diff options
Diffstat (limited to 'peanosfc.scm')
| -rw-r--r-- | peanosfc.scm | 49 |
1 files changed, 42 insertions, 7 deletions
diff --git a/peanosfc.scm b/peanosfc.scm index 4a4039a..8c1e1a9 100644 --- a/peanosfc.scm +++ b/peanosfc.scm @@ -19,17 +19,20 @@ (require 'array) +;;@code{(require 'peano-fill)} +;;@ftindex peano-fill + ;;; A. R. Butz. ;;; Space filling curves and mathematical programming. ;;; Information and Control, 12:314-330, 1968. -(define (integer->tet-array scalar rank) +(define (natural->tet-array scalar rank) (do ((tets '() (cons (modulo scl 3) tets)) (scl scalar (quotient scl 3))) ((zero? scl) (let* ((len (length tets)) (depth (quotient (+ len rank -1) rank))) - (define tra (make-array (A:fixN8b 0) rank depth)) + (define tra (make-array (A:fixZ8b 0) rank depth)) (set! tets (reverse tets)) (do ((idx (+ -1 depth) (+ -1 idx))) ((negative? idx)) @@ -40,7 +43,7 @@ (set! tets (cdr tets)))))) tra)))) -(define (tet-array->integer tra) +(define (tet-array->natural tra) (define rank (car (array-dimensions tra))) (define depth (cadr (array-dimensions tra))) (define val 0) @@ -95,15 +98,47 @@ ;;Returns a list of @2 nonnegative integer coordinates corresponding ;;to exact nonnegative integer @1. The lists returned by @0 for @1 ;;arguments 0 and 1 will differ in the first element. -(define (integer->peano-coordinates scalar rank) - (define tra (integer->tet-array scalar rank)) +(define (natural->peano-coordinates scalar rank) + (define tra (natural->tet-array scalar rank)) (peano-flip! tra) (tet-array->coordinates tra)) ;;@body ;;Returns an exact nonnegative integer corresponding to @1, a list of ;;nonnegative integer coordinates. -(define (peano-coordinates->integer coords) +(define (peano-coordinates->natural coords) (define tra (coordinates->tet-array coords)) (peano-flip! tra) - (tet-array->integer tra)) + (tet-array->natural tra)) + +;;@body +;;Returns a list of @2 integer coordinates corresponding to exact +;;integer @1. The lists returned by @0 for @1 arguments 0 and 1 will +;;differ in the first element. +(define (integer->peano-coordinates scalar rank) + (define three^rank (expt 3 rank)) + (do ((edx 1 (* edx three^rank)) + (m 0 (+ 1 m))) + ((>= (quotient edx 2) (abs scalar)) + (let ((tra (natural->tet-array (+ scalar (quotient edx 2)) rank)) + (offset (quotient (expt 3 m) 2))) + (peano-flip! tra) + (map (lambda (k) (* (if (odd? m) -1 1) (- k offset))) + (tet-array->coordinates tra)))))) + +;;@body +;;Returns an exact integer corresponding to @1, a list of integer +;;coordinates. +(define (peano-coordinates->integer coords) + (define cobs (apply max (map abs coords))) + (let loop ((xpo 1)) + (define offset (quotient (expt 3 xpo) 2)) + (if (>= offset cobs) + (let ((tra (coordinates->tet-array + (map (lambda (elt) (+ elt offset)) + coords)))) + (peano-flip! tra) + ((if (odd? xpo) - +) + (- (tet-array->natural tra) + (quotient (expt 3 (* (length coords) xpo)) 2)))) + (loop (+ 1 xpo))))) |