@code{(require 'space-filling)}
@ftindex space-filling

The algorithms and cell properties are described in
@url{http://people.csail.mit.edu/jaffer/Geometry/RMDSFF.pdf}


@defun make-cell type rank side precession


@defunx make-cell type rank side

@defunx make-cell type rank

@var{type} must be the symbol @code{diagonal}, @code{adjacent}, or
@code{centered}.  @var{rank} must be an integer larger than 1.  @var{side}, if
present, must be an even integer larger than 1 if @var{type} is
@code{adjacent} or an odd integer larger than 2 otherwise; @var{side}
defaults to the smallest value.  @var{precession}, if present, must be an integer
between 0 and @var{side}^@var{rank}-1; it is relevant only when @var{type} is
@code{diagonal} or @code{centered}.


@end defun
@defun make-cell Hamiltonian-path-vector precession

@defunx make-cell Hamiltonian-path-vector

@var{type} must be a vector of @var{side}^@var{rank} lists of @var{rank} of
integers encoding the coordinate positions of a Hamiltonian path on
the @var{rank}-dimensional grid of points starting and ending on
corners of the grid.  The starting corner must be the origin
(all-zero coordinates). If the side-length is even, then the ending
corner must be non-zero in only one coordinate; otherwise, the
ending corner must be the furthest diagonally opposite corner from
the origin.

@code{make-cell} returns a data object suitable for passing as the
first argument to @code{integer->coordinates} or
@code{coordinates->integer}.
@end defun

Hilbert, Peano, and centered Peano cells are generated
respectively by:
@example
(make-cell 'adjacent @var{rank} 2)   ; Hilbert
(make-cell 'diagonal @var{rank} 3)   ; Peano
(make-cell 'centered @var{rank} 3)   ; centered Peano
@end example

In the conversion procedures, if the cell is @code{diagonal} or
@code{adjacent}, then the coordinates and scalar must be nonnegative
integers.  If @code{centered}, then the integers can be negative.


@defun integer->coordinates cell u

@code{integer->coordinates} converts the integer @var{u} to a list of coordinates according to @var{cell}.
@end defun


@defun coordinates->integer cell v

@code{coordinates->integer} converts the list of coordinates @var{v} to an integer according to @var{cell}.
@end defun

@var{coordinates->integer} and @var{integer->coordinates} are
inverse functions when passed the same @var{cell} argument.