -<A NAME="IDX515"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:normalize</B> <I>modulus n</I> -<DD><P> - -Returns the integer <CODE>(modulo <VAR>n</VAR> (modulus->integer -<VAR>modulus</VAR>))</CODE> in the representation specified by <VAR>modulus</VAR>. -</P> -</DL> -The rest of these functions assume normalized arguments; That is, the -arguments are constrained by the following table: -<P> - -For all of these functions, if the first argument (<VAR>modulus</VAR>) is: -</P> -<DL COMPACT> -<DT><CODE>positive?</CODE> -<DD>Work as before. The result is between 0 and <VAR>modulus</VAR>. -<P> - -</P> -<DT><CODE>zero?</CODE> -<DD>The arguments are treated as integers. An integer is returned. -<P> - -</P> -<DT><CODE>negative?</CODE> -<DD>The arguments and result are treated as members of the integers modulo -<CODE>(+ 1 (* -2 <VAR>modulus</VAR>))</CODE>, but with <EM>symmetric</EM> -<A NAME="IDX516"></A> -representation; i.e. <CODE>(<= (- <VAR>modulus</VAR>) <VAR>n</VAR> -<VAR>modulus</VAR>)</CODE>. -</DL> -<P> - -If all the arguments are fixnums the computation will use only fixnums. -</P> -<P> - -<A NAME="IDX517"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:invertable?</B> <I>modulus k</I> -<DD><P> - -Returns <CODE>#t</CODE> if there exists an integer n such that <VAR>k</VAR> * n -== 1 mod <VAR>modulus</VAR>, and <CODE>#f</CODE> otherwise. -</P> -</DL> -<P> - -<A NAME="IDX518"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:invert</B> <I>modulus n2</I> -<DD><P> - -Returns an integer n such that 1 = (n * <VAR>n2</VAR>) mod <VAR>modulus</VAR>. If -<VAR>n2</VAR> has no inverse mod <VAR>modulus</VAR> an error is signaled. -</P> -</DL> -<P> - -<A NAME="IDX519"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:negate</B> <I>modulus n2</I> -<DD><P> - -Returns (-<VAR>n2</VAR>) mod <VAR>modulus</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX520"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:+</B> <I>modulus n2 n3</I> -<DD><P> - -Returns (<VAR>n2</VAR> + <VAR>n3</VAR>) mod <VAR>modulus</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX521"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:-</B> <I>modulus n2 n3</I> -<DD><P> - -Returns (<VAR>n2</VAR> - <VAR>n3</VAR>) mod <VAR>modulus</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX522"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:*</B> <I>modulus n2 n3</I> -<DD><P> - -Returns (<VAR>n2</VAR> * <VAR>n3</VAR>) mod <VAR>modulus</VAR>. -</P> -<P> - -The Scheme code for <CODE>modular:*</CODE> with negative <VAR>modulus</VAR> is -not completed for fixnum-only implementations. -</P> -</DL> -<P> - -<A NAME="IDX523"></A> -</P> -<DL> -<DT><U>Function:</U> <B>modular:expt</B> <I>modulus n2 n3</I> -<DD><P> - -Returns (<VAR>n2</VAR> ^ <VAR>n3</VAR>) mod <VAR>modulus</VAR>. -</P> -</DL> -<P> - -<A NAME="Prime Numbers"></A> -<HR SIZE="6"> -<A NAME="SEC96"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC95"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC97"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.3 Prime Numbers </H2> -<!--docid::SEC96::--> -<P> - -<CODE>(require 'factor)</CODE> -<A NAME="IDX524"></A> -<A NAME="IDX525"></A> -</P> -<P> - -<A NAME="IDX526"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>prime:prngs</B> -<DD><P> - -<VAR>prime:prngs</VAR> is the random-state (see section <A HREF="slib_5.html#SEC97">5.4 Random Numbers</A>) used by these -procedures. If you call these procedures from more than one thread -(or from interrupt), <CODE>random</CODE> may complain about reentrant -calls. -</P> -</DL> -<EM>Note:</EM> The prime test and generation procedures implement (or -use) the Solovay-Strassen primality test. See -<P> - -<UL> -<LI>Robert Solovay and Volker Strassen, -<CITE>A Fast Monte-Carlo Test for Primality</CITE>, -SIAM Journal on Computing, 1977, pp 84-85. -</UL> -<P> - -<A NAME="IDX527"></A> -</P> -<DL> -<DT><U>Function:</U> <B>jacobi-symbol</B> <I>p q</I> -<DD><P> - -Returns the value (+1, -1, or 0) of the Jacobi-Symbol of -exact non-negative integer <VAR>p</VAR> and exact positive odd integer <VAR>q</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX528"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>prime:trials</B> -<DD><P> - -<VAR>prime:trials</VAR> the maxinum number of iterations of Solovay-Strassen that will -be done to test a number for primality. -</P> -</DL> -<P> - -<A NAME="IDX529"></A> -</P> -<DL> -<DT><U>Function:</U> <B>prime?</B> <I>n</I> -<DD><P> - -Returns <CODE>#f</CODE> if <VAR>n</VAR> is composite; <CODE>#t</CODE> if <VAR>n</VAR> is prime. -There is a slight chance <CODE>(expt 2 (- prime:trials))</CODE> that a -composite will return <CODE>#t</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX530"></A> -</P> -<DL> -<DT><U>Function:</U> <B>primes<</B> <I>start count</I> -<DD><P> - -Returns a list of the first <VAR>count</VAR> prime numbers less than -<VAR>start</VAR>. If there are fewer than <VAR>count</VAR> prime numbers -less than <VAR>start</VAR>, then the returned list will have fewer than -<VAR>start</VAR> elements. -</P> -</DL> -<P> - -<A NAME="IDX531"></A> -</P> -<DL> -<DT><U>Function:</U> <B>primes></B> <I>start count</I> -<DD><P> - -Returns a list of the first <VAR>count</VAR> prime numbers greater than <VAR>start</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX532"></A> -</P> -<DL> -<DT><U>Function:</U> <B>factor</B> <I>k</I> -<DD><P> - -Returns a list of the prime factors of <VAR>k</VAR>. The order of the -factors is unspecified. In order to obtain a sorted list do -<CODE>(sort! (factor <VAR>k</VAR>) <)</CODE>. -</P> -</DL> -<P> - -<A NAME="Random Numbers"></A> -<HR SIZE="6"> -<A NAME="SEC97"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC96"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC98"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.4 Random Numbers </H2> -<!--docid::SEC97::--> -<P> - -<A NAME="IDX533"></A> -<A NAME="IDX534"></A> -A pseudo-random number generator is only as good as the tests it passes. -George Marsaglia of Florida State University developed a battery of -tests named <EM>DIEHARD</EM> (<A HREF="http://stat.fsu.edu/~geo/diehard.html">http://stat.fsu.edu/~geo/diehard.html</A>). -`<TT>diehard.c</TT>' has a bug which the patch -<A HREF="http://swissnet.ai.mit.edu/ftpdir/users/jaffer/diehard.c.pat">http://swissnet.ai.mit.edu/ftpdir/users/jaffer/diehard.c.pat</A> corrects. -</P> -<P> - -SLIB's PRNG generates 8 bits at a time. With the degenerate seed -`<SAMP>0</SAMP>', the numbers generated pass DIEHARD; but when bits are -combined from sequential bytes, tests fail. With the seed -`<SAMP>http://swissnet.ai.mit.edu/~jaffer/SLIB.html</SAMP>', all of those -tests pass. -</P> -<P> - -<TABLE BORDER="0" CELLSPACING="0"> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC98">5.4.1 Exact Random Numbers</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'random</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC99">5.4.2 Inexact Random Numbers</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'random-inexact</TD></TR> -</TABLE> -<P> - -<A NAME="Exact Random Numbers"></A> -<HR SIZE="6"> -<A NAME="SEC98"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC97"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC99"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC97"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.4.1 Exact Random Numbers </H3> -<!--docid::SEC98::--> -<P> - -<CODE>(require 'random)</CODE> -<A NAME="IDX535"></A> -</P> -<P> - -<A NAME="IDX536"></A> -</P> -<DL> -<DT><U>Function:</U> <B>random</B> <I>n state</I> -<DD><P> - -<A NAME="IDX537"></A> -<DT><U>Function:</U> <B>random</B> <I>n</I> -<DD></P> -<P> - -<VAR>n</VAR> must be an exact positive integer. <CODE>random</CODE> returns an exact integer -between zero (inclusive) and <VAR>n</VAR> (exclusive). The values returned by -<CODE>random</CODE> are uniformly distributed from 0 to <VAR>n</VAR>. -</P> -<P> - -The optional argument <VAR>state</VAR> must be of the type returned by -<CODE>(seed->random-state)</CODE> or <CODE>(make-random-state)</CODE>. It -defaults to the value of the variable <CODE>*random-state*</CODE>. This -object is used to maintain the state of the pseudo-random-number -generator and is altered as a side effect of calls to <CODE>random</CODE>. -</P> -</DL> -<A NAME="IDX538"></A> -<DL> -<DT><U>Variable:</U> <B>*random-state*</B> -<DD>Holds a data structure that encodes the internal state of the -random-number generator that <CODE>random</CODE> uses by default. The nature -of this data structure is implementation-dependent. It may be printed -out and successfully read back in, but may or may not function correctly -as a random-number state object in another implementation. -</DL> -<P> - -<A NAME="IDX539"></A> -</P> -<DL> -<DT><U>Function:</U> <B>copy-random-state</B> <I>state</I> -<DD><P> - -Returns a new copy of argument <VAR>state</VAR>. -</P> -<P> - -<A NAME="IDX540"></A> -<DT><U>Function:</U> <B>copy-random-state</B> -<DD>Returns a new copy of <CODE>*random-state*</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX541"></A> -</P> -<DL> -<DT><U>Function:</U> <B>seed->random-state</B> <I>seed</I> -<DD><P> - -Returns a new object of type suitable for use as the value of the -variable <CODE>*random-state*</CODE> or as a second argument to <CODE>random</CODE>. -The number or string <VAR>seed</VAR> is used to initialize the state. If -<CODE>seed->random-state</CODE> is called twice with arguments which are -<CODE>equal?</CODE>, then the returned data structures will be <CODE>equal?</CODE>. -Calling <CODE>seed->random-state</CODE> with unequal arguments will nearly -always return unequal states. -</P> -</DL> -<P> - -<A NAME="IDX542"></A> -</P> -<DL> -<DT><U>Function:</U> <B>make-random-state</B> -<DD><P> - -<A NAME="IDX543"></A> -<DT><U>Function:</U> <B>make-random-state</B> <I>obj</I> -<DD>Returns a new object of type suitable for use as the value of the -variable <CODE>*random-state*</CODE> or as a second argument to <CODE>random</CODE>. -If the optional argument <VAR>obj</VAR> is given, it should be a printable -Scheme object; the first 50 characters of its printed representation -will be used as the seed. Otherwise the value of <CODE>*random-state*</CODE> -is used as the seed. -</P> -</DL> -<P> - -<A NAME="Inexact Random Numbers"></A> -<HR SIZE="6"> -<A NAME="SEC99"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC98"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC100"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC97"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.4.2 Inexact Random Numbers </H3> -<!--docid::SEC99::--> -<P> - -<CODE>(require 'random-inexact)</CODE> -<A NAME="IDX544"></A> -</P> -<P> - -<A NAME="IDX545"></A> -</P> -<DL> -<DT><U>Function:</U> <B>random:uniform</B> -<DD><P> - -<A NAME="IDX546"></A> -<DT><U>Function:</U> <B>random:uniform</B> <I>state</I> -<DD>Returns an uniformly distributed inexact real random number in the -range between 0 and 1. -</P> -</DL> -<P> - -<A NAME="IDX547"></A> -</P> -<DL> -<DT><U>Function:</U> <B>random:exp</B> -<DD><P> - -<A NAME="IDX548"></A> -<DT><U>Function:</U> <B>random:exp</B> <I>state</I> -<DD>Returns an inexact real in an exponential distribution with mean 1. For -an exponential distribution with mean <VAR>u</VAR> use -<CODE>(* <VAR>u</VAR> (random:exp))</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX549"></A> -</P> -<DL> -<DT><U>Function:</U> <B>random:normal</B> -<DD><P> - -<A NAME="IDX550"></A> -<DT><U>Function:</U> <B>random:normal</B> <I>state</I> -<DD>Returns an inexact real in a normal distribution with mean 0 and -standard deviation 1. For a normal distribution with mean <VAR>m</VAR> and -standard deviation <VAR>d</VAR> use -<CODE>(+ <VAR>m</VAR> (* <VAR>d</VAR> (random:normal)))</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX551"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>random:normal-vector!</B> <I>vect</I> -<DD><P> - -<A NAME="IDX552"></A> -<DT><U>Procedure:</U> <B>random:normal-vector!</B> <I>vect state</I> -<DD>Fills <VAR>vect</VAR> with inexact real random numbers which are independent -and standard normally distributed (i.e., with mean 0 and variance 1). -</P> -</DL> -<P> - -<A NAME="IDX553"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>random:hollow-sphere!</B> <I>vect</I> -<DD><P> - -<A NAME="IDX554"></A> -<DT><U>Procedure:</U> <B>random:hollow-sphere!</B> <I>vect state</I> -<DD>Fills <VAR>vect</VAR> with inexact real random numbers the sum of whose -squares is equal to 1.0. Thinking of <VAR>vect</VAR> as coordinates in space -of dimension n = <CODE>(vector-length <VAR>vect</VAR>)</CODE>, the coordinates are -uniformly distributed over the surface of the unit n-shere. -</P> -</DL> -<P> - -<A NAME="IDX555"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>random:solid-sphere!</B> <I>vect</I> -<DD><P> - -<A NAME="IDX556"></A> -<DT><U>Procedure:</U> <B>random:solid-sphere!</B> <I>vect state</I> -<DD>Fills <VAR>vect</VAR> with inexact real random numbers the sum of whose -squares is less than 1.0. Thinking of <VAR>vect</VAR> as coordinates in -space of dimension <VAR>n</VAR> = <CODE>(vector-length <VAR>vect</VAR>)</CODE>, the -coordinates are uniformly distributed within the unit <VAR>n</VAR>-shere. -The sum of the squares of the numbers is returned. -</P> -</DL> -<P> - -<A NAME="Fast Fourier Transform"></A> -<HR SIZE="6"> -<A NAME="SEC100"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC99"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC101"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.5 Fast Fourier Transform </H2> -<!--docid::SEC100::--> -<P> - -<CODE>(require 'fft)</CODE> -<A NAME="IDX557"></A> -</P> -<P> - -<A NAME="IDX558"></A> -</P> -<DL> -<DT><U>Function:</U> <B>fft</B> <I>array</I> -<DD><P> - -<VAR>array</VAR> is an array of <CODE>(expt 2 n)</CODE> numbers. <CODE>fft</CODE> -returns an array of complex numbers comprising the -<EM>Discrete Fourier Transform</EM> of <VAR>array</VAR>. -<A NAME="IDX559"></A> -</P> -</DL> -<P> - -<A NAME="IDX560"></A> -</P> -<DL> -<DT><U>Function:</U> <B>fft-1</B> <I>array</I> -<DD><P> - -<CODE>fft-1</CODE> returns an array of complex numbers comprising the -inverse Discrete Fourier Transform of <VAR>array</VAR>. -</P> -</DL> -<CODE>(fft-1 (fft <VAR>array</VAR>))</CODE> will return an array of values close to -<VAR>array</VAR>. -<P> - -<TABLE><tr><td> </td><td class=example><pre>(fft '#(1 0+i -1 0-i 1 0+i -1 0-i)) => - -#(0.0 0.0 0.0+628.0783185208527e-18i 0.0 - 0.0 0.0 8.0-628.0783185208527e-18i 0.0) - -(fft-1 '#(0 0 0 0 0 0 8 0)) => - -#(1.0 -61.23031769111886e-18+1.0i -1.0 61.23031769111886e-18-1.0i - 1.0 -61.23031769111886e-18+1.0i -1.0 61.23031769111886e-18-1.0i) -</pre></td></tr></table><P> - -<A NAME="Cyclic Checksum"></A> -<HR SIZE="6"> -<A NAME="SEC101"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC100"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC102"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.6 Cyclic Checksum </H2> -<!--docid::SEC101::--> -<P> - -<CODE>(require 'crc)</CODE> -<A NAME="IDX561"></A> -Cyclic Redundancy Checks using Galois field GF(2) polynomial -arithmetic are used for error detection in many data transmission -and storage applications. -</P> -<P> - -The generator polynomials for various CRC protocols are availble -from many sources. But the polynomial is just one of many -parameters which must match in order for a CRC implementation to -interoperate with existing systems: -</P> -<P> - -<UL> - -<LI> -the byte-order and bit-order of the data stream; -<P> - -</P> -<LI> -whether the CRC or its inverse is being calculated; -<P> - -</P> -<LI> -the initial CRC value; and -<P> - -</P> -<LI> -whether and where the CRC value is appended (inverted -or non-inverted) to the data stream. -<P> - -</UL> -<P> - -There is even some controversy over the polynomials themselves. -</P> -<P> - -<A NAME="IDX562"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-32-polynomial</B> -<DD>For CRC-32, http://www2.sis.pitt.edu/~jkabara/tele-2100/lect08.html -gives x^32+x^26+x^23+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x^1+1. -<P> - -But -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html, -http://duchon.umuc.edu/Web_Pages/duchon/99_f_cm435/ShiftRegister.htm, -http://spinroot.com/spin/Doc/Book91_PDF/ch3.pdf, -http://www.erg.abdn.ac.uk/users/gorry/course/dl-pages/crc.html, -http://www.rad.com/networks/1994/err_con/crc_most.htm, and -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html, -http://www.nobugconsulting.ro/crc.php give -x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1. -</P> -<P> - -SLIB <CODE>crc-32-polynomial</CODE> uses the latter definition. -</P> -</DL> -<P> - -<A NAME="IDX563"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-ccitt-polynomial</B> -<DD><P> - -http://www.math.grin.edu/~rebelsky/Courses/CS364/2000S/Outlines/outline.12.html, -http://duchon.umuc.edu/Web_Pages/duchon/99_f_cm435/ShiftRegister.htm, -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html, -http://www2.sis.pitt.edu/~jkabara/tele-2100/lect08.html, and -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html give -CRC-CCITT: x^16+x^12+x^5+1. -</P> -</DL> -<P> - -<A NAME="IDX564"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-16-polynomial</B> -<DD><P> - -http://www.math.grin.edu/~rebelsky/Courses/CS364/2000S/Outlines/outline.12.html, -http://duchon.umuc.edu/Web_Pages/duchon/99_f_cm435/ShiftRegister.htm, -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html, -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html, and -http://www.usb.org/developers/data/crcdes.pdf give -CRC-16: x^16+x^15+x^2+1. -</P> -</DL> -<P> - -<A NAME="IDX565"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-12-polynomial</B> -<DD><P> - -http://www.math.grin.edu/~rebelsky/Courses/CS364/2000S/Outlines/outline.12.html, -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html, -http://www.it.iitb.ac.in/it605/lectures/link/node4.html, and -http://spinroot.com/spin/Doc/Book91_PDF/ch3.pdf give -CRC-12: x^12+x^11+x^3+x^2+1. -</P> -<P> - -But -http://www.ffldusoe.edu/Faculty/Denenberg/Topics/Networks/Error_Detection_Correction/crc.html, -http://duchon.umuc.edu/Web_Pages/duchon/99_f_cm435/ShiftRegister.htm, -http://www.eng.uwi.tt/depts/elec/staff/kimal/errorcc.html, -http://www.ee.uwa.edu.au/~roberto/teach/itc314/java/CRC/, -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html, and -http://www.efg2.com/Lab/Mathematics/CRC.htm give -CRC-12: x^12+x^11+x^3+x^2+x+1. -</P> -<P> - -These differ in bit 1 and calculations using them return different -values. With citations near evenly split, it is hard to know which is -correct. -</P> -</DL> -<P> - -<A NAME="IDX566"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-10-polynomial</B> -<DD><P> - -http://www.math.grin.edu/~rebelsky/Courses/CS364/2000S/Outlines/outline.12.html gives -CRC-10: x^10+x^9+x^5+x^4+1; -but -http://cell-relay.indiana.edu/cell-relay/publications/software/CRC/crc10.html, -http://www.it.iitb.ac.in/it605/lectures/link/node4.html, -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html, -http://www.techfest.com/networking/atm/atm.htm, -http://www.protocols.com/pbook/atmcell2.htm, and -http://www.nobugconsulting.ro/crc.php give -CRC-10: x^10+x^9+x^5+x^4+x+1. -</P> -</DL> -<P> - -<A NAME="IDX567"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>crc-08-polynomial</B> -<DD><P> - -http://www.math.grin.edu/~rebelsky/Courses/CS364/2000S/Outlines/outline.12.html, -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html, -http://www.it.iitb.ac.in/it605/lectures/link/node4.html, and -http://www.nobugconsulting.ro/crc.php give -CRC-8: x^8+x^2+x^1+1 -</P> -</DL> -<P> - -<A NAME="IDX568"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>atm-hec-polynomial</B> -<DD><P> - -http://cell-relay.indiana.edu/cell-relay/publications/software/CRC/32bitCRC.tutorial.html and -http://www.gpfn.sk.ca/~rhg/csc8550s02/crc.html give -ATM HEC: x^8+x^2+x+1. -</P> -</DL> -<P> - -<A NAME="IDX569"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>dowcrc-polynomial</B> -<DD><P> - -http://www.cs.ncl.ac.uk/people/harry.whitfield/home.formal/CRCs.html gives -DOWCRC: x^8+x^5+x^4+1. -</P> -</DL> -<P> - -<A NAME="IDX570"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>usb-token-polynomial</B> -<DD><P> - -http://www.usb.org/developers/data/crcdes.pdf and -http://www.nobugconsulting.ro/crc.php give -USB-token: x^5+x^2+1. -</P> -</DL> -<P> - -Each of these polynomial constants is a string of `<SAMP>1</SAMP>'s and -`<SAMP>0</SAMP>'s, the exponent of each power of <VAR>x</VAR> in descending order. -</P> -<P> - -<A NAME="IDX571"></A> -</P> -<DL> -<DT><U>Function:</U> <B>crc:make-table</B> <I>poly</I> -<DD><P> - -<VAR>poly</VAR> must be string of `<SAMP>1</SAMP>'s and `<SAMP>0</SAMP>'s beginning with -`<SAMP>1</SAMP>' and having length greater than 8. <CODE>crc:make-table</CODE> -returns a vector of 256 integers, such that: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(set! <VAR>crc</VAR> - (logxor (ash (logand (+ -1 (ash 1 (- <VAR>deg</VAR> 8))) <VAR>crc</VAR>) 8) - (vector-ref <VAR>crc-table</VAR> - (logxor (ash <VAR>crc</VAR> (- 8 <VAR>deg</VAR>)) <VAR>byte</VAR>)))) -</pre></td></tr></table><P> - -will compute the <VAR>crc</VAR> with the 8 additional bits in <VAR>byte</VAR>; -where <VAR>crc</VAR> is the previous accumulated CRC value, <VAR>deg</VAR> is -the degree of <VAR>poly</VAR>, and <VAR>crc-table</VAR> is the vector returned -by <CODE>crc:make-table</CODE>. -</P> -<P> - -If the implementation does not support <VAR>deg</VAR>-bit integers, then -<CODE>crc:make-table</CODE> returns #f. -</P> -<P> - -</P> -</DL> -<P> - -<A NAME="IDX572"></A> -</P> -<DL> -<DT><U>Function:</U> <B>cksum</B> <I>file</I> -<DD><P> - -Computes the P1003.2/D11.2 (POSIX.2) 32-bit checksum of <VAR>file</VAR>. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'crc) -<A NAME="IDX573"></A>(cksum (in-vicinity (library-vicinity) "ratize.scm")) -=> 157103930 -</pre></td></tr></table><P> - -<A NAME="IDX574"></A> -<DT><U>Function:</U> <B>cksum</B> <I>port</I> -<DD>Computes the checksum of the bytes read from <VAR>port</VAR> until the -end-of-file. -</P> -<P> - -</P> -</DL> -<P> - -<A NAME="IDX575"></A> -<CODE>cksum-string</CODE>, which returns the P1003.2/D11.2 (POSIX.2) 32-bit -checksum of the bytes in <VAR>str</VAR>, can be defined as follows: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'string-port) -(define (cksum-string str) (call-with-input-string str cksum)) -</pre></td></tr></table><P> - -<A NAME="IDX576"></A> -</P> -<DL> -<DT><U>Function:</U> <B>crc16</B> <I>file</I> -<DD><P> - -Computes the USB data-packet (16-bit) CRC of <VAR>file</VAR>. -</P> -<P> - -<A NAME="IDX577"></A> -<DT><U>Function:</U> <B>crc16</B> <I>port</I> -<DD>Computes the USB data-packet (16-bit) CRC of the bytes read from -<VAR>port</VAR> until the end-of-file. -</P> -<P> - -<CODE>crc16</CODE> calculates the same values as the crc16.pl program given -in http://www.usb.org/developers/data/crcdes.pdf. -</P> -<P> - -</P> -</DL> -<P> - -<A NAME="IDX578"></A> -</P> -<DL> -<DT><U>Function:</U> <B>crc5</B> <I>file</I> -<DD><P> - -Computes the USB token (5-bit) CRC of <VAR>file</VAR>. -</P> -<P> - -<A NAME="IDX579"></A> -<DT><U>Function:</U> <B>crc5</B> <I>port</I> -<DD>Computes the USB token (5-bit) CRC of the bytes read from -<VAR>port</VAR> until the end-of-file. -</P> -<P> - -<CODE>crc5</CODE> calculates the same values as the crc5.pl program given -in http://www.usb.org/developers/data/crcdes.pdf. -</P> -<P> - -</P> -</DL> -<P> - -<A NAME="Graphing"></A> -<HR SIZE="6"> -<A NAME="SEC102"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC101"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC103"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.7 Graphing </H2> -<!--docid::SEC102::--> -<P> - -<TABLE BORDER="0" CELLSPACING="0"> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC103">5.7.1 Character Plotting</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC104">5.7.2 PostScript Graphing</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -</TABLE> -<P> - -<A NAME="Character Plotting"></A> -<HR SIZE="6"> -<A NAME="SEC103"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC102"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC102"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.7.1 Character Plotting </H3> -<!--docid::SEC103::--> -<P> - -<CODE>(require 'charplot)</CODE> -<A NAME="IDX580"></A> -</P> -<P> - -<A NAME="IDX581"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>charplot:dimensions</B> -<DD>A list of the maximum height (number of lines) and maximum width (number -of columns) for the graph, its scales, and labels. -<P> - -The default value for <VAR>charplot:dimensions</VAR> is the -<CODE>output-port-height</CODE> and <CODE>output-port-width</CODE> of -<CODE>current-output-port</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX582"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>plot</B> <I>coords x-label y-label</I> -<DD><VAR>coords</VAR> is a list or vector of coordinates, lists of x and y -coordinates. <VAR>x-label</VAR> and <VAR>y-label</VAR> are strings with which to -label the x and y axes. -<P> - -Example: -<TABLE><tr><td> </td><td class=example><pre>(require 'charplot) -<A NAME="IDX583"></A>(set! charplot:dimensions '(20 55)) - -(define (make-points n) - (if (zero? n) - '() - (cons (list (/ n 6) (sin (/ n 6))) (make-points (1- n))))) - -(plot (make-points 40) "x" "Sin(x)") --| - Sin(x) _________________________________________ - 1|- **** | - | ** ** | - 0.75|- * * | - | * * | - 0.5|- * * | - | * *| - 0.25|- * * | - | * * | - 0|-------------------*------------------*--| - | * | - -0.25|- * * | - | * * | - -0.5|- * | - | * * | - -0.75|- * * | - | ** ** | - -1|- **** | - |:_____._____:_____._____:_____._____:____| - x 2 4 6 -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX584"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>plot</B> <I>func x1 x2</I> -<DD><A NAME="IDX585"></A> -<DT><U>Procedure:</U> <B>plot</B> <I>func x1 x2 npts</I> -<DD>Plots the function of one argument <VAR>func</VAR> over the range <VAR>x1</VAR> to -<VAR>x2</VAR>. If the optional integer argument <VAR>npts</VAR> is supplied, it -specifies the number of points to evaluate <VAR>func</VAR> at. -<P> - -<TABLE><tr><td> </td><td class=example><pre>(plot sin 0 (* 2 pi)) --| - _________________________________________ - 1|-: **** | - | : ** ** | - 0.75|-: * * | - | : * * | - 0.5|-: ** ** | - | : * * | - 0.25|-:** ** | - | :* * | - 0|-*------------------*--------------------| - | : * * | - -0.25|-: ** ** | - | : * * | - -0.5|-: * ** | - | : * * | - -0.75|-: * ** | - | : ** ** | - -1|-: **** | - |_:_____._____:_____._____:_____._____:___| - 0 2 4 6 -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX586"></A> -</P> -<DL> -<DT><U>Procedure:</U> <B>histograph</B> <I>data label</I> -<DD>Creates and displays a histogram of the numerical values contained in -vector or list <VAR>data</VAR> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'random-inexact) -(histograph (do ((idx 99 (+ -1 idx)) - (lst '() (cons (* .02 (random:normal)) lst))) - ((negative? idx) lst)) - "normal") --| - _________________________________________ - 8|- : I | - | : I | - 7|- I I : I | - | I I : I | - 6|- III I :I I | - | III I :I I | - 5|- IIIIIIIIII I | - | IIIIIIIIII I | - 4|- IIIIIIIIIIII | - | IIIIIIIIIIII | - 3|-I I I IIIIIIIIIIII II I | - | I I I IIIIIIIIIIII II I | - 2|-I I I IIIIIIIIIIIIIIIII I | - | I I I IIIIIIIIIIIIIIIII I | - 1|-II I I IIIIIIIIIIIIIIIIIIIII I I I | - | II I I IIIIIIIIIIIIIIIIIIIII I I I | - 0|-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII----| - |__.____:____.____:____.____:____.____:___| - normal -0.025 0 0.025 0.05 -</pre></td></tr></table></DL> -<P> - -<A NAME="PostScript Graphing"></A> -<HR SIZE="6"> -<A NAME="SEC104"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC103"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC105"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC102"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.7.2 PostScript Graphing </H3> -<!--docid::SEC104::--> -<P> - -<CODE>(require 'eps-graph)</CODE> -</P> -<P> - -This is a graphing package creating encapsulated-PostScript files. -Its motivations and design choice are described in -<A HREF="http://swissnet.ai.mit.edu/~jaffer/Docupage/grapheps">http://swissnet.ai.mit.edu/~jaffer/Docupage/grapheps</A> -</P> -<P> - -A dataset to be plotted is taken from a 2-dimensional array. -Corresponding coordinates are in rows. Coordinates from any -pair of columns can be plotted. -</P> -<P> - -<A NAME="IDX587"></A> -</P> -<DL> -<DT><U>Function:</U> <B>create-postscript-graph</B> <I>filename.eps size elt1 <small>...</small></I> -<DD><P> - -<VAR>filename.eps</VAR> should be a string naming an output file to be created. <VAR>size</VAR> -should be an exact integer, a list of two exact integers, or #f. -<VAR>elt1</VAR>, ... are values returned by graphing primitives described here. -</P> -<P> - -<CODE>create-postscript-graph</CODE> creates an <EM>Encapsulated-PostScript</EM> file named <VAR>filename.eps</VAR> containing -<A NAME="IDX588"></A> -graphs as directed by the <VAR>elt1</VAR>, ... arguments. -</P> -<P> - -The size of the graph is determined by the <VAR>size</VAR> argument. If a list -of two integers, they specify the width and height. If one integer, -then that integer is the width and the height is 3/4 of the width. -If #f, the graph will be 800 by 600. -</P> -</DL> -These graphing procedures should be called as arguments to -<CODE>create-postscript-graph</CODE>. The order of these arguments is -significant; PostScript graphics state is affected serially from the -first <VAR>elt</VAR> argument to the last. -<P> - -<A NAME="IDX589"></A> -</P> -<DL> -<DT><U>Function:</U> <B>whole-page</B> -<DD><P> - -Pushes a rectangle for the whole encapsulated page onto the -PostScript stack. This pushed rectangle is an implicit argument to -<CODE>partition-page</CODE> or <CODE>setup-plot</CODE>. -</P> -</DL> -<TABLE BORDER="0" CELLSPACING="0"> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC105">5.7.2.1 Column Ranges</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC106">5.7.2.2 Drawing the Graph</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC107">5.7.2.3 Graphics Context</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC108">5.7.2.4 Rectangles</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC109">5.7.2.5 Legending</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC110">5.7.2.6 Legacy Plotting</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC111">5.7.2.7 Example Graph</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP"></TD></TR> -</TABLE> -<P> - -<A NAME="Column Ranges"></A> -<HR SIZE="6"> -<A NAME="SEC105"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC106"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.1 Column Ranges </H4> -<!--docid::SEC105::--> -<P> - -A <EM>range</EM> is a list of two numbers, the minimum and the maximum. -<A NAME="IDX590"></A> -<A NAME="IDX591"></A> -Ranges can be given explicity or computed in PostScript by -<CODE>column-range</CODE>. -</P> -<P> - -<A NAME="IDX592"></A> -</P> -<DL> -<DT><U>Function:</U> <B>column-range</B> <I>array k</I> -<DD><P> - -Returns the range of values in 2-dimensional <VAR>array</VAR> column <VAR>k</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX593"></A> -</P> -<DL> -<DT><U>Function:</U> <B>pad-range</B> <I>range p</I> -<DD><P> - -Expands <VAR>range</VAR> by <VAR>p</VAR>/100 on each end. -</P> -</DL> -<P> - -<A NAME="IDX594"></A> -</P> -<DL> -<DT><U>Function:</U> <B>snap-range</B> <I>range</I> -<DD><P> - -Expands <VAR>range</VAR> to round number of ticks. -</P> -</DL> -<P> - -<A NAME="IDX595"></A> -</P> -<DL> -<DT><U>Function:</U> <B>combine-ranges</B> <I>range1 range2 <small>...</small></I> -<DD><P> - -Returns the minimal range covering all <VAR>range1</VAR>, <VAR>range2</VAR>, ... -</P> -</DL> -<P> - -<A NAME="IDX596"></A> -</P> -<DL> -<DT><U>Function:</U> <B>setup-plot</B> <I>x-range y-range pagerect</I> -<DD><P> - -<A NAME="IDX597"></A> -<DT><U>Function:</U> <B>setup-plot</B> <I>x-range y-range</I> -<DD><VAR>x-range</VAR> and <VAR>y-range</VAR> should each be a list of two numbers or the value returned -by <CODE>pad-range</CODE>, <CODE>snap-range</CODE>, or <CODE>combine-range</CODE>. -<VAR>pagerect</VAR> is the rectangle bounding the graph to be drawn; if missing, the -rectangle from the top of the PostScript stack is popped and used. -</P> -<P> - -Based on the given ranges, <CODE>setup-plot</CODE> sets up scaling and margins for making -a graph. The margins are sized proportional to the <VAR>fontheight</VAR> -value at the time of the call to setup-plot. <CODE>setup-plot</CODE> sets two variables: -</P> -<P> - -</P> -<DL COMPACT> -<DT><VAR>plotrect</VAR> -<DD>The region where data points will be plotted. -<DT><VAR>graphrect</VAR> -<DD>The <VAR>pagerect</VAR> argument to <CODE>setup-plot</CODE>. Includes plotrect, legends, etc. -</DL> -</DL> -<A NAME="Drawing the Graph"></A> -<HR SIZE="6"> -<A NAME="SEC106"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC105"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC107"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.2 Drawing the Graph </H4> -<!--docid::SEC106::--> -<P> - -<A NAME="IDX598"></A> -</P> -<DL> -<DT><U>Function:</U> <B>plot-column</B> <I>array x-column y-column proc3s</I> -<DD><P> - -Plots points with x coordinate in <VAR>x-column</VAR> of <VAR>array</VAR> and y coordinate <VAR>y-column</VAR> of -<VAR>array</VAR>. The symbol <VAR>proc3s</VAR> specifies the type of glyph or drawing style for -presenting these coordinates. -</P> -</DL> -The glyphs and drawing styles available are: -<P> - -</P> -<DL COMPACT> -<DT><CODE>line</CODE> -<DD>Draws line connecting points in order. -<DT><CODE>mountain</CODE> -<DD>Fill area below line connecting points. -<DT><CODE>cloud</CODE> -<DD>Fill area above line connecting points. -<DT><CODE>impulse</CODE> -<DD>Draw line from x-axis to each point. -<DT><CODE>bargraph</CODE> -<DD>Draw rectangle from x-axis to each point. -<DT><CODE>disc</CODE> -<DD>Solid round dot. -<DT><CODE>point</CODE> -<DD>Minimal point -- invisible if linewidth is 0. -<DT><CODE>square</CODE> -<DD>Square box. -<DT><CODE>diamond</CODE> -<DD>Square box at 45.o -<DT><CODE>plus</CODE> -<DD>Plus sign. -<DT><CODE>cross</CODE> -<DD>X sign. -<DT><CODE>triup</CODE> -<DD>Triangle pointing upward -<DT><CODE>tridown</CODE> -<DD>Triangle pointing downward -<DT><CODE>pentagon</CODE> -<DD>Five sided polygon -<DT><CODE>circle</CODE> -<DD>Hollow circle -</DL> -<P> - -<A NAME="Graphics Context"></A> -<HR SIZE="6"> -<A NAME="SEC107"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC106"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC108"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.3 Graphics Context </H4> -<!--docid::SEC107::--> -<P> - -<A NAME="IDX599"></A> -</P> -<DL> -<DT><U>Function:</U> <B>in-graphic-context</B> <I>arg <small>...</small></I> -<DD><P> - -Saves the current graphics state, executes <VAR>args</VAR>, then restores -to saved graphics state. -</P> -</DL> -<P> - -<A NAME="IDX600"></A> -</P> -<DL> -<DT><U>Function:</U> <B>set-color</B> <I>color</I> -<DD><P> - -<VAR>color</VAR> should be a string naming a Resene color, a saturate color, or a -number between 0 and 100. -</P> -<P> - -<CODE>set-color</CODE> sets the PostScript color to the color of the given string, or a -grey value between black (0) and white (100). -</P> -</DL> -<P> - -<A NAME="IDX601"></A> -</P> -<DL> -<DT><U>Function:</U> <B>set-font</B> <I>name fontheight</I> -<DD><P> - -<VAR>name</VAR> should be a (case-sensitive) string naming a PostScript font. -<VAR>fontheight</VAR> should be a positive real number. -</P> -<P> - -<CODE>set-font</CODE> Changes the current PostScript font to <VAR>name</VAR> with height equal to -<VAR>fontheight</VAR>. The default font is Helvetica (12pt). -</P> -</DL> -The base set of PostScript fonts is: -<P> - -</P> -<TABLE> -<TR><TD>Times </TD><TD> Times-Italic </TD><TD> Times-Bold </TD><TD> Times-BoldItalic</TD> -</TR> -<TR><TD>Helvetica </TD><TD> Helvetica-Oblique </TD><TD> Helvetica-Bold </TD><TD> Helvetica-BoldOblique</TD> -</TR> -<TR><TD>Courier </TD><TD> Courier-Oblique </TD><TD> Courier-Bold </TD><TD> Courier-BoldOblique</TD> -</TR> -<TR><TD>Symbol</TD> -</TR></TABLE> -<P> - -Line parameters do no affect fonts; they do effect glyphs. -</P> -<P> - -<A NAME="IDX602"></A> -</P> -<DL> -<DT><U>Function:</U> <B>set-linewidth</B> <I>w</I> -<DD><P> - -The default linewidth is 1. Setting it to 0 makes the lines drawn -as skinny as possible. Linewidth must be much smaller than -glyphsize for readable glyphs. -</P> -</DL> -<P> - -<A NAME="IDX603"></A> -</P> -<DL> -<DT><U>Function:</U> <B>set-linedash</B> <I>j k</I> -<DD><P> - -Lines are drawn <VAR>j</VAR>-on <VAR>k</VAR>-off. -</P> -<P> - -<A NAME="IDX604"></A> -<DT><U>Function:</U> <B>set-linedash</B> <I>j</I> -<DD>Lines are drawn <VAR>j</VAR>-on <VAR>j</VAR>-off. -</P> -<P> - -<A NAME="IDX605"></A> -<DT><U>Function:</U> <B>set-linedash</B> -<DD>Turns off dashing. -</P> -</DL> -<P> - -<A NAME="IDX606"></A> -</P> -<DL> -<DT><U>Function:</U> <B>set-glyphsize</B> <I>w</I> -<DD><P> - -Sets the (PostScript) variable glyphsize to <VAR>w</VAR>. The default -glyphsize is 6. -</P> -</DL> -The effects of <CODE>clip-to-rect</CODE> are also part of the graphic -context. -<P> - -<A NAME="Rectangles"></A> -<HR SIZE="6"> -<A NAME="SEC108"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC107"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC109"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.4 Rectangles </H4> -<!--docid::SEC108::--> -<P> - -A <EM>rectangle</EM> is a list of 4 numbers; the first two elements are -<A NAME="IDX607"></A> -the x and y coordinates of lower left corner of the rectangle. The -other two elements are the width and height of the rectangle. -</P> -<P> - -<A NAME="IDX608"></A> -</P> -<DL> -<DT><U>Function:</U> <B>whole-page</B> -<DD><P> - -Pushes a rectangle for the whole encapsulated page onto the -PostScript stack. This pushed rectangle is an implicit argument to -<CODE>partition-page</CODE> or <CODE>setup-plot</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX609"></A> -</P> -<DL> -<DT><U>Function:</U> <B>partition-page</B> <I>xparts yparts</I> -<DD><P> - -Pops the rectangle currently on top of the stack and pushes <VAR>xparts</VAR> * <VAR>yparts</VAR> -sub-rectangles onto the stack in decreasing y and increasing x order. -If you are drawing just one graph, then you don't need <CODE>partition-page</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX610"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>plotrect</B> -<DD><P> - -The rectangle where data points should be plotted. <VAR>plotrect</VAR> is set by -<CODE>setup-plot</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX611"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>graphrect</B> -<DD><P> - -The <VAR>pagerect</VAR> argument of the most recent call to -<CODE>setup-plot</CODE>. Includes plotrect, legends, etc. -</P> -</DL> -<P> - -<A NAME="IDX612"></A> -</P> -<DL> -<DT><U>Function:</U> <B>fill-rect</B> <I>rect</I> -<DD><P> - -fills <VAR>rect</VAR> with the current color. -</P> -</DL> -<P> - -<A NAME="IDX613"></A> -</P> -<DL> -<DT><U>Function:</U> <B>outline-rect</B> <I>rect</I> -<DD><P> - -Draws the perimiter of <VAR>rect</VAR> in the current color. -</P> -</DL> -<P> - -<A NAME="IDX614"></A> -</P> -<DL> -<DT><U>Function:</U> <B>clip-to-rect</B> <I>rect</I> -<DD><P> - -Modifies the current graphics-state so that nothing will be drawn -outside of the rectangle <VAR>rect</VAR>. Use <CODE>in-graphic-context</CODE> to limit -the extent of <CODE>clip-to-rect</CODE>. -</P> -</DL> -<A NAME="Legending"></A> -<HR SIZE="6"> -<A NAME="SEC109"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC108"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC110"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.5 Legending </H4> -<!--docid::SEC109::--> -<P> - -<A NAME="IDX615"></A> -</P> -<DL> -<DT><U>Function:</U> <B>title-top</B> <I>title subtitle</I> -<DD><P> - -<A NAME="IDX616"></A> -<DT><U>Function:</U> <B>title-top</B> <I>title</I> -<DD>Puts a <VAR>title</VAR> line and an optional <VAR>subtitle</VAR> line above the <CODE>graphrect</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX617"></A> -</P> -<DL> -<DT><U>Function:</U> <B>title-bottom</B> <I>title subtitle</I> -<DD><P> - -<A NAME="IDX618"></A> -<DT><U>Function:</U> <B>title-bottom</B> <I>title</I> -<DD>Puts a <VAR>title</VAR> line and an optional <VAR>subtitle</VAR> line below the <CODE>graphrect</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX619"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>topedge</B> -<DD><A NAME="IDX620"></A> -<DT><U>Variable:</U> <B>bottomedge</B> -<DD><P> - -These edge coordinates of <CODE>graphrect</CODE> are suitable for passing -as the first argument to <CODE>rule-horizontal</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX621"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>leftedge</B> -<DD><A NAME="IDX622"></A> -<DT><U>Variable:</U> <B>rightedge</B> -<DD><P> - -These edge coordinates of <CODE>graphrect</CODE> are suitable for passing -as the first argument to <CODE>rule-vertical</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX623"></A> -</P> -<DL> -<DT><U>Function:</U> <B>rule-vertical</B> <I>x-coord text tick-width</I> -<DD><P> - -Draws a vertical ruler with X coordinate <VAR>x-coord</VAR> and labeled with string -<VAR>text</VAR>. If <VAR>tick-width</VAR> is positive, then the ticks are <VAR>tick-width</VAR> long on the right side -of <VAR>x-coord</VAR>; and <VAR>text</VAR> and numeric legends are on the left. If <VAR>tick-width</VAR> is -negative, then the ticks are -<VAR>tick-width</VAR> long on the left side of <VAR>x-coord</VAR>; and <VAR>text</VAR> -and numeric legends are on the right. -</P> -</DL> -<P> - -<A NAME="IDX624"></A> -</P> -<DL> -<DT><U>Function:</U> <B>rule-horizontal</B> <I>x-coord text tick-height</I> -<DD><P> - -Draws a horizontal ruler with X coordinate <VAR>x-coord</VAR> and labeled with -string <VAR>text</VAR>. If <VAR>tick-height</VAR> is positive, then the ticks are <VAR>tick-height</VAR> long on the -right side of <VAR>x-coord</VAR>; and <VAR>text</VAR> and numeric legends are on the left. If <VAR>tick-height</VAR> -is negative, then the ticks are -<VAR>tick-height</VAR> long on the left side of <VAR>x-coord</VAR>; and -<VAR>text</VAR> and numeric legends are on the right. -</P> -</DL> -<P> - -<A NAME="IDX625"></A> -</P> -<DL> -<DT><U>Function:</U> <B>y-axis</B> -<DD><P> - -Draws the y-axis. -</P> -</DL> -<P> - -<A NAME="IDX626"></A> -</P> -<DL> -<DT><U>Function:</U> <B>x-axis</B> -<DD><P> - -Draws the x-axis. -</P> -</DL> -<P> - -<A NAME="IDX627"></A> -</P> -<DL> -<DT><U>Function:</U> <B>grid-verticals</B> -<DD><P> - -Draws vertical lines through <CODE>graphrect</CODE> at each tick on the -vertical ruler. -</P> -</DL> -<P> - -<A NAME="IDX628"></A> -</P> -<DL> -<DT><U>Function:</U> <B>grid-horizontals</B> -<DD><P> - -Draws horizontal lines through <CODE>graphrect</CODE> at each tick on the -horizontal ruler. -</P> -</DL> -<A NAME="Legacy Plotting"></A> -<HR SIZE="6"> -<A NAME="SEC110"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC109"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC111"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.6 Legacy Plotting </H4> -<!--docid::SEC110::--> -<P> - -<A NAME="IDX629"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>graph:dimensions</B> -<DD><P> - -A list of the width and height of the graph to be plotted using -<CODE>plot</CODE>. -</P> -</DL> -<P> - -<A NAME="IDX630"></A> -</P> -<DL> -<DT><U>Function:</U> <B>plot</B> <I>func x1 x2 npts</I> -<DD><P> - -<A NAME="IDX631"></A> -<DT><U>Function:</U> <B>plot</B> <I>func x1 x2</I> -<DD>Creates and displays using <CODE>(system "gv tmp.eps")</CODE> an -encapsulated PostScript graph of the function of one argument <VAR>func</VAR> -over the range <VAR>x1</VAR> to <VAR>x2</VAR>. If the optional integer argument <VAR>npts</VAR> is -supplied, it specifies the number of points to evaluate <VAR>func</VAR> at. -</P> -<P> - -<A NAME="IDX632"></A> -<DT><U>Function:</U> <B>plot</B> <I>coords x-label y-label</I> -<DD><VAR>coords</VAR> is a list or vector of coordinates, lists of x and y -coordinates. <VAR>x-label</VAR> and <VAR>y-label</VAR> are strings with which -to label the x and y axes. -</P> -</DL> -<A NAME="Example Graph"></A> -<HR SIZE="6"> -<A NAME="SEC111"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC110"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC112"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC104"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.7.2.7 Example Graph </H4> -<!--docid::SEC111::--> -<P> - -The file `<TT>am1.5.html</TT>', a table of solar irradiance, is fetched -with `<SAMP>wget</SAMP>' if it isn't already in the working directory. The -file is read and stored into an array, <VAR>irradiance</VAR>. -</P> -<P> - -<CODE>create-postscript-graph</CODE> is then called to create an -encapsulated-PostScript file, `<TT>solarad.eps</TT>'. The size of the -page is set to 600 by 300. <CODE>whole-page</CODE> is called and leaves -the rectangle on the PostScript stack. <CODE>setup-plot</CODE> is called -with a literal range for x and computes the range for column 1. -</P> -<P> - -Two calls to <CODE>top-title</CODE> are made so a different font can be -used for the lower half. <CODE>in-graphic-context</CODE> is used to limit -the scope of the font change. The graphing area is outlined and a -rule drawn on the left side. -</P> -<P> - -Because the X range was intentionally reduced, -<CODE>in-graphic-context</CODE> is called and <CODE>clip-to-rect</CODE> limits -drawing to the plotting area. A black line is drawn from data -column 1. That line is then overlayed with a mountain plot of the -same column colored "Bright Sun". -</P> -<P> - -After returning from the <CODE>in-graphic-context</CODE>, the bottom ruler -is drawn. Had it been drawn earlier, all its ticks would have been -painted over by the mountain plot. -</P> -<P> - -The color is then changed to `<SAMP>seagreen</SAMP>' and the same graphrect -is setup again, this time with a different Y scale, 0 to 1000. The -graphic context is again clipped to <VAR>plotrect</VAR>, linedash is set, -and column 2 is plotted as a dashed line. Finally the rightedge is -ruled. Having the line and its scale both in green helps -disambiguate the scales. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'eps-graph) -(require 'line-i/o) -(require 'string-port) - -(define irradiance - (let ((url "http://www.pv.unsw.edu.au/am1.5.html") - (file "am1.5.html")) - (define (read->list line) - (define elts '()) - (call-with-input-string line - (lambda (iprt) (do ((elt (read iprt) (read iprt))) - ((eof-object? elt) elts) - (set! elts (cons elt elts)))))) - (if (not (file-exists? file)) - (system (string-append "wget -c -O" file " " url))) - (call-with-input-file file - (lambda (iprt) - (define lines '()) - (do ((line (read-line iprt) (read-line iprt))) - ((eof-object? line) - (let ((nra (create-array (Ar64) - (length lines) - (length (car lines))))) - (do ((lns lines (cdr lns)) - (idx (+ -1 (length lines)) (+ -1 idx))) - ((null? lns) nra) - (do ((kdx (+ -1 (length (car lines))) (+ -1 kdx)) - (lst (car lns) (cdr lst))) - ((null? lst)) - (array-set! nra (car lst) idx kdx))))) - (if (and (positive? (string-length line)) - (char-numeric? (string-ref line 0))) - (set! lines (cons (read->list line) lines)))))))) - -(let ((xrange '(.25 2.5))) - (create-postscript-graph - "solarad.eps" '(600 300) - (whole-page) - (setup-plot xrange (column-range irradiance 1)) - (title-top - "Solar Irradiance http://www.pv.unsw.edu.au/am1.5.html") - (in-graphic-context - (set-font "Helvetica-Oblique" 12) - (title-top - "" - "Key Centre for Photovoltaic Engineering UNSW - Air Mass 1.5 Global Spectrum")) - (outline-rect plotrect) - (rule-vertical leftedge "W/(m^2.um)" 10) - (in-graphic-context (clip-to-rect plotrect) - (plot-column irradiance 0 1 'line) - (set-color "Bright Sun") - (plot-column irradiance 0 1 'mountain) - ) - (rule-horizontal bottomedge "Wavelength in .um" 5) - (set-color 'seagreen) - - (setup-plot xrange '(0 1000) graphrect) - (in-graphic-context (clip-to-rect plotrect) - (set-linedash 5 2) - (plot-column irradiance 0 2 'line)) - (rule-vertical rightedge "Integrated .W/(m^2)" -10) - )) - -(system "gv solarad.eps") -</pre></td></tr></table><P> - -<A NAME="Solid Modeling"></A> -<HR SIZE="6"> -<A NAME="SEC112"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC111"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.8 Solid Modeling </H2> -<!--docid::SEC112::--> -<P> - -<A NAME="Solid"> -<CODE>(require 'solid)</CODE> -</A> -<A NAME="IDX633"></A> -<A NAME="IDX634"></A> -<A NAME="IDX635"></A> -</P> -<P> - -<A HREF="http://swissnet.ai.mit.edu/~jaffer/Solid/#Example">http://swissnet.ai.mit.edu/~jaffer/Solid/#Example</A> gives an -example use of this package. -</P> -<P> - -<A NAME="IDX636"></A> -</P> -<DL> -<DT><U>Function:</U> <B>vrml</B> <I>node <small>...</small></I> -<DD>Returns the VRML97 string (including header) of the concatenation -of strings <VAR>nodes</VAR>, <small>...</small>. -</DL> -<P> - -<A NAME="IDX637"></A> -</P> -<DL> -<DT><U>Function:</U> <B>vrml-append</B> <I>node1 node2 <small>...</small></I> -<DD>Returns the concatenation with interdigitated newlines of -strings <VAR>node1</VAR>, <VAR>node2</VAR>, <small>...</small>. -</DL> -<P> - -<A NAME="IDX638"></A> -</P> -<DL> -<DT><U>Function:</U> <B>vrml-to-file</B> <I>file node <small>...</small></I> -<DD>Writes to file named <VAR>file</VAR> the VRML97 string (including header) of -the concatenation of strings <VAR>nodes</VAR>, <small>...</small>. -</DL> -<P> - -<A NAME="IDX639"></A> -</P> -<DL> -<DT><U>Function:</U> <B>world:info</B> <I>title info <small>...</small></I> -<DD>Returns a VRML97 string setting the title of the file in which -it appears to <VAR>title</VAR>. Additional strings <VAR>info</VAR>, <small>...</small> are comments. -</DL> -<P> - -VRML97 strings passed to <CODE>vrml</CODE> and <CODE>vrml-to-file</CODE> as -arguments will appear in the resulting VRML code. This string turns -off the headlight at the viewpoint: -<TABLE><tr><td> </td><td class=example><pre>" NavigationInfo {headlight FALSE}" -</pre></td></tr></table><P> - -<A NAME="IDX640"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:panorama</B> <I>front right back left top bottom</I> -<DD>Specifies the distant images on the inside faces of the cube -enclosing the virtual world. -</DL> -<P> - -<A NAME="IDX641"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:sphere</B> <I>colors angles</I> -<DD><P> - -<VAR>colors</VAR> is a list of color objects. Each may be of type <A HREF="slib_5.html#SEC119">color</A>, a 24-bit sRGB integer, or a list of 3 numbers -between 0.0 and 1.0. -</P> -<P> - -<VAR>angles</VAR> is a list of non-increasing angles the same length as -<VAR>colors</VAR>. Each angle is between 90 and -90 degrees. If 90 or -90 are not -elements of <VAR>angles</VAR>, then the color at the zenith and nadir are taken from -the colors paired with the angles nearest them. -</P> -<P> - -<CODE>scene:sphere</CODE> fills horizontal bands with interpolated colors on the backgroud -sphere encasing the world. -</P> -</DL> -<P> - -<A NAME="IDX642"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:sky-and-dirt</B> -<DD>Returns a blue and brown backgroud sphere encasing the world. -</DL> -<P> - -<A NAME="IDX643"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:sky-and-grass</B> -<DD>Returns a blue and green backgroud sphere encasing the world. -</DL> -<P> - -<A NAME="IDX644"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:sun</B> <I>latitude julian-day hour turbidity strength</I> -<DD><P> - -<A NAME="IDX645"></A> -<DT><U>Function:</U> <B>scene:sun</B> <I>latitude julian-day hour turbidity</I> -<DD></P> -<P> - -<VAR>latitude</VAR> is the virtual place's latitude in degrees. <VAR>julian-day</VAR> is an integer from -0 to 366, the day of the year. <VAR>hour</VAR> is a real number from 0 to 24 for -the time of day; 12 is noon. <VAR>turbidity</VAR> is the degree of fogginess described -in See section <A HREF="slib_5.html#SEC133">turbidity</A>. -</P> -<P> - -<CODE>scene:sun</CODE> returns a bright yellow, distant sphere where the sun would be at -<VAR>hour</VAR> on <VAR>julian-day</VAR> at <VAR>latitude</VAR>. If <VAR>strength</VAR> is positive, included is a light source of <VAR>strength</VAR> -(default 1). -</P> -</DL> -<P> - -<A NAME="IDX646"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:overcast</B> <I>latitude julian-day hour turbidity strength</I> -<DD><P> - -<A NAME="IDX647"></A> -<DT><U>Function:</U> <B>scene:overcast</B> <I>latitude julian-day hour turbidity</I> -<DD></P> -<P> - -<VAR>latitude</VAR> is the virtual place's latitude in degrees. <VAR>julian-day</VAR> is an integer from -0 to 366, the day of the year. <VAR>hour</VAR> is a real number from 0 to 24 for -the time of day; 12 is noon. <VAR>turbidity</VAR> is the degree of cloudiness described -in See section <A HREF="slib_5.html#SEC133">turbidity</A>. -</P> -<P> - -<CODE>scene:overcast</CODE> returns an overcast sky as it might look at <VAR>hour</VAR> on <VAR>julian-day</VAR> at <VAR>latitude</VAR>. If <VAR>strength</VAR> -is positive, included is an ambient light source of <VAR>strength</VAR> (default 1). -</P> -</DL> -Viewpoints are objects in the virtual world, and can be transformed -individually or with solid objects. -<P> - -<A NAME="IDX648"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:viewpoint</B> <I>name distance compass pitch</I> -<DD><P> - -<A NAME="IDX649"></A> -<DT><U>Function:</U> <B>scene:viewpoint</B> <I>name distance compass</I> -<DD>Returns a viewpoint named <VAR>name</VAR> facing the origin and placed <VAR>distance</VAR> from it. -<VAR>compass</VAR> is a number from 0 to 360 giving the compass heading. <VAR>pitch</VAR> is a -number from -90 to 90, defaulting to 0, specifying the angle from the -horizontal. -</P> -</DL> -<P> - -<A NAME="IDX650"></A> -</P> -<DL> -<DT><U>Function:</U> <B>scene:viewpoints</B> <I>proximity</I> -<DD>Returns 6 viewpoints, one at the center of each face of a cube -with sides 2 * <VAR>proximity</VAR>, centered on the origin. -</DL> -<A NAME="SEC113"></A> -<H3> Light Sources </H3> -<!--docid::SEC113::--> -<P> - -In VRML97, lights shine only on objects within the same children node -and descendants of that node. Although it would have been convenient -to let light direction be rotated by <CODE>solid:rotation</CODE>, this -restricts a rotated light's visibility to objects rotated with it. -</P> -<P> - -To workaround this limitation, these directional light source -procedures accept either Cartesian or spherical coordinates for -direction. A spherical coordinate is a list <CODE>(<VAR>theta</VAR> -<VAR>azimuth</VAR>)</CODE>; where <VAR>theta</VAR> is the angle in degrees from the -zenith, and <VAR>azimuth</VAR> is the angle in degrees due west of south. -</P> -<P> - -It is sometimes useful for light sources to be brighter than `<SAMP>1</SAMP>'. -When <VAR>intensity</VAR> arguments are greater than 1, these functions -gang multiple sources to reach the desired strength. -</P> -<P> - -<A NAME="IDX651"></A> -</P> -<DL> -<DT><U>Function:</U> <B>light:ambient</B> <I>color intensity</I> -<DD><P> - -<A NAME="IDX652"></A> -<DT><U>Function:</U> <B>light:ambient</B> <I>color</I> -<DD>Ambient light shines on all surfaces with which it is grouped. -</P> -<P> - -<VAR>color</VAR> is a an object of type <A HREF="slib_5.html#SEC119">color</A>, a 24-bit sRGB -integer, or a list of 3 numbers between 0.0 and 1.0. If <VAR>color</VAR> is #f, -then the default color will be used. <VAR>intensity</VAR> is a real non-negative number -defaulting to `<SAMP>1</SAMP>'. -</P> -<P> - -<CODE>light:ambient</CODE> returns a light source or sources of <VAR>color</VAR> with total strength of <VAR>intensity</VAR> -(or 1 if omitted). -</P> -</DL> -<P> - -<A NAME="IDX653"></A> -</P> -<DL> -<DT><U>Function:</U> <B>light:directional</B> <I>color direction intensity</I> -<DD><P> - -<A NAME="IDX654"></A> -<DT><U>Function:</U> <B>light:directional</B> <I>color direction</I> -<DD></P> -<P> - -<A NAME="IDX655"></A> -<DT><U>Function:</U> <B>light:directional</B> <I>color</I> -<DD>Directional light shines parallel rays with uniform intensity on all -objects with which it is grouped. -</P> -<P> - -<VAR>color</VAR> is a an object of type <A HREF="slib_5.html#SEC119">color</A>, a 24-bit sRGB -integer, or a list of 3 numbers between 0.0 and 1.0. If <VAR>color</VAR> is #f, -then the default color will be used. -</P> -<P> - -<VAR>direction</VAR> must be a list or vector of 2 or 3 numbers specifying the direction -to this light. If <VAR>direction</VAR> has 2 numbers, then these numbers are the angle -from zenith and the azimuth in degrees; if <VAR>direction</VAR> has 3 numbers, then -these are taken as a Cartesian vector specifying the direction to the -light source. The default direction is upwards; thus its light will -shine down. -</P> -<P> - -<VAR>intensity</VAR> is a real non-negative number defaulting to `<SAMP>1</SAMP>'. -</P> -<P> - -<CODE>light:directional</CODE> returns a light source or sources of <VAR>color</VAR> with total strength of <VAR>intensity</VAR>, -shining from <VAR>direction</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX656"></A> -</P> -<DL> -<DT><U>Function:</U> <B>light:beam</B> <I>attenuation radius aperture peak</I> -<DD><P> - -<A NAME="IDX657"></A> -<DT><U>Function:</U> <B>light:beam</B> <I>attenuation radius aperture</I> -<DD></P> -<P> - -<A NAME="IDX658"></A> -<DT><U>Function:</U> <B>light:beam</B> <I>attenuation radius</I> -<DD></P> -<P> - -<A NAME="IDX659"></A> -<DT><U>Function:</U> <B>light:beam</B> <I>attenuation</I> -<DD></P> -<P> - -<VAR>attenuation</VAR> is a list or vector of three nonnegative real numbers specifying -the reduction of intensity, the reduction of intensity with distance, -and the reduction of intensity as the square of distance. <VAR>radius</VAR> is the -distance beyond which the light does not shine. <VAR>radius</VAR> defaults to -`<SAMP>100</SAMP>'. -</P> -<P> - -<VAR>aperture</VAR> is a real number between 0 and 180, the angle centered on the -light's axis through which it sheds some light. <VAR>peak</VAR> is a real number -between 0 and 90, the angle of greatest illumination. -</P> -</DL> -<P> - -<A NAME="IDX660"></A> -</P> -<DL> -<DT><U>Function:</U> <B>light:point</B> <I>location color intensity beam</I> -<DD><P> - -<A NAME="IDX661"></A> -<DT><U>Function:</U> <B>light:point</B> <I>location color intensity</I> -<DD></P> -<P> - -<A NAME="IDX662"></A> -<DT><U>Function:</U> <B>light:point</B> <I>location color</I> -<DD></P> -<P> - -<A NAME="IDX663"></A> -<DT><U>Function:</U> <B>light:point</B> <I>location</I> -<DD></P> -<P> - -Point light radiates from <VAR>location</VAR>, intensity decreasing with distance, -towards all objects with which it is grouped. -</P> -<P> - -<VAR>color</VAR> is a an object of type <A HREF="slib_5.html#SEC119">color</A>, a 24-bit sRGB -integer, or a list of 3 numbers between 0.0 and 1.0. If <VAR>color</VAR> is #f, -then the default color will be used. <VAR>intensity</VAR> is a real non-negative number -defaulting to `<SAMP>1</SAMP>'. <VAR>beam</VAR> is a structure returned by -<CODE>light:beam</CODE> or #f. -</P> -<P> - -<CODE>light:point</CODE> returns a light source or sources at <VAR>location</VAR> of <VAR>color</VAR> with total strength -<VAR>intensity</VAR> and <VAR>beam</VAR> properties. Note that the pointlight itself is not visible. -To make it so, place an object with emissive appearance at <VAR>location</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX664"></A> -</P> -<DL> -<DT><U>Function:</U> <B>light:spot</B> <I>location direction color intensity beam</I> -<DD><P> - -<A NAME="IDX665"></A> -<DT><U>Function:</U> <B>light:spot</B> <I>location direction color intensity</I> -<DD></P> -<P> - -<A NAME="IDX666"></A> -<DT><U>Function:</U> <B>light:spot</B> <I>location direction color</I> -<DD></P> -<P> - -<A NAME="IDX667"></A> -<DT><U>Function:</U> <B>light:spot</B> <I>location direction</I> -<DD></P> -<P> - -<A NAME="IDX668"></A> -<DT><U>Function:</U> <B>light:spot</B> <I>location</I> -<DD></P> -<P> - -Spot light radiates from <VAR>location</VAR> towards <VAR>direction</VAR>, intensity decreasing with -distance, illuminating objects with which it is grouped. -</P> -<P> - -<VAR>direction</VAR> must be a list or vector of 2 or 3 numbers specifying the direction -to this light. If <VAR>direction</VAR> has 2 numbers, then these numbers are the angle -from zenith and the azimuth in degrees; if <VAR>direction</VAR> has 3 numbers, then -these are taken as a Cartesian vector specifying the direction to the -light source. The default direction is upwards; thus its light will -shine down. -</P> -<P> - -<VAR>color</VAR> is a an object of type <A HREF="slib_5.html#SEC119">color</A>, a 24-bit sRGB -integer, or a list of 3 numbers between 0.0 and 1.0. If <VAR>color</VAR> is #f, -then the default color will be used. -</P> -<P> - -<VAR>intensity</VAR> is a real non-negative number defaulting to `<SAMP>1</SAMP>'. -</P> -<P> - -<CODE>light:spot</CODE> returns a light source or sources at <VAR>location</VAR> of <VAR>direction</VAR> with total strength -<VAR>color</VAR>. Note that the spotlight itself is not visible. To make it so, -place an object with emissive appearance at <VAR>location</VAR>. -</P> -</DL> -<A NAME="SEC114"></A> -<H3> Object Primitives </H3> -<!--docid::SEC114::--> -<P> - -<A NAME="IDX669"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:box</B> <I>geometry appearance</I> -<DD><P> - -<A NAME="IDX670"></A> -<DT><U>Function:</U> <B>solid:box</B> <I>geometry</I> -<DD><VAR>geometry</VAR> must be a number or a list or vector of three numbers. If <VAR>geometry</VAR> is a -number, the <CODE>solid:box</CODE> returns a cube with sides of length <VAR>geometry</VAR> centered on the -origin. Otherwise, <CODE>solid:box</CODE> returns a rectangular box with dimensions <VAR>geometry</VAR> -centered on the origin. <VAR>appearance</VAR> determines the surface properties of the -returned object. -</P> -</DL> -<P> - -<A NAME="IDX671"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:cylinder</B> <I>radius height appearance</I> -<DD><P> - -<A NAME="IDX672"></A> -<DT><U>Function:</U> <B>solid:cylinder</B> <I>radius height</I> -<DD>Returns a right cylinder with dimensions <VAR>radius</VAR> and <CODE>(abs <VAR>height</VAR>)</CODE> -centered on the origin. If <VAR>height</VAR> is positive, then the cylinder ends -will be capped. <VAR>appearance</VAR> determines the surface properties of the returned -object. -</P> -</DL> -<P> - -<A NAME="IDX673"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:disk</B> <I>radius thickness appearance</I> -<DD><P> - -<A NAME="IDX674"></A> -<DT><U>Function:</U> <B>solid:disk</B> <I>radius thickness</I> -<DD><VAR>thickness</VAR> must be a positive real number. <CODE>solid:disk</CODE> returns a circular disk -with dimensions <VAR>radius</VAR> and <VAR>thickness</VAR> centered on the origin. <VAR>appearance</VAR> determines the -surface properties of the returned object. -</P> -</DL> -<P> - -<A NAME="IDX675"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:cone</B> <I>radius height appearance</I> -<DD><P> - -<A NAME="IDX676"></A> -<DT><U>Function:</U> <B>solid:cone</B> <I>radius height</I> -<DD>Returns an isosceles cone with dimensions <VAR>radius</VAR> and <VAR>height</VAR> centered on -the origin. <VAR>appearance</VAR> determines the surface properties of the returned -object. -</P> -</DL> -<P> - -<A NAME="IDX677"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:pyramid</B> <I>side height appearance</I> -<DD><P> - -<A NAME="IDX678"></A> -<DT><U>Function:</U> <B>solid:pyramid</B> <I>side height</I> -<DD>Returns an isosceles pyramid with dimensions <VAR>side</VAR> and <VAR>height</VAR> centered on -the origin. <VAR>appearance</VAR> determines the surface properties of the returned -object. -</P> -</DL> -<P> - -<A NAME="IDX679"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:sphere</B> <I>radius appearance</I> -<DD><P> - -<A NAME="IDX680"></A> -<DT><U>Function:</U> <B>solid:sphere</B> <I>radius</I> -<DD>Returns a sphere of radius <VAR>radius</VAR> centered on the origin. <VAR>appearance</VAR> determines -the surface properties of the returned object. -</P> -</DL> -<P> - -<A NAME="IDX681"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:ellipsoid</B> <I>geometry appearance</I> -<DD><P> - -<A NAME="IDX682"></A> -<DT><U>Function:</U> <B>solid:ellipsoid</B> <I>geometry</I> -<DD><VAR>geometry</VAR> must be a number or a list or vector of three numbers. If <VAR>geometry</VAR> is a -number, the <CODE>solid:ellipsoid</CODE> returns a sphere of diameter <VAR>geometry</VAR> centered on the origin. -Otherwise, <CODE>solid:ellipsoid</CODE> returns an ellipsoid with diameters <VAR>geometry</VAR> centered on the -origin. <VAR>appearance</VAR> determines the surface properties of the returned object. -</P> -</DL> -<P> - -<A NAME="IDX683"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:basrelief</B> <I>width height depth colorray appearance</I> -<DD><P> - -<A NAME="IDX684"></A> -<DT><U>Function:</U> <B>solid:basrelief</B> <I>width height depth appearance</I> -<DD></P> -<P> - -<A NAME="IDX685"></A> -<DT><U>Function:</U> <B>solid:basrelief</B> <I>width height depth</I> -<DD>One of <VAR>width</VAR>, <VAR>height</VAR>, or <VAR>depth</VAR> must be a 2-dimensional array; the others must -be real numbers giving the length of the basrelief in those -dimensions. The rest of this description assumes that <VAR>height</VAR> is an -array of heights. -</P> -<P> - -<CODE>solid:basrelief</CODE> returns a <VAR>width</VAR> by <VAR>depth</VAR> basrelief solid with heights per array <VAR>height</VAR> with -the buttom surface centered on the origin. -</P> -<P> - -If present, <VAR>appearance</VAR> determines the surface properties of the returned -object. If present, <VAR>colorray</VAR> must be an array of objects of type -<A HREF="slib_5.html#SEC119">color</A>, 24-bit sRGB integers or lists of 3 -numbers between 0.0 and 1.0. -</P> -<P> - -If <VAR>colorray</VAR>'s dimensions match <VAR>height</VAR>, then each element of <VAR>colorray</VAR> paints its -corresponding vertex of <VAR>height</VAR>. If <VAR>colorray</VAR> has all dimensions one smaller -than <VAR>height</VAR>, then each element of <VAR>colorray</VAR> paints the corresponding face of -<VAR>height</VAR>. Other dimensions for <VAR>colorray</VAR> are in error. -</P> -</DL> -<A NAME="SEC115"></A> -<H3> Surface Attributes </H3> -<!--docid::SEC115::--> -<P> - -<A NAME="IDX686"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor ambientIntensity specularColor shininess emissiveColor transparency</I> -<DD><P> - -<A NAME="IDX687"></A> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor ambientIntensity specularColor shininess emissiveColor</I> -<DD></P> -<P> - -<A NAME="IDX688"></A> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor ambientIntensity specularColor shininess</I> -<DD></P> -<P> - -<A NAME="IDX689"></A> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor ambientIntensity specularColor</I> -<DD></P> -<P> - -<A NAME="IDX690"></A> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor ambientIntensity</I> -<DD></P> -<P> - -<A NAME="IDX691"></A> -<DT><U>Function:</U> <B>solid:color</B> <I>diffuseColor</I> -<DD></P> -<P> - -Returns an <EM>appearance</EM>, the optical properties of the objects -<A NAME="IDX692"></A> -with which it is associated. <VAR>ambientIntensity</VAR>, <VAR>shininess</VAR>, and <VAR>transparency</VAR> must be numbers between 0 -and 1. <VAR>diffuseColor</VAR>, <VAR>specularColor</VAR>, and <VAR>emissiveColor</VAR> are objects of type <A HREF="slib_5.html#SEC119">color</A>, -24-bit sRGB integers or lists of 3 numbers between 0.0 and 1.0. -If a color argument is omitted or #f, then the default color will be used. -</P> -</DL> -<P> - -<A NAME="IDX693"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:texture</B> <I>image color scale rotation center translation</I> -<DD><P> - -<A NAME="IDX694"></A> -<DT><U>Function:</U> <B>solid:texture</B> <I>image color scale rotation center</I> -<DD></P> -<P> - -<A NAME="IDX695"></A> -<DT><U>Function:</U> <B>solid:texture</B> <I>image color scale rotation</I> -<DD></P> -<P> - -<A NAME="IDX696"></A> -<DT><U>Function:</U> <B>solid:texture</B> <I>image color scale</I> -<DD></P> -<P> - -<A NAME="IDX697"></A> -<DT><U>Function:</U> <B>solid:texture</B> <I>image color</I> -<DD></P> -<P> - -<A NAME="IDX698"></A> -<DT><U>Function:</U> <B>solid:texture</B> <I>image</I> -<DD></P> -<P> - -Returns an <EM>appearance</EM>, the optical properties of the objects -<A NAME="IDX699"></A> -with which it is associated. <VAR>image</VAR> is a string naming a JPEG or PNG -image resource. <VAR>color</VAR> is #f, a color, or the string returned by -<CODE>solid:color</CODE>. The rest of the optional arguments specify -2-dimensional transforms applying to the <VAR>image</VAR>. -</P> -<P> - -<VAR>scale</VAR> must be #f, a number, or list or vector of 2 numbers specifying the -scale to apply to <VAR>image</VAR>. <VAR>rotation</VAR> must be #f or the number of degrees to -rotate <VAR>image</VAR>. <VAR>center</VAR> must be #f or a list or vector of 2 numbers specifying -the center of <VAR>image</VAR> relative to the <VAR>image</VAR> dimensions. <VAR>translation</VAR> must be #f or a -list or vector of 2 numbers specifying the translation to apply to <VAR>image</VAR>. -</P> -</DL> -<A NAME="SEC116"></A> -<H3> Aggregating Objects </H3> -<!--docid::SEC116::--> -<P> - -<A NAME="IDX700"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:center-row-of</B> <I>number solid spacing</I> -<DD>Returns a row of <VAR>number</VAR> <VAR>solid</VAR> objects spaced evenly <VAR>spacing</VAR> apart. -</DL> -<P> - -<A NAME="IDX701"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:center-array-of</B> <I>number-a number-b solid spacing-a spacing-b</I> -<DD>Returns <VAR>number-b</VAR> rows, <VAR>spacing-b</VAR> apart, of <VAR>number-a</VAR> <VAR>solid</VAR> objects <VAR>spacing-a</VAR> apart. -</DL> -<P> - -<A NAME="IDX702"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:center-pile-of</B> <I>number-a number-b number-c solid spacing-a spacing-b spacing-c</I> -<DD>Returns <VAR>number-c</VAR> planes, <VAR>spacing-c</VAR> apart, of <VAR>number-b</VAR> rows, <VAR>spacing-b</VAR> apart, of <VAR>number-a</VAR> <VAR>solid</VAR> objects <VAR>spacing-a</VAR> apart. -</DL> -<P> - -<A NAME="IDX703"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:arrow</B> <I>center</I> -<DD><P> - -<VAR>center</VAR> must be a list or vector of three numbers. Returns an upward -pointing metallic arrow centered at <VAR>center</VAR>. -</P> -<P> - -<A NAME="IDX704"></A> -<DT><U>Function:</U> <B>solid:arrow</B> -<DD>Returns an upward pointing metallic arrow centered at the origin. -</P> -</DL> -<A NAME="SEC117"></A> -<H3> Spatial Transformations </H3> -<!--docid::SEC117::--> -<P> - -<A NAME="IDX705"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:translation</B> <I>center solid <small>...</small></I> -<DD><VAR>center</VAR> must be a list or vector of three numbers. <CODE>solid:translation</CODE> Returns an -aggregate of <VAR>solids</VAR>, <small>...</small> with their origin moved to <VAR>center</VAR>. -</DL> -<P> - -<A NAME="IDX706"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:scale</B> <I>scale solid <small>...</small></I> -<DD><VAR>scale</VAR> must be a number or a list or vector of three numbers. <CODE>solid:scale</CODE> -Returns an aggregate of <VAR>solids</VAR>, <small>...</small> scaled per <VAR>scale</VAR>. -</DL> -<P> - -<A NAME="IDX707"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solid:rotation</B> <I>axis angle solid <small>...</small></I> -<DD><VAR>axis</VAR> must be a list or vector of three numbers. <CODE>solid:rotation</CODE> Returns an -aggregate of <VAR>solids</VAR>, <small>...</small> rotated <VAR>angle</VAR> degrees around the axis <VAR>axis</VAR>. -</DL> -<P> - -<A NAME="Color"></A> -<HR SIZE="6"> -<A NAME="SEC118"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC112"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC119"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.9 Color </H2> -<!--docid::SEC118::--> -<P> - -<A NAME="Color"></A> -</P> -<P> - -<A HREF="http://swissnet.ai.mit.edu/~jaffer/Color">http://swissnet.ai.mit.edu/~jaffer/Color</A> -</P> -<P> - -The goals of this package are to provide methods to specify, compute, -and transform colors in a core set of additive color spaces. The color -spaces supported should be sufficient for working with the color data -encountered in practice and the literature. -</P> -<P> - -<TABLE BORDER="0" CELLSPACING="0"> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC119">5.9.1 Color Data-Type</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">'color</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC122">5.9.2 Color Spaces</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">XYZ, L*a*b*, L*u*v*, L*C*h, RGB709, sRGB</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC127">5.9.3 Spectra</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">Color Temperatures and CIEXYZ(1931)</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC128">5.9.4 Color Difference Metrics</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">Society of Dyers and Colorists</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC129">5.9.5 Color Conversions</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">Low-level</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC130">5.9.6 Color Names</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">in relational databases</TD></TR> -<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="slib_5.html#SEC133">5.9.7 Daylight</A></TD><TD> </TD><TD ALIGN="left" VALIGN="TOP">Sunlight and sky colors</TD></TR> -</TABLE> -<P> - -<A NAME="Color Data-Type"></A> -<HR SIZE="6"> -<A NAME="SEC119"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC120"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.1 Color Data-Type </H3> -<!--docid::SEC119::--> -<P> - -<A NAME="Color_Data-Type"></A> -<CODE>(require 'color)</CODE> -</P> -<P> - -<A NAME="IDX708"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color?</B> <I>obj</I> -<DD>Returns #t if <VAR>obj</VAR> is a color. -<P> - -<A NAME="IDX709"></A> -<DT><U>Function:</U> <B>color?</B> <I>obj typ</I> -<DD>Returns #t if <VAR>obj</VAR> is a color of color-space <VAR>typ</VAR>. The symbol -<VAR>typ</VAR> must be one of: -</P> -<P> - -<UL> -<LI> -CIEXYZ -<LI> -RGB709 -<LI> -L*a*b* -<LI> -L*u*v* -<LI> -sRGB -<LI> -e-sRGB -<LI> -L*C*h -</UL> -</DL> -<P> - -<A NAME="IDX710"></A> -</P> -<DL> -<DT><U>Function:</U> <B>make-color</B> <I>space arg <small>...</small></I> -<DD>Returns a color of type <VAR>space</VAR>. -</DL> -<P> - -<A NAME="IDX711"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-space</B> <I>color</I> -<DD>Returns the symbol for the color-space in which <VAR>color</VAR> is embedded. -</DL> -<P> - -<A NAME="IDX712"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-precision</B> <I>color</I> -<DD>For colors in digital color-spaces, <CODE>color-precision</CODE> returns the -number of bits used for each of the R, G, and B channels of the -encoding. Otherwise, <CODE>color-precision</CODE> returns #f -</DL> -<P> - -<A NAME="IDX713"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-white-point</B> <I>color</I> -<DD>Returns the white-point of <VAR>color</VAR> in all color-spaces except CIEXYZ. -</DL> -<P> - -<A NAME="IDX714"></A> -</P> -<DL> -<DT><U>Function:</U> <B>convert-color</B> <I>color space white-point</I> -<DD><A NAME="IDX715"></A> -<DT><U>Function:</U> <B>convert-color</B> <I>color space</I> -<DD><A NAME="IDX716"></A> -<DT><U>Function:</U> <B>convert-color</B> <I>color e-sRGB precision</I> -<DD>Converts <VAR>color</VAR> into <VAR>space</VAR> at optional <VAR>white-point</VAR>. -</DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC120"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC119"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC121"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.9.1.1 External Representation </H4> -<!--docid::SEC120::--> -<P> - -Each color encoding has an external, case-insensitive representation. -To ensure portability, the white-point for all color strings is D65. -<A NAME="DOCF4" HREF="slib_fot.html#FOOT4">(4)</A> -</P> -<P> - -</P> -<TABLE> -<TR><TD>Color Space</TD> -</TD><TD> External Representation -</TR> -<TR><TD>CIEXYZ</TD> -</TD><TD> CIEXYZ:<I><X></I>/<I><Y></I>/<I><Z></I> -</TR> -<TR><TD>RGB709</TD> -</TD><TD> RGBi:<I><R></I>/<I><G></I>/<I><B></I> -</TR> -<TR><TD>L*a*b*</TD> -</TD><TD> CIELAB:<I><L></I>/<I><a></I>/<I><b></I> -</TR> -<TR><TD>L*u*v*</TD> -</TD><TD> CIELuv:<I><L></I>/<I><u></I>/<I><v></I> -</TR> -<TR><TD>L*C*h</TD> -</TD><TD> CIELCh:<I><L></I>/<I><C></I>/<I><h></I> -</TR></TABLE> -<P> - -The <VAR>X</VAR>, <VAR>Y</VAR>, <VAR>Z</VAR>, <VAR>L</VAR>, <VAR>a</VAR>, <VAR>b</VAR>, <VAR>u</VAR>, -<VAR>v</VAR>, <VAR>C</VAR>, <VAR>h</VAR>, <VAR>R</VAR>, <VAR>G</VAR>, and <VAR>B</VAR> fields are -(Scheme) real numbers within the appropriate ranges. -</P> -<P> - -</P> -<TABLE> -<TR><TD>Color Space</TD> -</TD><TD> External Representation -</TR> -<TR><TD>sRGB</TD> -</TD><TD> sRGB:<I><R></I>/<I><G></I>/<I><B></I> -</TR> -<TR><TD>e-sRGB10</TD> -</TD><TD> e-sRGB10:<I><R></I>/<I><G></I>/<I><B></I> -</TR> -<TR><TD>e-sRGB12</TD> -</TD><TD> e-sRGB12:<I><R></I>/<I><G></I>/<I><B></I> -</TR> -<TR><TD>e-sRGB16</TD> -</TD><TD> e-sRGB16:<I><R></I>/<I><G></I>/<I><B></I> -</TR></TABLE> -<P> - -The <VAR>R</VAR>, <VAR>G</VAR>, and <VAR>B</VAR>, fields are non-negative exact decimal -integers within the appropriate ranges. -</P> -<P> - -Several additional syntaxes are supported by <CODE>string->color</CODE>: -</P> -<P> - -</P> -<TABLE> -<TR><TD>Color Space</TD> -</TD><TD> External Representation -</TR> -<TR><TD>sRGB</TD> -</TD><TD> sRGB:<I><RRGGBB></I> -</TR> -<TR><TD>sRGB</TD> -</TD><TD> #<I><RRGGBB></I> -</TR> -<TR><TD>sRGB</TD> -</TD><TD> 0x<I><RRGGBB></I> -</TR> -<TR><TD>sRGB</TD> -</TD><TD> #x<I><RRGGBB></I> -</TR></TABLE> -<P> - -Where <VAR>RRGGBB</VAR> is a non-negative six-digit hexadecimal number. -</P> -<P> - -<A NAME="IDX717"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->string</B> <I>color</I> -<DD>Returns a string representation of <VAR>color</VAR>. -</DL> -<P> - -<A NAME="IDX718"></A> -</P> -<DL> -<DT><U>Function:</U> <B>string->color</B> <I>string</I> -<DD>Returns the color represented by <VAR>string</VAR>. If <VAR>string</VAR> is not a -syntactically valid notation for a color, then <CODE>string->color</CODE> -returns #f. -</DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC121"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC120"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC122"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H4> 5.9.1.2 White </H4> -<!--docid::SEC121::--> -<P> - -We experience color relative to the illumination around us. -CIEXYZ coordinates, although subject to uniform scaling, are -objective. Thus other color spaces are specified relative to a -<A NAME="IDX719"></A> -<EM>white point</EM> in CIEXYZ coordinates. -<A NAME="IDX720"></A> -</P> -<P> - -The white point for digital color spaces is set to D65. For the other -spaces a <VAR>white-point</VAR> argument can be specified. The default if -none is specified is the white-point with which the color was created -or last converted; and D65 if none has been specified. -</P> -<P> - -<A NAME="IDX721"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>D65</B> -<DD>Is the color of 6500.K (blackbody) illumination. D65 is close -to the average color of daylight. -</DL> -<P> - -<A NAME="IDX722"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>D50</B> -<DD>Is the color of 5000.K (blackbody) illumination. D50 is the color of -indoor lighting by incandescent bulbs, whose filaments have -temperatures around 5000.K. -</DL> -<P> - -<A NAME="Color Spaces"></A> -<HR SIZE="6"> -<A NAME="SEC122"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC121"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC127"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.2 Color Spaces </H3> -<!--docid::SEC122::--> -<P> - -<A NAME="Color_Spaces"></A> -<A NAME="SEC123"></A> -<H4> Measurement-based Color Spaces </H4> -<!--docid::SEC123::--> -<P> - -<A NAME="IDX723"></A> -The <EM>tristimulus</EM> color spaces are those whose component values -<A NAME="IDX724"></A> -are proportional measurements of light intensity. The CIEXYZ(1931) -system provides 3 sets of spectra to convolve with a spectrum of -interest. The result of those convolutions is coordinates in CIEXYZ -space. All tristimuls color spaces are related to CIEXYZ by linear -transforms, namely matrix multiplication. Of the color spaces listed -here, CIEXYZ and RGB709 are tristimulus spaces. -</P> -<P> - -<A NAME="IDX725"></A> -</P> -<DL> -<DT><U>Color Space:</U> <B>CIEXYZ</B> -<DD>The CIEXYZ color space covers the full <EM>gamut</EM>. -<A NAME="IDX726"></A> -It is the basis for color-space conversions. -<P> - -CIEXYZ is a list of three inexact numbers between 0 and 1.1. -'(0. 0. 0.) is black; '(1. 1. 1.) is white. -</P> -</DL> -<P> - -<A NAME="IDX727"></A> -</P> -<DL> -<DT><U>Function:</U> <B>ciexyz->color</B> <I>xyz</I> -<DD><P> - -<VAR>xyz</VAR> must be a list of 3 numbers. If <VAR>xyz</VAR> is valid CIEXYZ coordinates, -then <CODE>ciexyz->color</CODE> returns the color specified by <VAR>xyz</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX728"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:ciexyz</B> <I>x y z</I> -<DD><P> - -Returns the CIEXYZ color composed of <VAR>x</VAR>, <VAR>y</VAR>, <VAR>z</VAR>. If the -coordinates do not encode a valid CIEXYZ color, then an error is -signaled. -</P> -</DL> -<P> - -<A NAME="IDX729"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->ciexyz</B> <I>color</I> -<DD>Returns the list of 3 numbers encoding <VAR>color</VAR> in CIEXYZ. -</DL> -<A NAME="IDX730"></A> -<DL> -<DT><U>Color Space:</U> <B>RGB709</B> -<DD>BT.709-4 (03/00) <CITE>Parameter values for the HDTV standards for -production and international programme exchange</CITE> specifies parameter -values for chromaticity, sampling, signal format, frame rates, etc., of -high definition television signals. -<P> - -An RGB709 color is represented by a list of three inexact numbers -between 0 and 1. '(0. 0. 0.) is black '(1. 1. 1.) is white. -</P> -</DL> -<P> - -<A NAME="IDX731"></A> -</P> -<DL> -<DT><U>Function:</U> <B>rgb709->color</B> <I>rgb</I> -<DD><P> - -<VAR>rgb</VAR> must be a list of 3 numbers. If <VAR>rgb</VAR> is valid RGB709 coordinates, -then <CODE>rgb709->color</CODE> returns the color specified by <VAR>rgb</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX732"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:rgb709</B> <I>r g b</I> -<DD><P> - -Returns the RGB709 color composed of <VAR>r</VAR>, <VAR>g</VAR>, <VAR>b</VAR>. If the -coordinates do not encode a valid RGB709 color, then an error is -signaled. -</P> -</DL> -<P> - -<A NAME="IDX733"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->rgb709</B> <I>color</I> -<DD>Returns the list of 3 numbers encoding <VAR>color</VAR> in RGB709. -</DL> -<A NAME="SEC124"></A> -<H4> Perceptual Uniformity </H4> -<!--docid::SEC124::--> -<P> - -Although properly encoding the chromaticity, tristimulus spaces do not -match the logarithmic response of human visual systems to intensity. -Minimum detectable differences between colors correspond to a smaller -range of distances (6:1) in the L*a*b* and L*u*v* spaces than in -tristimulus spaces (80:1). For this reason, color distances are -computed in L*a*b* (or L*C*h). -</P> -<P> - -<A NAME="IDX734"></A> -</P> -<DL> -<DT><U>Color Space:</U> <B>L*a*b*</B> -<DD>Is a CIE color space which better matches the human visual system's -perception of color. It is a list of three numbers: -<P> - -<UL> -<LI> -0 <= L* <= 100 (CIE <EM>Lightness</EM>) -<A NAME="IDX735"></A> -<P> - -</P> -<LI> --500 <= a* <= 500 -<LI> --200 <= b* <= 200 -</UL> -</DL> -<P> - -<A NAME="IDX736"></A> -</P> -<DL> -<DT><U>Function:</U> <B>l*a*b*->color</B> <I>L*a*b* white-point</I> -<DD><P> - -<VAR>L*a*b*</VAR> must be a list of 3 numbers. If <VAR>L*a*b*</VAR> is valid L*a*b* coordinates, -then <CODE>l*a*b*->color</CODE> returns the color specified by <VAR>L*a*b*</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX737"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:l*a*b*</B> <I>L* a* b* white-point</I> -<DD><P> - -Returns the L*a*b* color composed of <VAR>L*</VAR>, <VAR>a*</VAR>, <VAR>b*</VAR> with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX738"></A> -<DT><U>Function:</U> <B>color:l*a*b*</B> <I>L* a* b*</I> -<DD>Returns the L*a*b* color composed of <VAR>L*</VAR>, <VAR>a*</VAR>, <VAR>b*</VAR>. If the coordinates -do not encode a valid L*a*b* color, then an error is signaled. -</P> -</DL> -<P> - -<A NAME="IDX739"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->l*a*b*</B> <I>color white-point</I> -<DD><P> - -Returns the list of 3 numbers encoding <VAR>color</VAR> in L*a*b* with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX740"></A> -<DT><U>Function:</U> <B>color->l*a*b*</B> <I>color</I> -<DD>Returns the list of 3 numbers encoding <VAR>color</VAR> in L*a*b*. -</P> -</DL> -<A NAME="IDX741"></A> -<DL> -<DT><U>Color Space:</U> <B>L*u*v*</B> -<DD>Is another CIE encoding designed to better match the human visual -system's perception of color. -</DL> -<P> - -<A NAME="IDX742"></A> -</P> -<DL> -<DT><U>Function:</U> <B>l*u*v*->color</B> <I>L*u*v* white-point</I> -<DD><P> - -<VAR>L*u*v*</VAR> must be a list of 3 numbers. If <VAR>L*u*v*</VAR> is valid L*u*v* coordinates, -then <CODE>l*u*v*->color</CODE> returns the color specified by <VAR>L*u*v*</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX743"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:l*u*v*</B> <I>L* u* v* white-point</I> -<DD><P> - -Returns the L*u*v* color composed of <VAR>L*</VAR>, <VAR>u*</VAR>, <VAR>v*</VAR> with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX744"></A> -<DT><U>Function:</U> <B>color:l*u*v*</B> <I>L* u* v*</I> -<DD>Returns the L*u*v* color composed of <VAR>L*</VAR>, <VAR>u*</VAR>, <VAR>v*</VAR>. If the coordinates -do not encode a valid L*u*v* color, then an error is signaled. -</P> -</DL> -<P> - -<A NAME="IDX745"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->l*u*v*</B> <I>color white-point</I> -<DD><P> - -Returns the list of 3 numbers encoding <VAR>color</VAR> in L*u*v* with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX746"></A> -<DT><U>Function:</U> <B>color->l*u*v*</B> <I>color</I> -<DD>Returns the list of 3 numbers encoding <VAR>color</VAR> in L*u*v*. -</P> -</DL> -<A NAME="SEC125"></A> -<H4> Cylindrical Coordinates </H4> -<!--docid::SEC125::--> -<P> - -HSL (Hue Saturation Lightness), HSV (Hue Saturation Value), HSI (Hue -Saturation Intensity) and HCI (Hue Chroma Intensity) are cylindrical -color spaces (with angle hue). But these spaces are all defined in -terms device-dependent RGB spaces. -</P> -<P> - -One might wonder if there is some fundamental reason why intuitive -specification of color must be device-dependent. But take heart! A -cylindrical system can be based on L*a*b* and is used for predicting how -close colors seem to observers. -</P> -<P> - -<A NAME="IDX747"></A> -</P> -<DL> -<DT><U>Color Space:</U> <B>L*C*h</B> -<DD>Expresses the *a and b* of L*a*b* in polar coordinates. It is a list of -three numbers: -<P> - -<UL> -<LI> -0 <= L* <= 100 (CIE <EM>Lightness</EM>) -<A NAME="IDX748"></A> -<P> - -</P> -<LI> -C* (CIE <EM>Chroma</EM>) is the distance from the neutral (gray) axis. -<A NAME="IDX749"></A> -<LI> -0 <= h <= 360 (CIE <EM>Hue</EM>) is the angle. -<A NAME="IDX750"></A> -</UL> -<P> - -The colors by quadrant of h are: -</P> -<P> - -</P> -<TABLE> -<TR><TD>0 </TD><TD> red, orange, yellow </TD><TD> 90</TD> -</TR> -<TR><TD>90 </TD><TD> yellow, yellow-green, green </TD><TD> 180</TD> -</TR> -<TR><TD>180 </TD><TD> green, cyan (blue-green), blue </TD><TD> 270</TD> -</TR> -<TR><TD>270 </TD><TD> blue, purple, magenta </TD><TD> 360</TD> -</TR></TABLE> -<P> - -</P> -</DL> -<P> - -<A NAME="IDX751"></A> -</P> -<DL> -<DT><U>Function:</U> <B>l*c*h->color</B> <I>L*C*h white-point</I> -<DD><P> - -<VAR>L*C*h</VAR> must be a list of 3 numbers. If <VAR>L*C*h</VAR> is valid L*C*h coordinates, -then <CODE>l*c*h->color</CODE> returns the color specified by <VAR>L*C*h</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX752"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:l*c*h</B> <I>L* C* h white-point</I> -<DD><P> - -Returns the L*C*h color composed of <VAR>L*</VAR>, <VAR>C*</VAR>, <VAR>h</VAR> with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX753"></A> -<DT><U>Function:</U> <B>color:l*c*h</B> <I>L* C* h</I> -<DD>Returns the L*C*h color composed of <VAR>L*</VAR>, <VAR>C*</VAR>, <VAR>h</VAR>. If the coordinates -do not encode a valid L*C*h color, then an error is signaled. -</P> -</DL> -<P> - -<A NAME="IDX754"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->l*c*h</B> <I>color white-point</I> -<DD><P> - -Returns the list of 3 numbers encoding <VAR>color</VAR> in L*C*h with <VAR>white-point</VAR>. -</P> -<P> - -<A NAME="IDX755"></A> -<DT><U>Function:</U> <B>color->l*c*h</B> <I>color</I> -<DD>Returns the list of 3 numbers encoding <VAR>color</VAR> in L*C*h. -</P> -</DL> -<A NAME="SEC126"></A> -<H4> Digital Color Spaces </H4> -<!--docid::SEC126::--> -<P> - -The color spaces discussed so far are impractical for image data because -of numerical precision and computational requirements. In 1998 the IEC -adopted <CITE>A Standard Default Color Space for the Internet - sRGB</CITE> -(<A HREF="http://www.w3.org/Graphics/Color/sRGB">http://www.w3.org/Graphics/Color/sRGB</A>). sRGB was cleverly -designed to employ the 24-bit (256x256x256) color encoding already in -widespread use; and the 2.2 gamma intrinsic to CRT monitors. -</P> -<P> - -Conversion from CIEXYZ to digital (sRGB) color spaces is accomplished by -conversion first to a RGB709 tristimulus space with D65 white-point; -then each coordinate is individually subjected to the same non-linear -mapping. Inverse operations in the reverse order create the inverse -transform. -</P> -<P> - -<A NAME="IDX756"></A> -</P> -<DL> -<DT><U>Color Space:</U> <B>sRGB</B> -<DD>Is "A Standard Default Color Space for the Internet". Most display -monitors will work fairly well with sRGB directly. Systems using ICC -profiles -<A NAME="IDX757"></A> -<A NAME="DOCF5" HREF="slib_fot.html#FOOT5">(5)</A> -should work very well with sRGB. -<P> - -</P> -</DL> -<P> - -<A NAME="IDX758"></A> -</P> -<DL> -<DT><U>Function:</U> <B>srgb->color</B> <I>rgb</I> -<DD><P> - -<VAR>rgb</VAR> must be a list of 3 numbers. If <VAR>rgb</VAR> is valid sRGB coordinates, -then <CODE>srgb->color</CODE> returns the color specified by <VAR>rgb</VAR>; otherwise returns #f. -</P> -</DL> -<P> - -<A NAME="IDX759"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:srgb</B> <I>r g b</I> -<DD><P> - -Returns the sRGB color composed of <VAR>r</VAR>, <VAR>g</VAR>, <VAR>b</VAR>. If the -coordinates do not encode a valid sRGB color, then an error is -signaled. -</P> -</DL> -<A NAME="IDX760"></A> -<DL> -<DT><U>Color Space:</U> <B>xRGB</B> -<DD>Represents the equivalent sRGB color with a single 24-bit integer. The -most significant 8 bits encode red, the middle 8 bits blue, and the -least significant 8 bits green. -</DL> -<P> - -<A NAME="IDX761"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->srgb</B> <I>color</I> -<DD><P> - -Returns the list of 3 integers encoding <VAR>color</VAR> in sRGB. -</P> -</DL> -<P> - -<A NAME="IDX762"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->xrgb</B> <I>color</I> -<DD>Returns the 24-bit integer encoding <VAR>color</VAR> in sRGB. -</DL> -<P> - -<A NAME="IDX763"></A> -</P> -<DL> -<DT><U>Function:</U> <B>xrgb->color</B> <I>k</I> -<DD><P> - -Returns the sRGB color composed of the 24-bit integer <VAR>k</VAR>. -</P> -</DL> -<A NAME="IDX764"></A> -<DL> -<DT><U>Color Space:</U> <B>e-sRGB</B> -<DD>Is "Photography - Electronic still picture imaging - Extended sRGB color -encoding" (PIMA 7667:2001). It extends the gamut of sRGB; and its -higher precision numbers provide a larger dynamic range. -<P> - -A triplet of integers represent e-sRGB colors. Three precisions are -supported: -</P> -<P> - -</P> -<DL COMPACT> -<DT>e-sRGB10 -<DD>0 to 1023 -<DT>e-sRGB12 -<DD>0 to 4095 -<DT>e-sRGB16 -<DD>0 to 65535 -</DL> -</DL> -<P> - -<A NAME="IDX765"></A> -</P> -<DL> -<DT><U>Function:</U> <B>e-srgb->color</B> <I>precision rgb</I> -<DD><VAR>precision</VAR> must be the integer 10, 12, or 16. <VAR>rgb</VAR> must be a list of 3 -numbers. If <VAR>rgb</VAR> is valid e-sRGB coordinates, then <CODE>e-srgb->color</CODE> returns the color -specified by <VAR>rgb</VAR>; otherwise returns #f. -</DL> -<P> - -<A NAME="IDX766"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:e-srgb</B> <I>10 r g b</I> -<DD><P> - -Returns the e-sRGB10 color composed of integers <VAR>r</VAR>, <VAR>g</VAR>, <VAR>b</VAR>. -</P> -<P> - -<A NAME="IDX767"></A> -<DT><U>Function:</U> <B>color:e-srgb</B> <I>12 r g b</I> -<DD>Returns the e-sRGB12 color composed of integers <VAR>r</VAR>, <VAR>g</VAR>, <VAR>b</VAR>. -</P> -<P> - -<A NAME="IDX768"></A> -<DT><U>Function:</U> <B>color:e-srgb</B> <I>16 r g b</I> -<DD>Returns the e-sRGB16 color composed of integers <VAR>r</VAR>, <VAR>g</VAR>, <VAR>b</VAR>. -If the coordinates do not encode a valid e-sRGB color, then an error -is signaled. -</P> -</DL> -<P> - -<A NAME="IDX769"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color->e-srgb</B> <I>precision color</I> -<DD><VAR>precision</VAR> must be the integer 10, 12, or 16. <CODE>color->e-srgb</CODE> returns the list of 3 -integers encoding <VAR>color</VAR> in sRGB10, sRGB12, or sRGB16. -</DL> -<P> - -<A NAME="Spectra"></A> -<HR SIZE="6"> -<A NAME="SEC127"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC122"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC128"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.3 Spectra </H3> -<!--docid::SEC127::--> -<P> - -<A NAME="Spectra"></A> -The following functions compute colors from spectra, scale color -luminance, and extract chromaticity. XYZ is used in the names of -procedures for unnormalized colors; the coordinates of CIEXYZ colors are -constrained as described in <A HREF="slib_5.html#SEC122">5.9.2 Color Spaces</A>. -</P> -<P> - -<CODE>(require 'color-space)</CODE> -</P> -<P> - -A spectrum may be represented as: -</P> -<P> - -<UL> -<LI> -A procedure of one argument accepting real numbers from 380e-9 to -780e-9, the wavelength in meters; or -<LI> -A vector of real numbers representing intensity samples evenly spaced -over some range of wavelengths overlapping the range 380e-9 to 780e-9. -</UL> -<P> - -CIEXYZ values are calculated as dot-product with the X, Y (Luminance), -and Z <EM>Spectral Tristimulus Values</EM>. The files `<TT>cie1931.xyz</TT>' -and `<TT>cie1964.xyz</TT>' in the distribution contain these CIE-defined -values. -<A NAME="IDX770"></A> -</P> -<P> - -<A NAME="IDX771"></A> -</P> -<DL> -<DT><U>Feature:</U> <B>cie1964</B> -<DD><A NAME="IDX772"></A> -Loads the Spectral Tristimulus Values defining <CITE>CIE 1964 -Supplementary Standard Colorimetric Observer</CITE>. -<A NAME="IDX773"></A> -<DT><U>Feature:</U> <B>cie1931</B> -<DD><A NAME="IDX774"></A> -Loads the Spectral Tristimulus Values defining <CITE>CIE 1931 -Supplementary Standard Colorimetric Observer</CITE>. -<A NAME="IDX775"></A> -<DT><U>Feature:</U> <B>ciexyz</B> -<DD><A NAME="IDX776"></A> -Requires Spectral Tristimulus Values, defaulting to cie1931. -</DL> -<P> - -<CODE>(require 'cie1964)</CODE> or <CODE>(require 'cie1931)</CODE> will -<A NAME="IDX777"></A> -<CODE>load-ciexyz</CODE> specific values used by the following spectrum -conversion procedures. The spectrum conversion procedures -<CODE>(require 'ciexyz)</CODE> to assure that a set is loaded. -</P> -<P> - -<A NAME="IDX778"></A> -</P> -<DL> -<DT><U>Function:</U> <B>spectrum->XYZ</B> <I>proc</I> -<DD><VAR>proc</VAR> must be a function of one argument. <CODE>spectrum->XYZ</CODE> -computes the CIEXYZ(1931) values for the spectrum returned by <VAR>proc</VAR> -when called with arguments from 380e-9 to 780e-9, the wavelength in -meters. -<P> - -<A NAME="IDX779"></A> -<DT><U>Function:</U> <B>spectrum->XYZ</B> <I>spectrum x1 x2</I> -<DD><VAR>x1</VAR> and <VAR>x2</VAR> must be positive real numbers specifying the -wavelengths (in meters) corresponding to the zeroth and last elements of -vector or list <VAR>spectrum</VAR>. <CODE>spectrum->XYZ</CODE> returns the -CIEXYZ(1931) values for a light source with spectral values proportional -to the elements of <VAR>spectrum</VAR> at evenly spaced wavelengths between -<VAR>x1</VAR> and <VAR>x2</VAR>. -</P> -<P> - -Compute the colors of 6500.K and 5000.K blackbody radiation: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'color-space) -(define xyz (spectrum->XYZ (blackbody-spectrum 6500))) -(define y_n (cadr xyz)) -(map (lambda (x) (/ x y_n)) xyz) - => (0.9687111145512467 1.0 1.1210875945303613) - -(define xyz (spectrum->XYZ (blackbody-spectrum 5000))) -(map (lambda (x) (/ x y_n)) xyz) - => (0.2933441826889158 0.2988931825387761 0.25783646831201573) -</pre></td></tr></table><P> - -<A NAME="IDX780"></A> -<DT><U>Function:</U> <B>spectrum->CIEXYZ</B> <I>proc</I> -<DD><A NAME="IDX781"></A> -<DT><U>Function:</U> <B>spectrum->CIEXYZ</B> <I>spectrum x1 x2</I> -<DD><CODE>spectrum->CIEXYZ</CODE> computes the CIEXYZ(1931) values for the -spectrum, scaled so their sum is 1. -</P> -</DL> -<P> - -<A NAME="IDX782"></A> -</P> -<DL> -<DT><U>Function:</U> <B>spectrum->chromaticity</B> <I>proc</I> -<DD><A NAME="IDX783"></A> -<DT><U>Function:</U> <B>spectrum->chromaticity</B> <I>spectrum x1 x2</I> -<DD>Computes the chromaticity for the given spectrum. -</DL> -<P> - -<A NAME="IDX784"></A> -</P> -<DL> -<DT><U>Function:</U> <B>wavelength->XYZ</B> <I>w</I> -<DD><A NAME="IDX785"></A> -<DT><U>Function:</U> <B>wavelength->chromaticity</B> <I>w</I> -<DD><A NAME="IDX786"></A> -<DT><U>Function:</U> <B>wavelength->CIEXYZ</B> <I>w</I> -<DD><VAR>w</VAR> must be a number between 380e-9 to 780e-9. -<CODE>wavelength->XYZ</CODE> returns (unnormalized) XYZ values for a -monochromatic light source with wavelength <VAR>w</VAR>. -<CODE>wavelength->chromaticity</CODE> returns the chromaticity for a -monochromatic light source with wavelength <VAR>w</VAR>. -<CODE>wavelength->CIEXYZ</CODE> returns XYZ values for the saturated color -having chromaticity of a monochromatic light source with wavelength -<VAR>w</VAR>. -</DL> -<P> - -<A NAME="IDX787"></A> -</P> -<DL> -<DT><U>Function:</U> <B>blackbody-spectrum</B> <I>temp</I> -<DD><A NAME="IDX788"></A> -<DT><U>Function:</U> <B>blackbody-spectrum</B> <I>temp span</I> -<DD>Returns a procedure of one argument (wavelength in meters), which -returns the radiance of a black body at <VAR>temp</VAR>. -<P> - -The optional argument <VAR>span</VAR> is the wavelength analog of bandwidth. -With the default <VAR>span</VAR> of 1.nm (1e-9.m), the values returned by the -procedure correspond to the power of the photons with wavelengths -<VAR>w</VAR> to <VAR>w</VAR>+1e-9. -</P> -</DL> -<P> - -<A NAME="IDX789"></A> -</P> -<DL> -<DT><U>Function:</U> <B>temperature->XYZ</B> <I>x</I> -<DD>The positive number <VAR>x</VAR> is a temperature in degrees kelvin. -<CODE>temperature->XYZ</CODE> computes the CIEXYZ(1931) values for the -spectrum of a black body at temperature <VAR>x</VAR>. -<P> - -Compute the chromaticities of 6500.K and 5000.K blackbody radiation: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'color-space) -(XYZ->chromaticity (temperature->XYZ 6500)) - => (0.3135191660557008 0.3236456786200268) - -(XYZ->chromaticity (temperature->XYZ 5000)) - => (0.34508082841161052 0.3516084965163377) -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX790"></A> -</P> -<DL> -<DT><U>Function:</U> <B>temperature->CIEXYZ</B> <I>x</I> -<DD>The positive number <VAR>x</VAR> is a temperature in degrees kelvin. -<CODE>temperature->CIEXYZ</CODE> computes the CIEXYZ(1931) values for the -spectrum of a black body at temperature <VAR>x</VAR>, scaled to be just -inside the RGB709 gamut. -</DL> -<P> - -<A NAME="IDX791"></A> -</P> -<DL> -<DT><U>Function:</U> <B>temperature->chromaticity</B> <I>x</I> -<DD></DL> -<P> - -<A NAME="IDX792"></A> -</P> -<DL> -<DT><U>Function:</U> <B>XYZ:normalize</B> <I>xyz</I> -<DD><VAR>xyz</VAR> is a list of three non-negative real numbers. -<CODE>XYZ:normalize</CODE> returns a list of numbers proportional to -<VAR>xyz</VAR>; scaled so their sum is 1. -</DL> -<P> - -<A NAME="IDX793"></A> -</P> -<DL> -<DT><U>Function:</U> <B>XYZ:normalize-colors</B> <I>colors <small>...</small></I> -<DD><VAR>colors</VAR> is a list of XYZ triples. <CODE>XYZ:normalize-colors</CODE> -scales all the triples by a common factor such that the maximum sum of -numbers in a scaled triple is 1. -</DL> -<P> - -<A NAME="IDX794"></A> -</P> -<DL> -<DT><U>Function:</U> <B>XYZ->chromaticity</B> <I>xyz</I> -<DD>Returns a two element list: the x and y components of <VAR>xyz</VAR> -normalized to 1 (= <VAR>x</VAR> + <VAR>y</VAR> + <VAR>z</VAR>). -</DL> -<P> - -<A NAME="IDX795"></A> -</P> -<DL> -<DT><U>Function:</U> <B>chromaticity->CIEXYZ</B> <I>x y</I> -<DD>Returns the list of <VAR>x</VAR>, and <VAR>y</VAR>, 1 - <VAR>y</VAR> - <VAR>x</VAR>. -</DL> -<P> - -<A NAME="IDX796"></A> -</P> -<DL> -<DT><U>Function:</U> <B>chromaticity->whitepoint</B> <I>x y</I> -<DD>Returns the CIEXYZ(1931) values having luminosity 1 and chromaticity -<VAR>x</VAR> and <VAR>y</VAR>. -</DL> -<P> - -<A NAME="IDX797"></A> -Many color datasets are expressed in <EM>xyY</EM> format; chromaticity with -CIE luminance (Y). But xyY is not a CIE standard like CIEXYZ, CIELAB, -and CIELUV. Although chrominance is well defined, the luminance -component is sometimes scaled to 1, sometimes to 100, but usually has no -obvious range. With no given whitepoint, the only reasonable course is -to ascertain the luminance range of a dataset and normalize the values -to lie from 0 to 1. -</P> -<P> - -<A NAME="IDX798"></A> -</P> -<DL> -<DT><U>Function:</U> <B>XYZ->xyY</B> <I>xyz</I> -<DD>Returns a three element list: the <VAR>x</VAR> and <VAR>y</VAR> components of -<VAR>XYZ</VAR> normalized to 1, and CIE luminance <VAR>Y</VAR>. -</DL> -<P> - -<A NAME="IDX799"></A> -</P> -<DL> -<DT><U>Function:</U> <B>xyY->XYZ</B> <I>xyY</I> -<DD></DL> -<P> - -<A NAME="IDX800"></A> -</P> -<DL> -<DT><U>Function:</U> <B>xyY:normalize-colors</B> <I>colors</I> -<DD><VAR>colors</VAR> is a list of xyY triples. <CODE>xyY:normalize-colors</CODE> -scales each chromaticity so it sums to 1 or less; and divides the -<VAR>Y</VAR> values by the maximum <VAR>Y</VAR> in the dataset, so all lie between -0 and 1. -<P> - -<A NAME="IDX801"></A> -<DT><U>Function:</U> <B>xyY:normalize-colors</B> <I>colors n</I> -<DD>If <VAR>n</VAR> is positive real, then <CODE>xyY:normalize-colors</CODE> divides -the <VAR>Y</VAR> values by <VAR>n</VAR> times the maximum <VAR>Y</VAR> in the dataset. -</P> -<P> - -If <VAR>n</VAR> is an exact non-positive integer, then -<CODE>xyY:normalize-colors</CODE> divides the <VAR>Y</VAR> values by the maximum of -the <VAR>Y</VAR>s in the dataset excepting the -<VAR>n</VAR> largest <VAR>Y</VAR> -values. -</P> -<P> - -In all cases, returned <VAR>Y</VAR> values are limited to lie from 0 to 1. -</P> -</DL> -<P> - -Why would one want to normalize to other than 1? If the sun or its -reflection is the brightest object in a scene, then normalizing to its -luminance will tend to make the rest of the scene very dark. As with -photographs, limiting the specular highlights looks better than -darkening everything else. -</P> -<P> - -The results of measurements being what they are, -<CODE>xyY:normalize-colors</CODE> is extremely tolerant. Negative numbers are -replaced with zero, and chromaticities with sums greater than one are -scaled to sum to one. -</P> -<P> - -<A NAME="Color Difference Metrics"></A> -<HR SIZE="6"> -<A NAME="SEC128"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC127"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC129"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.4 Color Difference Metrics </H3> -<!--docid::SEC128::--> -<P> - -<A NAME="Color_Difference_Metrics"></A> -</P> -<P> - -<CODE>(require 'color-space)</CODE> -</P> -<P> - -The low-level metric functions operate on lists of 3 numbers, lab1, -lab2, lch1, or lch2. -</P> -<P> - -<CODE>(require 'color)</CODE> -</P> -<P> - -The wrapped functions operate on objects of type color, color1 and -color2 in the function entries. -</P> -<P> - -<A NAME="IDX802"></A> -</P> -<DL> -<DT><U>Function:</U> <B>L*a*b*:DE*</B> <I>lab1 lab2</I> -<DD>Returns the Euclidean distance between <VAR>lab1</VAR> and <VAR>lab2</VAR>. -<P> - -<A NAME="IDX803"></A> -<DT><U>Function:</U> <B>CIE:DE*</B> <I>color1 color2 white-point</I> -<DD><A NAME="IDX804"></A> -<DT><U>Function:</U> <B>CIE:DE*</B> <I>color1 color2</I> -<DD>Returns the Euclidean distance in L*a*b* space between <VAR>color1</VAR> and -<VAR>color2</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX805"></A> -</P> -<DL> -<DT><U>Function:</U> <B>L*C*h:DE*94</B> <I>lch1 lch2 parametric-factors</I> -<DD><A NAME="IDX806"></A> -<DT><U>Function:</U> <B>L*C*h:DE*94</B> <I>lch1 lch2</I> -<DD><P> - -<A NAME="IDX807"></A> -<DT><U>Function:</U> <B>CIE:DE*94</B> <I>color1 color2 parametric-factors</I> -<DD><A NAME="IDX808"></A> -<DT><U>Function:</U> <B>CIE:DE*94</B> <I>color1 color2</I> -<DD></P> -<P> - -Measures distance in the L*C*h cylindrical color-space. -The three axes are individually scaled (depending on C*) in their -contributions to the total distance. -</P> -<P> - -The CIE has defined reference conditions under which the metric with -default parameters can be expected to perform well. These are: -</P> -<P> - -<UL> -<LI> -The specimens are homogeneous in colour. -<LI> -The colour difference (CIELAB) is <= 5 units. -<LI> -They are placed in direct edge contact. -<LI> -Each specimen subtends an angle of >4 degrees to the assessor, whose -colour vision is normal. -<LI> -They are illuminated at 1000 lux, and viewed against a background of -uniform grey, with L* of 50, under illumination simulating D65. -</UL> -<P> - -The <VAR>parametric-factors</VAR> argument is a list of 3 quantities kL, kC -and kH. <VAR>parametric-factors</VAR> independently adjust each -colour-difference term to account for any deviations from the reference -viewing conditions. Under the reference conditions explained above, the -default is kL = kC = kH = 1. -</P> -</DL> -<P> - -The Color Measurement Committee of The Society of Dyers and Colorists in -Great Britain created a more sophisticated color-distance function for -use in judging the consistency of dye lots. With CMC:DE* it is possible -to use a single value pass/fail tolerance for all shades. -</P> -<P> - -<A NAME="IDX809"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CMC-DE</B> <I>lch1 lch2 parametric-factors</I> -<DD><A NAME="IDX810"></A> -<DT><U>Function:</U> <B>CMC-DE</B> <I>lch1 lch2 l c</I> -<DD><A NAME="IDX811"></A> -<DT><U>Function:</U> <B>CMC-DE</B> <I>lch1 lch2 l</I> -<DD><A NAME="IDX812"></A> -<DT><U>Function:</U> <B>CMC-DE</B> <I>lch1 lch2</I> -<DD><P> - -<A NAME="IDX813"></A> -<DT><U>Function:</U> <B>CMC:DE*</B> <I>color1 color2 l c</I> -<DD><A NAME="IDX814"></A> -<DT><U>Function:</U> <B>CMC:DE*</B> <I>color1 color2</I> -<DD></P> -<P> - -<CODE>CMC:DE</CODE> is a L*C*h metric. The <VAR>parametric-factors</VAR> -argument is a list of 2 numbers <VAR>l</VAR> and <VAR>c</VAR>. <VAR>l</VAR> and -<VAR>c</VAR> parameterize this metric. 1 and 1 are recommended for -perceptibility; the default, 2 and 1, for acceptability. -</P> -</DL> -<P> - -<A NAME="Color Conversions"></A> -<HR SIZE="6"> -<A NAME="SEC129"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC128"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC130"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.5 Color Conversions </H3> -<!--docid::SEC129::--> -<P> - -<A NAME="Color_Conversions"></A> -</P> -<P> - -This package contains the low-level color conversion and color metric -routines operating on lists of 3 numbers. There is no type or range -checking. -</P> -<P> - -<CODE>(require 'color-space)</CODE> -</P> -<P> - -<A NAME="IDX815"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>CIEXYZ:D65</B> -<DD>Is the color of 6500.K (blackbody) illumination. D65 is close to the -average color of daylight. -</DL> -<P> - -<A NAME="IDX816"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>CIEXYZ:D50</B> -<DD>Is the color of 5000.K (blackbody) illumination. D50 is the color of -indoor lighting by incandescent bulbs. -</DL> -<P> - -<A NAME="IDX817"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>CIEXYZ:A</B> -<DD><A NAME="IDX818"></A> -<DT><U>Constant:</U> <B>CIEXYZ:B</B> -<DD><A NAME="IDX819"></A> -<DT><U>Constant:</U> <B>CIEXYZ:C</B> -<DD><A NAME="IDX820"></A> -<DT><U>Constant:</U> <B>CIEXYZ:E</B> -<DD>CIE 1931 illuminants normalized to 1 = y. -</DL> -<P> - -<A NAME="IDX821"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color:linear-transform</B> <I>matrix row</I> -<DD></DL> -<P> - -<A NAME="IDX822"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->RGB709</B> <I>xyz</I> -<DD><A NAME="IDX823"></A> -<DT><U>Function:</U> <B>RGB709->CIEXYZ</B> <I>srgb</I> -<DD></DL> -<P> - -<A NAME="IDX824"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->L*u*v*</B> <I>xyz white-point</I> -<DD><A NAME="IDX825"></A> -<DT><U>Function:</U> <B>CIEXYZ->L*u*v*</B> <I>xyz</I> -<DD><A NAME="IDX826"></A> -<DT><U>Function:</U> <B>L*u*v*->CIEXYZ</B> <I>L*u*v* white-point</I> -<DD><A NAME="IDX827"></A> -<DT><U>Function:</U> <B>L*u*v*->CIEXYZ</B> <I>L*u*v*</I> -<DD>The <VAR>white-point</VAR> defaults to CIEXYZ:D65. -</DL> -<P> - -<A NAME="IDX828"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->L*a*b*</B> <I>xyz white-point</I> -<DD><A NAME="IDX829"></A> -<DT><U>Function:</U> <B>CIEXYZ->L*a*b*</B> <I>xyz</I> -<DD><A NAME="IDX830"></A> -<DT><U>Function:</U> <B>L*a*b*->CIEXYZ</B> <I>L*a*b* white-point</I> -<DD><A NAME="IDX831"></A> -<DT><U>Function:</U> <B>L*a*b*->CIEXYZ</B> <I>L*a*b*</I> -<DD>The XYZ <VAR>white-point</VAR> defaults to CIEXYZ:D65. -</DL> -<P> - -<A NAME="IDX832"></A> -</P> -<DL> -<DT><U>Function:</U> <B>L*a*b*->L*C*h</B> <I>L*a*b*</I> -<DD><A NAME="IDX833"></A> -<DT><U>Function:</U> <B>L*C*h->L*a*b*</B> <I>L*C*h</I> -<DD></DL> -<P> - -<A NAME="IDX834"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->sRGB</B> <I>xyz</I> -<DD><A NAME="IDX835"></A> -<DT><U>Function:</U> <B>sRGB->CIEXYZ</B> <I>srgb</I> -<DD></DL> -<P> - -<A NAME="IDX836"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->xRGB</B> <I>xyz</I> -<DD><A NAME="IDX837"></A> -<DT><U>Function:</U> <B>xRGB->CIEXYZ</B> <I>srgb</I> -<DD></DL> -<P> - -<A NAME="IDX838"></A> -</P> -<DL> -<DT><U>Function:</U> <B>sRGB->xRGB</B> <I>xyz</I> -<DD><A NAME="IDX839"></A> -<DT><U>Function:</U> <B>xRGB->sRGB</B> <I>srgb</I> -<DD></DL> -<P> - -<A NAME="IDX840"></A> -</P> -<DL> -<DT><U>Function:</U> <B>CIEXYZ->e-sRGB</B> <I>n xyz</I> -<DD><A NAME="IDX841"></A> -<DT><U>Function:</U> <B>e-sRGB->CIEXYZ</B> <I>n srgb</I> -<DD></DL> -<P> - -<A NAME="IDX842"></A> -</P> -<DL> -<DT><U>Function:</U> <B>sRGB->e-sRGB</B> <I>n srgb</I> -<DD><A NAME="IDX843"></A> -<DT><U>Function:</U> <B>e-sRGB->sRGB</B> <I>n srgb</I> -<DD>The integer <VAR>n</VAR> must be 10, 12, or 16. Because sRGB and e-sRGB use -the same RGB709 chromaticities, conversion between them is simpler than -conversion through CIEXYZ. -</DL> -<P> - -Do not convert e-sRGB precision through <CODE>e-sRGB->sRGB</CODE> then -<CODE>sRGB->e-sRGB</CODE> -- values would be truncated to 8-bits! -</P> -<P> - -<A NAME="IDX844"></A> -</P> -<DL> -<DT><U>Function:</U> <B>e-sRGB->e-sRGB</B> <I>n1 srgb n2</I> -<DD>The integers <VAR>n1</VAR> and <VAR>n2</VAR> must be 10, 12, or 16. -<CODE>e-sRGB->e-sRGB</CODE> converts <VAR>srgb</VAR> to e-sRGB of precision -<VAR>n2</VAR>. -</DL> -<P> - -<A NAME="Color Names"></A> -<HR SIZE="6"> -<A NAME="SEC130"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC129"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC133"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.6 Color Names </H3> -<!--docid::SEC130::--> -<P> - -<A NAME="Color_Names"></A> -<CODE>(require 'color-names)</CODE> -<A NAME="IDX845"></A> -</P> -<P> - -Rather than ballast the color dictionaries with numbered grays, -<CODE>file->color-dictionary</CODE> discards them. They are provided -through the <CODE>grey</CODE> procedure: -</P> -<P> - -<A NAME="IDX846"></A> -</P> -<DL> -<DT><U>Function:</U> <B>grey</B> <I>k</I> -<DD><P> - -Returns <CODE>(inexact->exact (round (* k 2.55)))</CODE>, the X11 color -grey<I><k></I>. -</P> -</DL> -A color dictionary is a database table relating <EM>canonical</EM> -<A NAME="IDX847"></A> -color-names to color-strings -(see section <A HREF="slib_5.html#SEC119">External Representation</A>). -<P> - -The column names in a color dictionary are unimportant; the first -field is the key, and the second is the color-string. -</P> -<P> - -<A NAME="IDX848"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-name:canonicalize</B> <I>name</I> -<DD>Returns a downcased copy of the string or symbol <VAR>name</VAR> with -`<SAMP>_</SAMP>', `<SAMP>-</SAMP>', and whitespace removed. -</DL> -<P> - -<A NAME="IDX849"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-name->color</B> <I>name table1 table2 <small>...</small></I> -<DD><P> - -<VAR>table1</VAR>, <VAR>table2</VAR>, <small>...</small> must be color-dictionary tables. <CODE>color-name->color</CODE> searches for the -canonical form of <VAR>name</VAR> in <VAR>table1</VAR>, <VAR>table2</VAR>, <small>...</small> in order; returning the -color-string of the first matching record; #f otherwise. -</P> -</DL> -<P> - -<A NAME="IDX850"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-dictionaries->lookup</B> <I>table1 table2 <small>...</small></I> -<DD><P> - -<VAR>table1</VAR>, <VAR>table2</VAR>, <small>...</small> must be color-dictionary tables. <CODE>color-dictionaries->lookup</CODE> returns a -procedure which searches for the canonical form of its string argument -in <VAR>table1</VAR>, <VAR>table2</VAR>, <small>...</small>; returning the color-string of the first matching -record; and #f otherwise. -</P> -</DL> -<P> - -<A NAME="IDX851"></A> -</P> -<DL> -<DT><U>Function:</U> <B>color-dictionary</B> <I>name rdb base-table-type</I> -<DD><P> - -<VAR>rdb</VAR> must be a string naming a relational database file; and the symbol -<VAR>name</VAR> a table therein. The database will be opened as -<VAR>base-table-type</VAR>. <CODE>color-dictionary</CODE> returns the read-only table <VAR>name</VAR> in database -<VAR>name</VAR> if it exists; #f otherwise. -</P> -<P> - -<A NAME="IDX852"></A> -<DT><U>Function:</U> <B>color-dictionary</B> <I>name rdb</I> -<DD></P> -<P> - -<VAR>rdb</VAR> must be an open relational database or a string naming a relational -database file; and the symbol <VAR>name</VAR> a table therein. <CODE>color-dictionary</CODE> returns the -read-only table <VAR>name</VAR> in database <VAR>name</VAR> if it exists; #f otherwise. -</P> -</DL> -<P> - -<A NAME="IDX853"></A> -</P> -<DL> -<DT><U>Function:</U> <B>load-color-dictionary</B> <I>name rdb base-table-type</I> -<DD><P> - -<A NAME="IDX854"></A> -<DT><U>Function:</U> <B>load-color-dictionary</B> <I>name rdb</I> -<DD></P> -<P> - -<VAR>rdb</VAR> must be a string naming a relational database file; and the symbol -<VAR>name</VAR> a table therein. If the symbol <VAR>base-table-type</VAR> is provided, the database will -be opened as <VAR>base-table-type</VAR>. <CODE>load-color-dictionary</CODE> creates a top-level definition of the symbol <VAR>name</VAR> -to a lookup procedure for the color dictionary <VAR>name</VAR> in <VAR>rdb</VAR>. -</P> -<P> - -The value returned by <CODE>load-color-dictionary</CODE> is unspecified. -</P> -</DL> -<P> - -<A NAME="SEC131"></A> -<H4> Dictionary Creation </H4> -<!--docid::SEC131::--> -<P> - -<CODE>(require 'color-database)</CODE> -<A NAME="IDX855"></A> -</P> -<P> - -<A NAME="IDX856"></A> -</P> -<DL> -<DT><U>Function:</U> <B>file->color-dictionary</B> <I>file table-name rdb base-table-type</I> -<DD><P> - -<A NAME="IDX857"></A> -<DT><U>Function:</U> <B>file->color-dictionary</B> <I>file table-name rdb</I> -<DD></P> -<P> - -<VAR>rdb</VAR> must be an open relational database or a string naming a relational -database file, <VAR>table-name</VAR> a symbol, and the string <VAR>file</VAR> must name an existing -file with colornames and their corresponding xRGB (6-digit hex) -values. <CODE>file->color-dictionary</CODE> creates a table <VAR>table-name</VAR> in <VAR>rdb</VAR> and enters the associations found -in <VAR>file</VAR> into it. -</P> -</DL> -<P> - -<A NAME="IDX858"></A> -</P> -<DL> -<DT><U>Function:</U> <B>url->color-dictionary</B> <I>url table-name rdb base-table-type</I> -<DD><P> - -<A NAME="IDX859"></A> -<DT><U>Function:</U> <B>url->color-dictionary</B> <I>url table-name rdb</I> -<DD></P> -<P> - -<VAR>rdb</VAR> must be an open relational database or a string naming a relational -database file and <VAR>table-name</VAR> a symbol. <CODE>url->color-dictionary</CODE> retrieves the resource named by the -string <VAR>url</VAR> using the <EM>wget</EM> program; then calls -<A NAME="IDX860"></A> -<CODE>file->color-dictionary</CODE> to enter its associations in <VAR>table-name</VAR> in <VAR>url</VAR>. -</P> -</DL> -This section has detailed the procedures for creating and loading -color dictionaries. So where are the dictionaries to load? -<P> - -<A HREF="http://swissnet.ai.mit.edu/~jaffer/Color/Dictionaries.html">http://swissnet.ai.mit.edu/~jaffer/Color/Dictionaries.html</A> -</P> -<P> - -Describes and evaluates several color-name dictionaries on the web. -The following procedure creates a database containing two of these -dictionaries. -</P> -<P> - -<A NAME="IDX861"></A> -</P> -<DL> -<DT><U>Function:</U> <B>make-slib-color-name-db</B> -<DD><P> - -Creates an alist-table relational database in library-vicinity -containing the <EM>Resene</EM> and <EM>saturate</EM> color-name -<A NAME="IDX862"></A> -<A NAME="IDX863"></A> -dictionaries. -</P> -<P> - -If the files `<TT>resenecolours.txt</TT>' and `<TT>saturate.txt</TT>' exist in -the library-vicinity, then they used as the source of color-name -data. Otherwise, <CODE>make-slib-color-name-db</CODE> calls url->color-dictionary with the URLs of -appropriate source files. -</P> -</DL> -<P> - -<A NAME="SEC132"></A> -<H4> The Short List </H4> -<!--docid::SEC132::--> -<P> - -<CODE>(require 'saturate)</CODE> -<A NAME="IDX864"></A> -</P> -<P> - -<A NAME="IDX865"></A> -</P> -<DL> -<DT><U>Function:</U> <B>saturate</B> <I>name</I> -<DD>Looks for <VAR>name</VAR> among the 19 saturated colors from -<CITE>Approximate Colors on CIE Chromaticity Diagram</CITE>: -<P> - -</P> -<TABLE> -<TR><TD>reddish orange </TD><TD> orange </TD><TD> yellowish orange </TD><TD> yellow</TD> -</TR> -<TR><TD>greenish yellow </TD><TD> yellow green </TD><TD> yellowish green </TD><TD> green</TD> -</TR> -<TR><TD>bluish green </TD><TD> blue green </TD><TD> greenish blue </TD><TD> blue</TD> -</TR> -<TR><TD>purplish blue </TD><TD> bluish purple </TD><TD> purple </TD><TD> reddish purple</TD> -</TR> -<TR><TD>red purple </TD><TD> purplish red </TD><TD> red</TD> -</TR></TABLE> -<P> - -(<A HREF="http://swissnet.ai.mit.edu/~jaffer/Color/saturate.pdf">http://swissnet.ai.mit.edu/~jaffer/Color/saturate.pdf</A>). If -<VAR>name</VAR> is found, the corresponding color is returned. Otherwise #f -is returned. Use saturate only for light source colors. -</P> -</DL> -<P> - -Resene Paints Limited, New Zealand's largest privately-owned and -operated paint manufacturing company, has generously made their -<CITE>Resene RGB Values List</CITE> available. -</P> -<P> - -<CODE>(require 'resene)</CODE> -<A NAME="IDX866"></A> -</P> -<P> - -<A NAME="IDX867"></A> -</P> -<DL> -<DT><U>Function:</U> <B>resene</B> <I>name</I> -<DD>Looks for <VAR>name</VAR> among the 1300 entries in the Resene color-name -dictionary (<A HREF="http://swissnet.ai.mit.edu/~jaffer/Color/resene.pdf">http://swissnet.ai.mit.edu/~jaffer/Color/resene.pdf</A>). -If <VAR>name</VAR> is found, the corresponding color is returned. Otherwise -#f is returned. The <CITE>Resene RGB Values List</CITE> is an excellent -source for surface colors. -</DL> -<P> - -If you include the <EM>Resene RGB Values List</EM> in binary form in a -program, then you must include its license with your program: -</P> -<P> - -<BLOCKQUOTE> -Resene RGB Values List<BR> -For further information refer to http://www.resene.co.nz<BR> -Copyright Resene Paints Ltd 2001 -<P> - -Permission to copy this dictionary, to modify it, to redistribute it, -to distribute modified versions, and to use it for any purpose is -granted, subject to the following restrictions and understandings. -</P> -<P> - -<OL> -<LI> -Any text copy made of this dictionary must include this copyright -notice in full. -<P> - -</P> -<LI> -Any redistribution in binary form must reproduce this copyright -notice in the documentation or other materials provided with the -distribution. -<P> - -</P> -<LI> -Resene Paints Ltd makes no warranty or representation that this -dictionary is error-free, and is under no obligation to provide any -services, by way of maintenance, update, or otherwise. -<P> - -</P> -<LI> -There shall be no use of the name of Resene or Resene Paints Ltd -in any advertising, promotional, or sales literature without prior -written consent in each case. -<P> - -</P> -<LI> -These RGB colour formulations may not be used to the detriment of -Resene Paints Ltd. -</OL> -</BLOCKQUOTE> -<P> - -<A NAME="Daylight"></A> -<HR SIZE="6"> -<A NAME="SEC133"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC130"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC134"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC118"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H3> 5.9.7 Daylight </H3> -<!--docid::SEC133::--> -<P> - -<A NAME="Daylight"></A> -<CODE>(require 'daylight)</CODE> -<A NAME="IDX868"></A> -<A NAME="IDX869"></A> -<A NAME="IDX870"></A> -<A NAME="IDX871"></A> -</P> -<P> - -This package calculates the colors of sky as detailed in:<BR> -<A HREF="http://www.cs.utah.edu/vissim/papers/sunsky/sunsky.pdf">http://www.cs.utah.edu/vissim/papers/sunsky/sunsky.pdf</A><BR> -<CITE>A Practical Analytic Model for Daylight</CITE><BR> -A. J. Preetham, Peter Shirley, Brian Smits -</P> -<P> - -<A NAME="IDX872"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solar-hour</B> <I>julian-day hour</I> -<DD><P> - -Returns the solar-time in hours given the integer <VAR>julian-day</VAR> in the range 1 to -366, and the local time in hours. -</P> -<P> - -To be meticulous, subtract 4 minutes for each degree of longitude west -of the standard meridian of your time zone. -</P> -</DL> -<P> - -<A NAME="IDX873"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solar-declination</B> <I>julian-day</I> -<DD><P> - -</P> -</DL> -<P> - -<A NAME="IDX874"></A> -</P> -<DL> -<DT><U>Function:</U> <B>solar-polar</B> <I>declination latitude solar-hour</I> -<DD>Returns a list of <VAR>theta_s</VAR>, the solar angle from the -zenith, and <VAR>phi_s</VAR>, the solar azimuth. 0 <= <VAR>theta_s</VAR> -measured in degrees. <VAR>phi_s</VAR> is measured in degrees from due -south; west of south being positive. -</DL> -In the following procedures, the number 0 <= <VAR>theta_s</VAR> <= 90 is -the solar angle from the zenith in degrees. -<P> - -<A NAME="IDX875"></A> -Turbidity is a measure of the fraction of scattering due to haze as -opposed to molecules. This is a convenient quantity because it can be -estimated based on visibility of distant objects. This model fails -for turbidity values less than 1.3. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre> _______________________________________________________________ -512|-: | - | * pure-air | -256|-:** | - | : ** exceptionally-clear | -128|-: * | - | : ** | - 64|-: * | - | : ** very-clear | - 32|-: ** | - | : ** | - 16|-: *** clear | - | : **** | - 8|-: **** | - | : **** light-haze | - 4|-: **** | - | : ****** | - 2|-: ******** haze thin-| - | : *********** fog | - 1|-:----------------------------------------------------*******--| - |_:____.____:____.____:____.____:____.____:____.____:____.____:_| - 1 2 4 8 16 32 64 - Meterorological range (km) versus Turbidity -</pre></td></tr></table><P> - -<A NAME="IDX876"></A> -</P> -<DL> -<DT><U>Function:</U> <B>sunlight-spectrum</B> <I>turbidity theta_s</I> -<DD>Returns a vector of 41 values, the spectrum of sunlight from -380.nm to 790.nm for a given <VAR>turbidity</VAR> and <VAR>theta_s</VAR>. -</DL> -<P> - -<A NAME="IDX877"></A> -</P> -<DL> -<DT><U>Function:</U> <B>sunlight-xyz</B> <I>turbidity theta_s</I> -<DD>Returns (unnormalized) XYZ values for color of sunlight for a -given <VAR>turbidity</VAR> and <VAR>theta_s</VAR>. -</DL> -<P> - -<A NAME="IDX878"></A> -</P> -<DL> -<DT><U>Function:</U> <B>sunlight-ciexyz</B> <I>turbidity theta_s</I> -<DD>Given <VAR>turbidity</VAR> and <VAR>theta_s</VAR>, <CODE>sunlight-ciexyz</CODE> returns the CIEXYZ triple for color of -sunlight scaled to be just inside the RGB709 gamut. -</DL> -<P> - -<A NAME="IDX879"></A> -</P> -<DL> -<DT><U>Function:</U> <B>zenith-xyy</B> <I>turbidity theta_s</I> -<DD>Returns the xyY (chromaticity and luminance) at the zenith. The -Luminance has units kcd/m^2. -</DL> -<P> - -<A NAME="IDX880"></A> -</P> -<DL> -<DT><U>Function:</U> <B>overcast-sky-color-xyy</B> <I>turbidity theta_s</I> -<DD><VAR>turbidity</VAR> is a positive real number expressing the amount of light -scattering. The real number <VAR>theta_s</VAR> is the solar angle from the zenith in -degrees. -<P> - -<CODE>overcast-sky-color-xyy</CODE> returns a function of one angle <VAR>theta</VAR>, the angle from the -zenith of the viewing direction (in degrees); and returning the xyY -value for light coming from that elevation of the sky. -</P> -</DL> -<P> - -<A NAME="IDX881"></A> -</P> -<DL> -<DT><U>Function:</U> <B>clear-sky-color-xyy</B> <I>turbidity theta_s phi_s</I> -<DD><A NAME="IDX882"></A> -<DT><U>Function:</U> <B>sky-color-xyy</B> <I>turbidity theta_s phi_s</I> -<DD><VAR>turbidity</VAR> is a positive real number expressing the amount of light -scattering. The real number <VAR>theta_s</VAR> is the solar angle from the zenith in -degrees. The real number <VAR>phi_s</VAR> is the solar angle from south. -<P> - -<CODE>clear-sky-color-xyy</CODE> returns a function of two angles, <VAR>theta</VAR> and <VAR>phi</VAR> which -specify the angles from the zenith and south meridian of the viewing -direction (in degrees); returning the xyY value for light coming from -that direction of the sky. -</P> -<P> - -<CODE>sky-color-xyY</CODE> calls <CODE>overcast-sky-color-xyY</CODE> for -<VAR>turbidity</VAR> <= 20; otherwise the <CODE>clear-sky-color-xyy</CODE> function. -</P> -</DL> -<P> - -<A NAME="Root Finding"></A> -<HR SIZE="6"> -<A NAME="SEC134"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC133"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC135"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.10 Root Finding </H2> -<!--docid::SEC134::--> -<P> - -<CODE>(require 'root)</CODE> -<A NAME="IDX883"></A> -</P> -<P> - -<A NAME="IDX884"></A> -</P> -<DL> -<DT><U>Function:</U> <B>newton:find-integer-root</B> <I>f df/dx x0</I> -<DD>Given integer valued procedure <VAR>f</VAR>, its derivative (with respect to -its argument) <VAR>df/dx</VAR>, and initial integer value <VAR>x0</VAR> for which -<VAR>df/dx</VAR>(<VAR>x0</VAR>) is non-zero, returns an integer <VAR>x</VAR> for which -<VAR>f</VAR>(<VAR>x</VAR>) is closer to zero than either of the integers adjacent -to <VAR>x</VAR>; or returns <CODE>#f</CODE> if such an integer can't be found. -<P> - -To find the closest integer to a given integers square root: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(define (integer-sqrt y) - (newton:find-integer-root - (lambda (x) (- (* x x) y)) - (lambda (x) (* 2 x)) - (ash 1 (quotient (integer-length y) 2)))) - -(integer-sqrt 15) => 4 -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX885"></A> -</P> -<DL> -<DT><U>Function:</U> <B>integer-sqrt</B> <I>y</I> -<DD>Given a non-negative integer <VAR>y</VAR>, returns the rounded square-root of -<VAR>y</VAR>. -</DL> -<P> - -<A NAME="IDX886"></A> -</P> -<DL> -<DT><U>Function:</U> <B>newton:find-root</B> <I>f df/dx x0 prec</I> -<DD>Given real valued procedures <VAR>f</VAR>, <VAR>df/dx</VAR> of one (real) -argument, initial real value <VAR>x0</VAR> for which <VAR>df/dx</VAR>(<VAR>x0</VAR>) is -non-zero, and positive real number <VAR>prec</VAR>, returns a real <VAR>x</VAR> -for which <CODE>abs</CODE>(<VAR>f</VAR>(<VAR>x</VAR>)) is less than <VAR>prec</VAR>; or -returns <CODE>#f</CODE> if such a real can't be found. -<P> - -If <VAR>prec</VAR> is instead a negative integer, <CODE>newton:find-root</CODE> -returns the result of -<VAR>prec</VAR> iterations. -</P> -</DL> -<P> - -H. J. Orchard, <CITE>The Laguerre Method for Finding the Zeros of -Polynomials</CITE>, IEEE Transactions on Circuits and Systems, Vol. 36, -No. 11, November 1989, pp 1377-1381. -</P> -<P> - -<BLOCKQUOTE> -There are 2 errors in Orchard's Table II. Line k=2 for starting -value of 1000+j0 should have Z_k of 1.0475 + j4.1036 and line k=2 -for starting value of 0+j1000 should have Z_k of 1.0988 + j4.0833. -</BLOCKQUOTE> -<P> - -<A NAME="IDX887"></A> -</P> -<DL> -<DT><U>Function:</U> <B>laguerre:find-root</B> <I>f df/dz ddf/dz^2 z0 prec</I> -<DD>Given complex valued procedure <VAR>f</VAR> of one (complex) argument, its -derivative (with respect to its argument) <VAR>df/dx</VAR>, its second -derivative <VAR>ddf/dz^2</VAR>, initial complex value <VAR>z0</VAR>, and positive -real number <VAR>prec</VAR>, returns a complex number <VAR>z</VAR> for which -<CODE>magnitude</CODE>(<VAR>f</VAR>(<VAR>z</VAR>)) is less than <VAR>prec</VAR>; or returns -<CODE>#f</CODE> if such a number can't be found. -<P> - -If <VAR>prec</VAR> is instead a negative integer, <CODE>laguerre:find-root</CODE> -returns the result of -<VAR>prec</VAR> iterations. -</P> -</DL> -<P> - -<A NAME="IDX888"></A> -</P> -<DL> -<DT><U>Function:</U> <B>laguerre:find-polynomial-root</B> <I>deg f df/dz ddf/dz^2 z0 prec</I> -<DD>Given polynomial procedure <VAR>f</VAR> of integer degree <VAR>deg</VAR> of one -argument, its derivative (with respect to its argument) <VAR>df/dx</VAR>, its -second derivative <VAR>ddf/dz^2</VAR>, initial complex value <VAR>z0</VAR>, and -positive real number <VAR>prec</VAR>, returns a complex number <VAR>z</VAR> for -which <CODE>magnitude</CODE>(<VAR>f</VAR>(<VAR>z</VAR>)) is less than <VAR>prec</VAR>; or -returns <CODE>#f</CODE> if such a number can't be found. -<P> - -If <VAR>prec</VAR> is instead a negative integer, -<CODE>laguerre:find-polynomial-root</CODE> returns the result of -<VAR>prec</VAR> -iterations. -</P> -</DL> -<P> - -<A NAME="IDX889"></A> -</P> -<DL> -<DT><U>Function:</U> <B>secant:find-root</B> <I>f x0 x1 prec</I> -<DD><A NAME="IDX890"></A> -<DT><U>Function:</U> <B>secant:find-bracketed-root</B> <I>f x0 x1 prec</I> -<DD>Given a real valued procedure <VAR>f</VAR> and two real valued starting -points <VAR>x0</VAR> and <VAR>x1</VAR>, returns a real <VAR>x</VAR> for which -<CODE>(abs (f x))</CODE> is less than <VAR>prec</VAR>; or returns -<CODE>#f</CODE> if such a real can't be found. -<P> - -If <VAR>x0</VAR> and <VAR>x1</VAR> are chosen such that they bracket a root, that is -<TABLE><tr><td> </td><td class=example><pre>(or (< (f x0) 0 (f x1)) - (< (f x1) 0 (f x0))) -</pre></td></tr></table>then the root returned will be between <VAR>x0</VAR> and <VAR>x1</VAR>, and -<VAR>f</VAR> will not be passed an argument outside of that interval. -<P> - -<CODE>secant:find-bracketed-root</CODE> will return <CODE>#f</CODE> unless <VAR>x0</VAR> -and <VAR>x1</VAR> bracket a root. -</P> -<P> - -The secant method is used until a bracketing interval is found, at which point -a modified <I>regula falsi</I> method is used. -</P> -<P> - -If <VAR>prec</VAR> is instead a negative integer, <CODE>secant:find-root</CODE> -returns the result of -<VAR>prec</VAR> iterations. -</P> -<P> - -If <VAR>prec</VAR> is a procedure it should accept 5 arguments: <VAR>x0</VAR> -<VAR>f0</VAR> <VAR>x1</VAR> <VAR>f1</VAR> and <VAR>count</VAR>, where <VAR>f0</VAR> will be -<CODE>(f x0)</CODE>, <VAR>f1</VAR> <CODE>(f x1)</CODE>, and <VAR>count</VAR> the number of -iterations performed so far. <VAR>prec</VAR> should return non-false -if the iteration should be stopped. -</P> -</DL> -<P> - -<A NAME="Minimizing"></A> -<HR SIZE="6"> -<A NAME="SEC135"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC134"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC136"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.11 Minimizing </H2> -<!--docid::SEC135::--> -<P> - -<CODE>(require 'minimize)</CODE> -<A NAME="IDX891"></A> -<A NAME="IDX892"></A> -</P> -<P> - -</P> -<P> - -The Golden Section Search -<A NAME="DOCF6" HREF="slib_fot.html#FOOT6">(6)</A> -algorithm finds minima of functions which -are expensive to compute or for which derivatives are not available. -Although optimum for the general case, convergence is slow, -requiring nearly 100 iterations for the example (x^3-2x-5). -</P> -<P> - -</P> -<P> - -If the derivative is available, Newton-Raphson is probably a better -choice. If the function is inexpensive to compute, consider -approximating the derivative. -</P> -<P> - -<A NAME="IDX893"></A> -</P> -<DL> -<DT><U>Function:</U> <B>golden-section-search</B> <I>f x0 x1 prec</I> -<DD><P> - -<VAR>x_0</VAR> are <VAR>x_1</VAR> real numbers. The (single argument) -procedure <VAR>f</VAR> is unimodal over the open interval (<VAR>x_0</VAR>, -<VAR>x_1</VAR>). That is, there is exactly one point in the interval for -which the derivative of <VAR>f</VAR> is zero. -</P> -<P> - -<CODE>golden-section-search</CODE> returns a pair (<VAR>x</VAR> . <VAR>f</VAR>(<VAR>x</VAR>)) where <VAR>f</VAR>(<VAR>x</VAR>) -is the minimum. The <VAR>prec</VAR> parameter is the stop criterion. If -<VAR>prec</VAR> is a positive number, then the iteration continues until -<VAR>x</VAR> is within <VAR>prec</VAR> from the true value. If <VAR>prec</VAR> is -a negative integer, then the procedure will iterate <VAR>-prec</VAR> -times or until convergence. If <VAR>prec</VAR> is a procedure of seven -arguments, <VAR>x0</VAR>, <VAR>x1</VAR>, <VAR>a</VAR>, <VAR>b</VAR>, <VAR>fa</VAR>, <VAR>fb</VAR>, -and <VAR>count</VAR>, then the iterations will stop when the procedure -returns <CODE>#t</CODE>. -</P> -<P> - -Analytically, the minimum of x^3-2x-5 is 0.816497. -<TABLE><tr><td> </td><td class=example><pre>(define func (lambda (x) (+ (* x (+ (* x x) -2)) -5))) -(golden-section-search func 0 1 (/ 10000)) - ==> (816.4883855245578e-3 . -6.0886621077391165) -(golden-section-search func 0 1 -5) - ==> (819.6601125010515e-3 . -6.088637561916407) -(golden-section-search func 0 1 - (lambda (a b c d e f g ) (= g 500))) - ==> (816.4965933140557e-3 . -6.088662107903635) -</pre></td></tr></table></DL> -<P> - -<A NAME="Commutative Rings"></A> -<HR SIZE="6"> -<A NAME="SEC136"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC135"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC137"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.12 Commutative Rings </H2> -<!--docid::SEC136::--> -<P> - -Scheme provides a consistent and capable set of numeric functions. -Inexacts implement a field; integers a commutative ring (and Euclidean -domain). This package allows one to use basic Scheme numeric functions -with symbols and non-numeric elements of commutative rings. -</P> -<P> - -<CODE>(require 'commutative-ring)</CODE> -<A NAME="IDX894"></A> -<A NAME="IDX895"></A> -</P> -<P> - -The <EM>commutative-ring</EM> package makes the procedures <CODE>+</CODE>, -<CODE>-</CODE>, <CODE>*</CODE>, <CODE>/</CODE>, and <CODE>^</CODE> <EM>careful</EM> in the sense -<A NAME="IDX896"></A> -that any non-numeric arguments they do not reduce appear in the -expression output. In order to see what working with this package is -like, self-set all the single letter identifiers (to their corresponding -symbols). -<A NAME="IDX897"></A> -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(define a 'a) -<small>...</small> -(define z 'z) -</pre></td></tr></table><P> - -Or just <CODE>(require 'self-set)</CODE>. Now try some sample expressions: -<A NAME="IDX898"></A> -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(+ (+ a b) (- a b)) => (* a 2) -(* (+ a b) (+ a b)) => (^ (+ a b) 2) -(* (+ a b) (- a b)) => (* (+ a b) (- a b)) -(* (- a b) (- a b)) => (^ (- a b) 2) -(* (- a b) (+ a b)) => (* (+ a b) (- a b)) -(/ (+ a b) (+ c d)) => (/ (+ a b) (+ c d)) -(^ (+ a b) 3) => (^ (+ a b) 3) -(^ (+ a 2) 3) => (^ (+ 2 a) 3) -</pre></td></tr></table><P> - -Associative rules have been applied and repeated addition and -multiplication converted to multiplication and exponentiation. -</P> -<P> - -We can enable distributive rules, thus expanding to sum of products -form: -<TABLE><tr><td> </td><td class=example><pre>(set! *ruleset* (combined-rulesets distribute* distribute/)) - -(* (+ a b) (+ a b)) => (+ (* 2 a b) (^ a 2) (^ b 2)) -(* (+ a b) (- a b)) => (- (^ a 2) (^ b 2)) -(* (- a b) (- a b)) => (- (+ (^ a 2) (^ b 2)) (* 2 a b)) -(* (- a b) (+ a b)) => (- (^ a 2) (^ b 2)) -(/ (+ a b) (+ c d)) => (+ (/ a (+ c d)) (/ b (+ c d))) -(/ (+ a b) (- c d)) => (+ (/ a (- c d)) (/ b (- c d))) -(/ (- a b) (- c d)) => (- (/ a (- c d)) (/ b (- c d))) -(/ (- a b) (+ c d)) => (- (/ a (+ c d)) (/ b (+ c d))) -(^ (+ a b) 3) => (+ (* 3 a (^ b 2)) (* 3 b (^ a 2)) (^ a 3) (^ b 3)) -(^ (+ a 2) 3) => (+ 8 (* a 12) (* (^ a 2) 6) (^ a 3)) -</pre></td></tr></table><P> - -Use of this package is not restricted to simple arithmetic expressions: -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'determinant) - -(determinant '((a b c) (d e f) (g h i))) => -(- (+ (* a e i) (* b f g) (* c d h)) (* a f h) (* b d i) (* c e g)) -</pre></td></tr></table><P> - -Currently, only <CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE>, <CODE>/</CODE>, and <CODE>^</CODE> -support non-numeric elements. Expressions with <CODE>-</CODE> are converted -to equivalent expressions without <CODE>-</CODE>, so behavior for <CODE>-</CODE> is -not defined separately. <CODE>/</CODE> expressions are handled similarly. -</P> -<P> - -This list might be extended to include <CODE>quotient</CODE>, <CODE>modulo</CODE>, -<CODE>remainder</CODE>, <CODE>lcm</CODE>, and <CODE>gcd</CODE>; but these work only for -the more restrictive Euclidean (Unique Factorization) Domain. -<A NAME="IDX899"></A> -<A NAME="IDX900"></A> -</P> -<P> - -<HR SIZE="6"> -<A NAME="SEC137"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC136"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC138"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.13 Rules and Rulesets </H2> -<!--docid::SEC137::--> -<P> - -The <EM>commutative-ring</EM> package allows control of ring properties -through the use of <EM>rulesets</EM>. -</P> -<P> - -<A NAME="IDX901"></A> -</P> -<DL> -<DT><U>Variable:</U> <B>*ruleset*</B> -<DD>Contains the set of rules currently in effect. Rules defined by -<CODE>cring:define-rule</CODE> are stored within the value of *ruleset* at the -time <CODE>cring:define-rule</CODE> is called. If <VAR>*ruleset*</VAR> is -<CODE>#f</CODE>, then no rules apply. -</DL> -<P> - -<A NAME="IDX902"></A> -</P> -<DL> -<DT><U>Function:</U> <B>make-ruleset</B> <I>rule1 <small>...</small></I> -<DD><A NAME="IDX903"></A> -<DT><U>Function:</U> <B>make-ruleset</B> <I>name rule1 <small>...</small></I> -<DD>Returns a new ruleset containing the rules formed by applying -<CODE>cring:define-rule</CODE> to each 4-element list argument <VAR>rule</VAR>. If -the first argument to <CODE>make-ruleset</CODE> is a symbol, then the database -table created for the new ruleset will be named <VAR>name</VAR>. Calling -<CODE>make-ruleset</CODE> with no rule arguments creates an empty ruleset. -</DL> -<P> - -<A NAME="IDX904"></A> -</P> -<DL> -<DT><U>Function:</U> <B>combined-rulesets</B> <I>ruleset1 <small>...</small></I> -<DD><A NAME="IDX905"></A> -<DT><U>Function:</U> <B>combined-rulesets</B> <I>name ruleset1 <small>...</small></I> -<DD>Returns a new ruleset containing the rules contained in each ruleset -argument <VAR>ruleset</VAR>. If the first argument to -<CODE>combined-ruleset</CODE> is a symbol, then the database table created for -the new ruleset will be named <VAR>name</VAR>. Calling -<CODE>combined-ruleset</CODE> with no ruleset arguments creates an empty -ruleset. -</DL> -<P> - -Two rulesets are defined by this package. -</P> -<P> - -<A NAME="IDX906"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>distribute*</B> -<DD>Contains the ruleset to distribute multiplication over addition and -subtraction. -</DL> -<P> - -<A NAME="IDX907"></A> -</P> -<DL> -<DT><U>Constant:</U> <B>distribute/</B> -<DD>Contains the ruleset to distribute division over addition and -subtraction. -<P> - -Take care when using both <VAR>distribute*</VAR> and <VAR>distribute/</VAR> -simultaneously. It is possible to put <CODE>/</CODE> into an infinite loop. -</P> -</DL> -<P> - -You can specify how sum and product expressions containing non-numeric -elements simplify by specifying the rules for <CODE>+</CODE> or <CODE>*</CODE> for -cases where expressions involving objects reduce to numbers or to -expressions involving different non-numeric elements. -</P> -<P> - -<A NAME="IDX908"></A> -</P> -<DL> -<DT><U>Function:</U> <B>cring:define-rule</B> <I>op sub-op1 sub-op2 reduction</I> -<DD>Defines a rule for the case when the operation represented by symbol -<VAR>op</VAR> is applied to lists whose <CODE>car</CODE>s are <VAR>sub-op1</VAR> and -<VAR>sub-op2</VAR>, respectively. The argument <VAR>reduction</VAR> is a -procedure accepting 2 arguments which will be lists whose <CODE>car</CODE>s -are <VAR>sub-op1</VAR> and <VAR>sub-op2</VAR>. -<P> - -<A NAME="IDX909"></A> -<DT><U>Function:</U> <B>cring:define-rule</B> <I>op sub-op1 'identity reduction</I> -<DD>Defines a rule for the case when the operation represented by symbol -<VAR>op</VAR> is applied to a list whose <CODE>car</CODE> is <VAR>sub-op1</VAR>, and -some other argument. <VAR>Reduction</VAR> will be called with the list whose -<CODE>car</CODE> is <VAR>sub-op1</VAR> and some other argument. -</P> -<P> - -If <VAR>reduction</VAR> returns <CODE>#f</CODE>, the reduction has failed and other -reductions will be tried. If <VAR>reduction</VAR> returns a non-false value, -that value will replace the two arguments in arithmetic (<CODE>+</CODE>, -<CODE>-</CODE>, and <CODE>*</CODE>) calculations involving non-numeric elements. -</P> -<P> - -The operations <CODE>+</CODE> and <CODE>*</CODE> are assumed commutative; hence both -orders of arguments to <VAR>reduction</VAR> will be tried if necessary. -</P> -<P> - -The following rule is the definition for distributing <CODE>*</CODE> over -<CODE>+</CODE>. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(cring:define-rule - '* '+ 'identity - (lambda (exp1 exp2) - (apply + (map (lambda (trm) (* trm exp2)) (cdr exp1)))))) -</pre></td></tr></table></DL> -<P> - -<HR SIZE="6"> -<A NAME="SEC138"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC137"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC139"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.14 How to Create a Commutative Ring </H2> -<!--docid::SEC138::--> -<P> - -The first step in creating your commutative ring is to write procedures -to create elements of the ring. A non-numeric element of the ring must -be represented as a list whose first element is a symbol or string. -This first element identifies the type of the object. A convenient and -clear convention is to make the type-identifying element be the same -symbol whose top-level value is the procedure to create it. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(define (n . list1) - (cond ((and (= 2 (length list1)) - (eq? (car list1) (cadr list1))) - 0) - ((not (term< (first list1) (last1 list1))) - (apply n (reverse list1))) - (else (cons 'n list1)))) - -(define (s x y) (n x y)) - -(define (m . list1) - (cond ((neq? (first list1) (term_min list1)) - (apply m (cyclicrotate list1))) - ((term< (last1 list1) (cadr list1)) - (apply m (reverse (cyclicrotate list1)))) - (else (cons 'm list1)))) -</pre></td></tr></table><P> - -Define a procedure to multiply 2 non-numeric elements of the ring. -Other multiplicatons are handled automatically. Objects for which rules -have <EM>not</EM> been defined are not changed. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(define (n*n ni nj) - (let ((list1 (cdr ni)) (list2 (cdr nj))) - (cond ((null? (intersection list1 list2)) #f) - ((and (eq? (last1 list1) (first list2)) - (neq? (first list1) (last1 list2))) - (apply n (splice list1 list2))) - ((and (eq? (first list1) (first list2)) - (neq? (last1 list1) (last1 list2))) - (apply n (splice (reverse list1) list2))) - ((and (eq? (last1 list1) (last1 list2)) - (neq? (first list1) (first list2))) - (apply n (splice list1 (reverse list2)))) - ((and (eq? (last1 list1) (first list2)) - (eq? (first list1) (last1 list2))) - (apply m (cyclicsplice list1 list2))) - ((and (eq? (first list1) (first list2)) - (eq? (last1 list1) (last1 list2))) - (apply m (cyclicsplice (reverse list1) list2))) - (else #f)))) -</pre></td></tr></table><P> - -Test the procedures to see if they work. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>;;; where cyclicrotate(list) is cyclic rotation of the list one step -;;; by putting the first element at the end -(define (cyclicrotate list1) - (append (rest list1) (list (first list1)))) -;;; and where term_min(list) is the element of the list which is -;;; first in the term ordering. -(define (term_min list1) - (car (sort list1 term<))) -(define (term< sym1 sym2) - (string<? (symbol->string sym1) (symbol->string sym2))) -(define first car) -(define rest cdr) -(define (last1 list1) (car (last-pair list1))) -(define (neq? obj1 obj2) (not (eq? obj1 obj2))) -;;; where splice is the concatenation of list1 and list2 except that their -;;; common element is not repeated. -(define (splice list1 list2) - (cond ((eq? (last1 list1) (first list2)) - (append list1 (cdr list2))) - (else (slib:error 'splice list1 list2)))) -;;; where cyclicsplice is the result of leaving off the last element of -;;; splice(list1,list2). -(define (cyclicsplice list1 list2) - (cond ((and (eq? (last1 list1) (first list2)) - (eq? (first list1) (last1 list2))) - (butlast (splice list1 list2) 1)) - (else (slib:error 'cyclicsplice list1 list2)))) - -(N*N (S a b) (S a b)) => (m a b) -</pre></td></tr></table><P> - -Then register the rule for multiplying type N objects by type N objects. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(cring:define-rule '* 'N 'N N*N)) -</pre></td></tr></table><P> - -Now we are ready to compute! -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(define (t) - (define detM - (+ (* (S g b) - (+ (* (S f d) - (- (* (S a f) (S d g)) (* (S a g) (S d f)))) - (* (S f f) - (- (* (S a g) (S d d)) (* (S a d) (S d g)))) - (* (S f g) - (- (* (S a d) (S d f)) (* (S a f) (S d d)))))) - (* (S g d) - (+ (* (S f b) - (- (* (S a g) (S d f)) (* (S a f) (S d g)))) - (* (S f f) - (- (* (S a b) (S d g)) (* (S a g) (S d b)))) - (* (S f g) - (- (* (S a f) (S d b)) (* (S a b) (S d f)))))) - (* (S g f) - (+ (* (S f b) - (- (* (S a d) (S d g)) (* (S a g) (S d d)))) - (* (S f d) - (- (* (S a g) (S d b)) (* (S a b) (S d g)))) - (* (S f g) - (- (* (S a b) (S d d)) (* (S a d) (S d b)))))) - (* (S g g) - (+ (* (S f b) - (- (* (S a f) (S d d)) (* (S a d) (S d f)))) - (* (S f d) - (- (* (S a b) (S d f)) (* (S a f) (S d b)))) - (* (S f f) - (- (* (S a d) (S d b)) (* (S a b) (S d d)))))))) - (* (S b e) (S c a) (S e c) - detM - )) -(pretty-print (t)) --| -(- (+ (m a c e b d f g) - (m a c e b d g f) - (m a c e b f d g) - (m a c e b f g d) - (m a c e b g d f) - (m a c e b g f d)) - (* 2 (m a b e c) (m d f g)) - (* (m a c e b d) (m f g)) - (* (m a c e b f) (m d g)) - (* (m a c e b g) (m d f))) -</pre></td></tr></table><P> - -<A NAME="Matrix Algebra"></A> -<HR SIZE="6"> -<A NAME="SEC139"></A> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC138"> < </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> > </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> Up </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<H2> 5.15 Matrix Algebra </H2> -<!--docid::SEC139::--> -<P> - -<CODE>(require 'determinant)</CODE> -<A NAME="IDX910"></A> -</P> -<P> - -A Matrix can be either a list of lists (rows) or an array. -As with linear-algebra texts, this package uses 1-based coordinates. -</P> -<P> - -<A NAME="IDX911"></A> -</P> -<DL> -<DT><U>Function:</U> <B>matrix->lists</B> <I>matrix</I> -<DD><P> - -Returns the list-of-lists form of <VAR>matrix</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX912"></A> -</P> -<DL> -<DT><U>Function:</U> <B>matrix->array</B> <I>matrix</I> -<DD><P> - -Returns the (ones-based) array form of <VAR>matrix</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX913"></A> -</P> -<DL> -<DT><U>Function:</U> <B>determinant</B> <I>matrix</I> -<DD><P> - -<VAR>matrix</VAR> must be a square matrix. -<CODE>determinant</CODE> returns the determinant of <VAR>matrix</VAR>. -</P> -<P> - -<TABLE><tr><td> </td><td class=example><pre>(require 'determinant) -(determinant '((1 2) (3 4))) => -2 -(determinant '((1 2 3) (4 5 6) (7 8 9))) => 0 -</pre></td></tr></table></DL> -<P> - -<A NAME="IDX914"></A> -</P> -<DL> -<DT><U>Function:</U> <B>transpose</B> <I>matrix</I> -<DD><P> - -Returns a copy of <VAR>matrix</VAR> flipped over the diagonal containing the 1,1 -element. -</P> -</DL> -<P> - -<A NAME="IDX915"></A> -</P> -<DL> -<DT><U>Function:</U> <B>matrix:product</B> <I>m1 m2</I> -<DD><P> - -Returns the product of matrices <VAR>m1</VAR> and <VAR>m2</VAR>. -</P> -</DL> -<P> - -<A NAME="IDX916"></A> -</P> -<DL> -<DT><U>Function:</U> <B>matrix:inverse</B> <I>matrix</I> -<DD><P> - -<VAR>matrix</VAR> must be a square matrix. -If <VAR>matrix</VAR> is singlar, then <CODE>matrix:inverse</CODE> returns #f; otherwise <CODE>matrix:inverse</CODE> returns the -<CODE>matrix:product</CODE> inverse of <VAR>matrix</VAR>. -</P> -</DL> -<P> - -<A NAME="Database Packages"></A> -<HR SIZE="6"> -<TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0> -<TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_5.html#SEC88"> << </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_6.html#SEC140"> >> </A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib.html#SEC_Top">Top</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_toc.html#SEC_Contents">Contents</A>]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD> -<TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="slib_abt.html#SEC_About"> ? </A>]</TD> -</TR></TABLE> -<BR> -<FONT SIZE="-1"> -This document was generated -by <I>Steve Langasek</I> on <I>January, 10 2005</I> -using <A HREF="http://texi2html.cvshome.org"><I>texi2html</I></A> -</FONT> - -</BODY> -</HTML> |