;;; "colorspc.scm" color-space conversions
Copyright 2001 , 2002  
;
;Permission to copy this software, 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.
;
1 .   Any copy made of this software must include this copyright notice
;in full.
;
2 .   I have made no warranty or representation that the operation of
;this software will be error-free, and I am under no obligation to
;provide any services, by way of maintenance, update, or otherwise.
;
3 .   In conjunction with products arising from the use of this
;material, there shall be no use of my name in any advertising,
;promotional, or sales literature without prior written consent in
;each case.

(require 'logical)
(require 'multiarg/and-)
(require-if 'compiling 'sort)
(require-if 'compiling 'ciexyz)
;@
(define (color:linear-transform matrix row)
  (map (lambda (mrow) (apply + (map * mrow row)))
       matrix))

(define RGB709:into-matrix
  '((  3.240479 -1.537150 -0.498535 )
    ( -0.969256  1.875992  0.041556 )
    (  0.055648 -0.204043  1.057311 )))

;;; -2001.PDF gives
;;; matrix identical to sRGB:from-matrix, but colors drift under
  repeated conversions to and from CIEXYZ .   Instead use RGB709 .

(define RGB709:from-matrix
  '((  0.412453  0.357580  0.180423 )
    (  0.212671  0.715160  0.072169 )
    (  0.019334  0.119193  0.950227 )))

;; From /~ncs/color/t_convert.html
;@
(define (CIEXYZ->RGB709 XYZ)
  (color:linear-transform RGB709:into-matrix XYZ))
(define (RGB709->CIEXYZ rgb)
  (color:linear-transform RGB709:from-matrix rgb))

;;; From 

(define sRGB-log
  (lambda (sv)
    (if (<= sv 0.00304)
	(* 12.92 sv)
	(+ -0.055 (* 1.055 (expt sv 10/24))))))
(define sRGB-exp
  (lambda (x)
    (if (<= x 0.03928)
	(/ x 12.92)
	(expt (/ (+ 0.055 x) 1.055) 2.4))))

;; Clipping as recommended by sRGB spec.
;@
(define (CIEXYZ->sRGB XYZ)
  (map (lambda (sv)
	 (inexact->exact (round (* 255 (sRGB-log (max 0 (min 1 sv)))))))
       (color:linear-transform RGB709:into-matrix XYZ)))
(define (sRGB->CIEXYZ sRGB)
  (color:linear-transform
   RGB709:from-matrix
   (map sRGB-exp
	(map (lambda (b8v) (/ b8v 255.0)) sRGB))))

  sRGB values are sometimes written as 24 - bit integers 0xRRGGBB
;@
(define (xRGB->sRGB xRGB)
  (list (ash xRGB -16)
	(logand (ash xRGB -8) 255)
	(logand xRGB 255)))
(define (sRGB->xRGB sRGB)
  (apply + (map * sRGB '(#x10000 #x100 #x1))))
;@
(define (xRGB->CIEXYZ xRGB) (sRGB->CIEXYZ (xRGB->sRGB xRGB)))
(define (CIEXYZ->xRGB xyz)   (sRGB->xRGB (CIEXYZ->sRGB xyz)))

;;;  -2001.PDF
;;;	    Photography - Electronic still picture imaging -
;;;		 Extended sRGB color encoding - e-sRGB

(define e-sRGB-log
  (lambda (sv)
    (cond ((< sv -0.0031308)
	   (- 0.055 (* 1.055 (expt (- sv) 10/24))))
	  ((<= sv 0.0031308)
	   (* 12.92 sv))
	  (else (+ -0.055 (* 1.055 (expt sv 10/24)))))))
(define e-sRGB-exp
  (lambda (x)
    (cond ((< x -0.04045)
	   (- (expt (/ (- 0.055 x) 1.055) 2.4)))
	  ((<= x 0.04045)
	   (/ x 12.92))
	  (else (expt (/ (+ 0.055 x) 1.055) 2.4)))))
;@
(define (CIEXYZ->e-sRGB n XYZ)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x)
	 (+ (inexact->exact (round (* x 255 two^n-9))) offset))
       (map e-sRGB-log
	    (color:linear-transform
	     RGB709:into-matrix
	     XYZ))))
;@
(define (e-sRGB->CIEXYZ n rgb)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (color:linear-transform
   RGB709:from-matrix
   (map e-sRGB-exp
	(map (lambda (b8v) (/ (- b8v offset) 255.0 two^n-9))
	     rgb))))
;@
(define (sRGB->e-sRGB n sRGB)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x) (+ offset (* two^n-9 x))) sRGB))
;@
(define (e-sRGB->sRGB n rgb)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x) (/ (- x offset) two^n-9)) rgb))
;@
(define (e-sRGB->e-sRGB n rgb m)
  (define shft (- m n))
  (cond ((zero? shft) rgb)
	(else (map (lambda (x) (ash x shft)) rgb))))

;;; From /~ncs/color/t_convert.html

  CIE 1976 L*a*b * is based directly on CIE XYZ and is an attampt to
;;; linearize the perceptibility of color differences. The non-linear
;;; relations for L*, a*, and b* are intended to mimic the logarithmic
;;; response of the eye. Coloring information is referred to the color
;;; of the white point of the system, subscript n.

  L * is CIE lightness
      L * = 116 * ( Y / Yn)^1/3 - 16     for Y / Yn > 0.008856
      L * = 903.3 * Y / Yn              otherwise

(define (CIE:Y/Yn->L* Y/Yn)
  (if (> Y/Yn 0.008856)
      (+ -16 (* 116 (expt Y/Yn 1/3)))
      (* 903.3 Y/Yn)))
(define (CIE:L*->Y/Yn L*)
  (cond ((<= L* (* 903.3 0.008856))
	 (/ L* 903.3))
	((<= L* 100.)
	 (expt (/ (+ L* 16) 116) 3))
	(else 1)))

  a * = 500 * ( f(X / Xn ) - f(Y / Yn ) )
  b * = 200 * ( f(Y / Yn ) - f(Z / Zn ) )
      where f(t ) = t^1/3               for t > 0.008856
            f(t ) = 7.787 * t + 16/116 otherwise

(define (ab-log t)
  (if (> t 0.008856)
      (expt t 1/3)
      (+ 16/116 (* t 7.787))))
(define (ab-exp f)
  (define f3 (expt f 3))
  (if (> f3 0.008856)
      f3
      (/ (- f 16/116) 7.787)))
;@
(define (CIEXYZ->L*a*b* XYZ . white-point)
  (apply (lambda (X/Xn Y/Yn Z/Zn)
	   (list (CIE:Y/Yn->L* Y/Yn)
		 (* 500 (- (ab-log X/Xn) (ab-log Y/Yn)))
		 (* 200 (- (ab-log Y/Yn) (ab-log Z/Zn)))))
	 (map / XYZ (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))))

  Here Xn , Yn and  are the tristimulus values of the reference white .
;@
(define (L*a*b*->CIEXYZ L*a*b* . white-point)
  (apply (lambda (Xn Yn Zn)
	   (apply (lambda (L* a* b*)
		    (let* ((Y/Yn (CIE:L*->Y/Yn L*))
			   (fY/Yn (ab-log Y/Yn)))
		      (list (* Xn (ab-exp (+ fY/Yn (/ a* 500))))
			    (* Yn Y/Yn)
			    (* Zn (ab-exp (+ fY/Yn (/ b* -200)))))))
		  L*a*b*))
	 (if (null? white-point)
	     CIEXYZ:D65
	     (car white-point))))

  XYZ to CIELUV

  CIE 1976 L*u*u * ( CIELUV ) is based directly on CIE XYZ and is another
;;; attampt to linearize the perceptibility of color differences.  L* is
  CIE lightness as for L*a*b * above .   The non - linear relations for u *
;;; and v* are:

      u * =   13 L * ( u ' - un ' )
      v * =   13 L * ( v ' - vn ' )

  The quantities un ' and vn ' refer to the reference white or the light
  source ; for the 2.o observer and illuminant C , un ' = 0.2009 , vn ' =
  0.4610 . Equations for u ' and v ' are given below :

      u ' = 4 X / ( X + 15 Y + 3 Z )
      v ' = 9 Y / ( X + 15 Y + 3 Z )

(define (XYZ->uv XYZ)
  (apply (lambda (X Y Z)
	   (define denom (+ X (* 15 Y) (* 3 Z)))
	   (if (zero? denom)
	       '(4. 9.)
	       (list (/ (* 4 X) denom)
		     (/ (* 9 Y) denom))))
	 XYZ))
;@
(define (CIEXYZ->L*u*v* XYZ . white-point)
  (set! white-point (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))
  (let* ((Y/Yn (/ (cadr XYZ) (cadr white-point)))
	 (L* (CIE:Y/Yn->L* Y/Yn)))
    (cons L* (map (lambda (q) (* 13 L* q))
		  (map - (XYZ->uv XYZ) (XYZ->uv white-point))))))

  CIELUV to XYZ

  The transformation from CIELUV to XYZ is performed as following :

      u ' = u / ( 13 L * ) + un
      v ' = v / ( 13 L * ) + vn
      X = 9 Y u ' / 4 v '
      Z = ( 12 Y - 3 Y u ' - 20 Y v ' ) / 4 v '
;@
(define (L*u*v*->CIEXYZ L*u*v* . white-point)
  (set! white-point (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))
  (apply (lambda (un vn)
	   (apply (lambda (L* u* v*)
		    (if (not (positive? L*))
			'(0. 0. 0.)
			(let* ((up (+ (/ u* 13 L*) un))
			       (vp (+ (/ v* 13 L*) vn))
			       (Y (* (CIE:L*->Y/Yn L*) (cadr white-point))))
			  (list (/ (* 9 Y up) 4 vp)
				Y
				(/ (* Y (+ 12 (* -3 up) (* -20 vp))) 4 vp)))))
		  L*u*v*))
	 (XYZ->uv white-point)))

;;; /~poynton/PDFs/coloureq.pdf

(define pi (* 4 (atan 1)))
(define pi/180 (/ pi 180))
;@
(define (L*a*b*->L*C*h lab)
  (define h (/ (atan (caddr lab) (cadr lab)) pi/180))
  (list (car lab)
	(sqrt (apply + (map * (cdr lab) (cdr lab))))
	(if (negative? h) (+ 360 h) h)))
;@
(define (L*C*h->L*a*b* lch)
  (apply (lambda (L* C* h)
	   (set! h (* h pi/180))
	   (list L*
		 (* C* (cos h))
		 (* C* (sin h))))
	 lch))
;@
(define (L*a*b*:DE* lab1 lab2)
  (sqrt (apply + (map (lambda (x) (* x x)) (map - lab1 lab2)))))

;;; 

(define (color:process-params parametric-factors)
  (define ans
    (case (length parametric-factors)
      ((0) #f)
      ((1) (if (list? parametric-factors)
	       (apply color:process-params parametric-factors)
	       (append parametric-factors '(1 1))))
      ((2) (append parametric-factors '(1)))
      ((3) parametric-factors)
      (else (slib:error 'parametric-factors 'too-many parametric-factors))))
  (and ans
       (for-each (lambda (obj)
		   (if (not (number? obj))
		       (slib:error 'parametric-factors 'not 'number? obj)))
		 ans))
  ans)
;@
(define (L*C*h:DE*94 lch1 lch2 . parametric-factors)
  (define C* (sqrt (* (cadr lch1) (cadr lch2)))) ;Geometric mean
  (sqrt (apply + (map /
		      (map (lambda (x) (* x x)) (map - lch1 lch2))
		      (list 1		; S_l
  S_c
			    (+ 1 (* .015 C*))) ; S_h
		      (or (color:process-params parametric-factors)
			  '(1 1 1))))))

  CMC - DE is designed only for small color - differences .   But try to do
;;; something reasonable for large differences.  Use bisector (h*) of
  the hue angles if separated by less than 90.o ; otherwise , pick h of
;;; the color with larger C*.
;@
(define (CMC-DE lch1 lch2 . parametric-factors)
  (apply (lambda (L* C* h_)		;Geometric means
	   (let ((ang1 (* pi/180 (caddr lch1)))
		 (ang2 (* pi/180 (caddr lch2))))
	     (cond ((>= 90 (abs (/ (atan (sin (- ang1 ang2))
					 (cos (- ang1 ang2)))
				   pi/180)))
		    (set! h_ (/ (atan (+ (sin ang1) (sin ang2))
				      (+ (cos ang1) (cos ang2)))
				pi/180)))
		   ((>= (cadr lch1) (cadr lch2)) (caddr lch1))
		   (else (caddr lch2))))
	   (let* ((C*^4 (expt C* 4))
		  (f    (sqrt (/ C*^4 (+ C*^4 1900))))
		  (T    (if (and (> h_ 164) (< h_ 345))
			    (+ 0.56 (abs (* 0.2 (cos (* (+ h_ 168) pi/180)))))
			    (+ 0.36 (abs (* 0.4 (cos (* (+ h_ 35) pi/180)))))))
		  (S_l  (if (< L* 16)
			    0.511
			    (/ (* 0.040975 L*) (+ 1 (* 0.01765 L*)))))
		  (S_c  (+ (/ (* 0.0638 C*) (+ 1 (* 0.0131 C*))) 0.638))
		  (S_h  (* S_c (+ (* (+ -1 T) f) 1))))
	     (sqrt (apply
		    + (map /
			   (map (lambda (x) (* x x)) (map - lch1 lch2))
			   (list S_l S_c S_h)
			   (or (color:process-params parametric-factors)
			       '(2 1 1)))))))
	 (map sqrt (map * lch1 lch2))))

;;; Chromaticity
;@
(define (XYZ->chromaticity XYZ)
  (define sum (apply + XYZ))
  (list (/ (car XYZ) sum) (/ (cadr XYZ) sum)))
;@
(define (chromaticity->CIEXYZ x y)
  (list x y (- 1 x y)))
(define (chromaticity->whitepoint x y)
  (list (/ x y) 1 (/ (- 1 x y) y)))
;@
(define (XYZ->xyY XYZ)
  (define sum (apply + XYZ))
  (if (zero? sum)
      '(0 0 0)
      (list (/ (car XYZ) sum) (/ (cadr XYZ) sum) (cadr XYZ))))
;@
(define (xyY->XYZ xyY)
  (define x (car xyY))
  (define y (cadr xyY))
  (if (zero? y)
      '(0 0 0)
      (let ((Y/y (/ (caddr xyY) y)))
	(list (* Y/y x) (caddr xyY) (* Y/y (- 1 x y))))))
;@
(define (xyY:normalize-colors lst . n)
  (define (nthcdr n lst) (if (zero? n) lst (nthcdr (+ -1 n) (cdr lst))))
  (define Ys (map caddr lst))
  (set! n (if (null? n) 1 (car n)))
  (let ((max-Y (if (positive? n)
		   (* n (apply max Ys))
		   (let ()
		     (require 'sort)
		     (apply max (nthcdr (- n) (sort Ys >=)))))))
    (map (lambda (xyY)
	   (let ((x (max 0 (car xyY)))
		 (y (max 0 (cadr xyY))))
	     (define sum (max 1 (+ x y)))
	     (list (/ x sum)
		   (/ y sum)
		   (max 0 (min 1 (/ (caddr xyY) max-Y))))))
	 lst)))

;;;  -dtp.net/aim/technology/cie_xyz/cie_xyz.htm:
      0.312713 0.329016
  ( define CIEXYZ : D65 ( chromaticity->whitepoint 0.312713 0.329016 ) )
  ( define CIEXYZ : D65 ( chromaticity->whitepoint 0.3127 0.3290 ) )
;@
(define CIEXYZ:D50 (chromaticity->whitepoint 0.3457 0.3585))

  With its 16 - bit resolution , e - sRGB-16 is extremely sensitive to
  whitepoint .   Even the 6 digits of precision specified above is
  insufficient to make ( color->e - srgb 16 d65 ) = = > ( 57216 57216 57216 )
;@
(define CIEXYZ:D65 (e-sRGB->CIEXYZ 16 '(57216 57216 57216)))

   CIE 1931 :
;@
  2856.K
  4874.K
(define CIEXYZ:C (chromaticity->whitepoint 0.31006 0.31616)) ; 6774.K
(define CIEXYZ:E (chromaticity->whitepoint 1/3 1/3)) ; 5400.K

;;; Converting spectra
(define cie:x-bar #f)
(define cie:y-bar #f)
(define cie:z-bar #f)
;@
(define (load-ciexyz . path)
  (let ((path (if (null? path)
		  (in-vicinity (library-vicinity) "cie1931.xyz")
		  (car path))))
    (set! cie:x-bar (make-vector 80))
    (set! cie:y-bar (make-vector 80))
    (set! cie:z-bar (make-vector 80))
    (call-with-input-file path
      (lambda (iprt)
	(do ((wlen 380 (+ 5 wlen))
	     (idx 0 (+ 1 idx)))
	    ((>= wlen 780))
	  (let ((rlen (read iprt)))
	    (if (not (eqv? wlen rlen))
		(slib:error path 'expected wlen 'not rlen))
	    (vector-set! cie:x-bar idx (read iprt))
	    (vector-set! cie:y-bar idx (read iprt))
	    (vector-set! cie:z-bar idx (read iprt))))))))
;@
(define (read-cie-illuminant path)
  (define siv (make-vector 107))
  (call-with-input-file path
    (lambda (iprt)
      (do ((idx 0 (+ 1 idx)))
	  ((>= idx 107) siv)
	(vector-set! siv idx (read iprt))))))
;@
(define (read-normalized-illuminant path)
  (define siv (read-cie-illuminant path))
  (let ((yw (/ (cadr (spectrum->XYZ siv 300e-9 830e-9)))))
    (illuminant-map (lambda (w x) (* x yw)) siv)))
;@
(define (illuminant-map proc siv)
  (define prod (make-vector 107))
  (do ((idx 106 (+ -1 idx))
       (w 830e-9 (+ -5e-9 w)))
      ((negative? idx) prod)
    (vector-set! prod idx (proc w (vector-ref siv idx)))))
;@
(define (illuminant-map->XYZ proc siv)
  (spectrum->XYZ (illuminant-map proc siv) 300e-9 830e-9))
;@
(define (wavelength->XYZ wl)
  (if (not cie:y-bar) (require 'ciexyz))
  (set! wl (- (/ wl 5.e-9) 380/5))
  (if (<= 0 wl (+ -1 400/5))
      (let* ((wlf (inexact->exact (floor wl)))
	     (res (- wl wlf)))
	(define (interpolate vect idx res)
	  (+ (* res (vector-ref vect idx))
	     (* (- 1 res) (vector-ref vect (+ 1 idx)))))
	(list (interpolate cie:x-bar wlf res)
	      (interpolate cie:y-bar wlf res)
	      (interpolate cie:z-bar wlf res)))
      (slib:error 'wavelength->XYZ 'out-of-range wl)))
(define (wavelength->chromaticity wl)
  (XYZ->chromaticity (wavelength->XYZ wl)))
;@
(define (spectrum->XYZ . args)
  (define x 0)
  (define y 0)
  (define z 0)
  (if (not cie:y-bar) (require 'ciexyz))
  (case (length args)
    ((1)
     (set! args (car args))
     (do ((wvln 380.e-9 (+ 5.e-9 wvln))
	  (idx 0 (+ 1 idx)))
	 ((>= idx 80) (map (lambda (x) (/ x 80)) (list x y z)))
       (let ((inten (args wvln)))
	 (set! x (+ x (* (vector-ref cie:x-bar idx) inten)))
	 (set! y (+ y (* (vector-ref cie:y-bar idx) inten)))
	 (set! z (+ z (* (vector-ref cie:z-bar idx) inten))))))
    ((3)
     (let* ((vect (if (list? (car args)) (list->vector (car args)) (car args)))
	    (vlen (vector-length vect))
	    (x1 (cadr args))
	    (x2 (caddr args))
	    (xinc (/ (- x2 x1) (+ -1 vlen)))
	    (x->j (lambda (x) (inexact->exact (round (/ (- x x1) xinc)))))
	    (x->k (lambda (x) (inexact->exact (round (/ (- x 380.e-9) 5.e-9)))))
	    (j->x (lambda (j) (+ x1 (* j xinc))))
	    (k->x (lambda (k) (+ 380.e-9 (* k 5.e-9))))
	    (xlo (max (min x1 x2) 380.e-9))
	    (xhi (min (max x1 x2) 780.e-9))
	    (jhi (x->j xhi))
	    (khi (x->k xhi))
	    (jinc (if (negative? xinc) -1 1)))
       (if (<= (abs xinc) 5.e-9)
	   (do ((wvln (j->x (x->j xlo)) (+ wvln (abs xinc)))
		(jdx (x->j xlo) (+ jdx jinc)))
	       ((>= jdx jhi)
		(let ((nsmps (abs (- jhi (x->j xlo)))))
		  (map (lambda (x) (/ x nsmps)) (list x y z))))
	     (let ((ciedex (min 79 (x->k wvln)))
		   (inten (vector-ref vect jdx)))
	       (set! x (+ x (* (vector-ref cie:x-bar ciedex) inten)))
	       (set! y (+ y (* (vector-ref cie:y-bar ciedex) inten)))
	       (set! z (+ z (* (vector-ref cie:z-bar ciedex) inten)))))
	   (do ((wvln (k->x (x->k xlo)) (+ wvln 5.e-9))
		(kdx (x->k xlo) (+ kdx 1)))
	       ((>= kdx khi)
		(let ((nsmps (abs (- khi (x->k xlo)))))
		  (map (lambda (x) (/ x nsmps)) (list x y z))))
	     (let ((inten (vector-ref vect (x->j wvln))))
	       (set! x (+ x (* (vector-ref cie:x-bar kdx) inten)))
	       (set! y (+ y (* (vector-ref cie:y-bar kdx) inten)))
	       (set! z (+ z (* (vector-ref cie:z-bar kdx) inten))))))))
    (else (slib:error 'spectrum->XYZ 'wna args))))
(define (spectrum->chromaticity . args)
  (XYZ->chromaticity (apply spectrum->XYZ args)))
;@
(define blackbody-spectrum
  (let* ((c 2.998e8)
	 (h 6.626e-34)
	 (h*c (* h c))
	 (k 1.381e-23)
	 (pi*2*h*c*c (* 2 pi h*c c)))
    (lambda (temp . span)
      (define h*c/kT (/ h*c k temp))
      (define pi*2*h*c*c*span
	(* pi*2*h*c*c (if (null? span) 1.e-9 (car span))))
      (lambda (x)
	(/ pi*2*h*c*c*span
	   (expt x 5)
	   (- (exp (/ h*c/kT x)) 1))))))
;@
(define (temperature->XYZ temp . span)
was .5e-9
(define (temperature->chromaticity temp)
  (XYZ->chromaticity (temperature->XYZ temp)))

 "colorspc.scm" color-space conversions

Permission to copy this software, 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.

in full.

this software will be error-free, and I am under no obligation to
provide any services, by way of maintenance, update, or otherwise.

material, there shall be no use of my name in any advertising,
promotional, or sales literature without prior written consent in
each case.
@
 -2001.PDF gives
 matrix identical to sRGB:from-matrix, but colors drift under
 From /~ncs/color/t_convert.html
@
 From 
 Clipping as recommended by sRGB spec.
@
@
@
  -2001.PDF
	    Photography - Electronic still picture imaging -
		 Extended sRGB color encoding - e-sRGB
@
@
@
@
@
 From /~ncs/color/t_convert.html
 linearize the perceptibility of color differences. The non-linear
 relations for L*, a*, and b* are intended to mimic the logarithmic
 response of the eye. Coloring information is referred to the color
 of the white point of the system, subscript n.
@
@
 attampt to linearize the perceptibility of color differences.  L* is
 and v* are:
 for the 2.o observer and illuminant C , un ' = 0.2009 , vn ' =
@
@
 /~poynton/PDFs/coloureq.pdf
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Geometric mean
 S_l
 S_h
 something reasonable for large differences.  Use bisector (h*) of
 otherwise , pick h of
 the color with larger C*.
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Geometric means
 Chromaticity
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  -dtp.net/aim/technology/cie_xyz/cie_xyz.htm:
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 6774.K
 5400.K
 Converting spectra
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Copyright 2001 , 2002  
1 .   Any copy made of this software must include this copyright notice
2 .   I have made no warranty or representation that the operation of
3 .   In conjunction with products arising from the use of this

(require 'logical)
(require 'multiarg/and-)
(require-if 'compiling 'sort)
(require-if 'compiling 'ciexyz)
(define (color:linear-transform matrix row)
  (map (lambda (mrow) (apply + (map * mrow row)))
       matrix))

(define RGB709:into-matrix
  '((  3.240479 -1.537150 -0.498535 )
    ( -0.969256  1.875992  0.041556 )
    (  0.055648 -0.204043  1.057311 )))

  repeated conversions to and from CIEXYZ .   Instead use RGB709 .

(define RGB709:from-matrix
  '((  0.412453  0.357580  0.180423 )
    (  0.212671  0.715160  0.072169 )
    (  0.019334  0.119193  0.950227 )))

(define (CIEXYZ->RGB709 XYZ)
  (color:linear-transform RGB709:into-matrix XYZ))
(define (RGB709->CIEXYZ rgb)
  (color:linear-transform RGB709:from-matrix rgb))


(define sRGB-log
  (lambda (sv)
    (if (<= sv 0.00304)
	(* 12.92 sv)
	(+ -0.055 (* 1.055 (expt sv 10/24))))))
(define sRGB-exp
  (lambda (x)
    (if (<= x 0.03928)
	(/ x 12.92)
	(expt (/ (+ 0.055 x) 1.055) 2.4))))

(define (CIEXYZ->sRGB XYZ)
  (map (lambda (sv)
	 (inexact->exact (round (* 255 (sRGB-log (max 0 (min 1 sv)))))))
       (color:linear-transform RGB709:into-matrix XYZ)))
(define (sRGB->CIEXYZ sRGB)
  (color:linear-transform
   RGB709:from-matrix
   (map sRGB-exp
	(map (lambda (b8v) (/ b8v 255.0)) sRGB))))

  sRGB values are sometimes written as 24 - bit integers 0xRRGGBB
(define (xRGB->sRGB xRGB)
  (list (ash xRGB -16)
	(logand (ash xRGB -8) 255)
	(logand xRGB 255)))
(define (sRGB->xRGB sRGB)
  (apply + (map * sRGB '(#x10000 #x100 #x1))))
(define (xRGB->CIEXYZ xRGB) (sRGB->CIEXYZ (xRGB->sRGB xRGB)))
(define (CIEXYZ->xRGB xyz)   (sRGB->xRGB (CIEXYZ->sRGB xyz)))


(define e-sRGB-log
  (lambda (sv)
    (cond ((< sv -0.0031308)
	   (- 0.055 (* 1.055 (expt (- sv) 10/24))))
	  ((<= sv 0.0031308)
	   (* 12.92 sv))
	  (else (+ -0.055 (* 1.055 (expt sv 10/24)))))))
(define e-sRGB-exp
  (lambda (x)
    (cond ((< x -0.04045)
	   (- (expt (/ (- 0.055 x) 1.055) 2.4)))
	  ((<= x 0.04045)
	   (/ x 12.92))
	  (else (expt (/ (+ 0.055 x) 1.055) 2.4)))))
(define (CIEXYZ->e-sRGB n XYZ)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x)
	 (+ (inexact->exact (round (* x 255 two^n-9))) offset))
       (map e-sRGB-log
	    (color:linear-transform
	     RGB709:into-matrix
	     XYZ))))
(define (e-sRGB->CIEXYZ n rgb)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (color:linear-transform
   RGB709:from-matrix
   (map e-sRGB-exp
	(map (lambda (b8v) (/ (- b8v offset) 255.0 two^n-9))
	     rgb))))
(define (sRGB->e-sRGB n sRGB)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x) (+ offset (* two^n-9 x))) sRGB))
(define (e-sRGB->sRGB n rgb)
  (define two^n-9 (ash 1 (- n 9)))
  (define offset (* 3 (ash 1 (- n 3))))
  (map (lambda (x) (/ (- x offset) two^n-9)) rgb))
(define (e-sRGB->e-sRGB n rgb m)
  (define shft (- m n))
  (cond ((zero? shft) rgb)
	(else (map (lambda (x) (ash x shft)) rgb))))


  CIE 1976 L*a*b * is based directly on CIE XYZ and is an attampt to

  L * is CIE lightness
      L * = 116 * ( Y / Yn)^1/3 - 16     for Y / Yn > 0.008856
      L * = 903.3 * Y / Yn              otherwise

(define (CIE:Y/Yn->L* Y/Yn)
  (if (> Y/Yn 0.008856)
      (+ -16 (* 116 (expt Y/Yn 1/3)))
      (* 903.3 Y/Yn)))
(define (CIE:L*->Y/Yn L*)
  (cond ((<= L* (* 903.3 0.008856))
	 (/ L* 903.3))
	((<= L* 100.)
	 (expt (/ (+ L* 16) 116) 3))
	(else 1)))

  a * = 500 * ( f(X / Xn ) - f(Y / Yn ) )
  b * = 200 * ( f(Y / Yn ) - f(Z / Zn ) )
      where f(t ) = t^1/3               for t > 0.008856
            f(t ) = 7.787 * t + 16/116 otherwise

(define (ab-log t)
  (if (> t 0.008856)
      (expt t 1/3)
      (+ 16/116 (* t 7.787))))
(define (ab-exp f)
  (define f3 (expt f 3))
  (if (> f3 0.008856)
      f3
      (/ (- f 16/116) 7.787)))
(define (CIEXYZ->L*a*b* XYZ . white-point)
  (apply (lambda (X/Xn Y/Yn Z/Zn)
	   (list (CIE:Y/Yn->L* Y/Yn)
		 (* 500 (- (ab-log X/Xn) (ab-log Y/Yn)))
		 (* 200 (- (ab-log Y/Yn) (ab-log Z/Zn)))))
	 (map / XYZ (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))))

  Here Xn , Yn and  are the tristimulus values of the reference white .
(define (L*a*b*->CIEXYZ L*a*b* . white-point)
  (apply (lambda (Xn Yn Zn)
	   (apply (lambda (L* a* b*)
		    (let* ((Y/Yn (CIE:L*->Y/Yn L*))
			   (fY/Yn (ab-log Y/Yn)))
		      (list (* Xn (ab-exp (+ fY/Yn (/ a* 500))))
			    (* Yn Y/Yn)
			    (* Zn (ab-exp (+ fY/Yn (/ b* -200)))))))
		  L*a*b*))
	 (if (null? white-point)
	     CIEXYZ:D65
	     (car white-point))))

  XYZ to CIELUV

  CIE 1976 L*u*u * ( CIELUV ) is based directly on CIE XYZ and is another
  CIE lightness as for L*a*b * above .   The non - linear relations for u *

      u * =   13 L * ( u ' - un ' )
      v * =   13 L * ( v ' - vn ' )

  The quantities un ' and vn ' refer to the reference white or the light
  0.4610 . Equations for u ' and v ' are given below :

      u ' = 4 X / ( X + 15 Y + 3 Z )
      v ' = 9 Y / ( X + 15 Y + 3 Z )

(define (XYZ->uv XYZ)
  (apply (lambda (X Y Z)
	   (define denom (+ X (* 15 Y) (* 3 Z)))
	   (if (zero? denom)
	       '(4. 9.)
	       (list (/ (* 4 X) denom)
		     (/ (* 9 Y) denom))))
	 XYZ))
(define (CIEXYZ->L*u*v* XYZ . white-point)
  (set! white-point (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))
  (let* ((Y/Yn (/ (cadr XYZ) (cadr white-point)))
	 (L* (CIE:Y/Yn->L* Y/Yn)))
    (cons L* (map (lambda (q) (* 13 L* q))
		  (map - (XYZ->uv XYZ) (XYZ->uv white-point))))))

  CIELUV to XYZ

  The transformation from CIELUV to XYZ is performed as following :

      u ' = u / ( 13 L * ) + un
      v ' = v / ( 13 L * ) + vn
      X = 9 Y u ' / 4 v '
      Z = ( 12 Y - 3 Y u ' - 20 Y v ' ) / 4 v '
(define (L*u*v*->CIEXYZ L*u*v* . white-point)
  (set! white-point (if (null? white-point)
			CIEXYZ:D65
			(car white-point)))
  (apply (lambda (un vn)
	   (apply (lambda (L* u* v*)
		    (if (not (positive? L*))
			'(0. 0. 0.)
			(let* ((up (+ (/ u* 13 L*) un))
			       (vp (+ (/ v* 13 L*) vn))
			       (Y (* (CIE:L*->Y/Yn L*) (cadr white-point))))
			  (list (/ (* 9 Y up) 4 vp)
				Y
				(/ (* Y (+ 12 (* -3 up) (* -20 vp))) 4 vp)))))
		  L*u*v*))
	 (XYZ->uv white-point)))


(define pi (* 4 (atan 1)))
(define pi/180 (/ pi 180))
(define (L*a*b*->L*C*h lab)
  (define h (/ (atan (caddr lab) (cadr lab)) pi/180))
  (list (car lab)
	(sqrt (apply + (map * (cdr lab) (cdr lab))))
	(if (negative? h) (+ 360 h) h)))
(define (L*C*h->L*a*b* lch)
  (apply (lambda (L* C* h)
	   (set! h (* h pi/180))
	   (list L*
		 (* C* (cos h))
		 (* C* (sin h))))
	 lch))
(define (L*a*b*:DE* lab1 lab2)
  (sqrt (apply + (map (lambda (x) (* x x)) (map - lab1 lab2)))))


(define (color:process-params parametric-factors)
  (define ans
    (case (length parametric-factors)
      ((0) #f)
      ((1) (if (list? parametric-factors)
	       (apply color:process-params parametric-factors)
	       (append parametric-factors '(1 1))))
      ((2) (append parametric-factors '(1)))
      ((3) parametric-factors)
      (else (slib:error 'parametric-factors 'too-many parametric-factors))))
  (and ans
       (for-each (lambda (obj)
		   (if (not (number? obj))
		       (slib:error 'parametric-factors 'not 'number? obj)))
		 ans))
  ans)
(define (L*C*h:DE*94 lch1 lch2 . parametric-factors)
  (sqrt (apply + (map /
		      (map (lambda (x) (* x x)) (map - lch1 lch2))
  S_c
		      (or (color:process-params parametric-factors)
			  '(1 1 1))))))

  CMC - DE is designed only for small color - differences .   But try to do
(define (CMC-DE lch1 lch2 . parametric-factors)
	   (let ((ang1 (* pi/180 (caddr lch1)))
		 (ang2 (* pi/180 (caddr lch2))))
	     (cond ((>= 90 (abs (/ (atan (sin (- ang1 ang2))
					 (cos (- ang1 ang2)))
				   pi/180)))
		    (set! h_ (/ (atan (+ (sin ang1) (sin ang2))
				      (+ (cos ang1) (cos ang2)))
				pi/180)))
		   ((>= (cadr lch1) (cadr lch2)) (caddr lch1))
		   (else (caddr lch2))))
	   (let* ((C*^4 (expt C* 4))
		  (f    (sqrt (/ C*^4 (+ C*^4 1900))))
		  (T    (if (and (> h_ 164) (< h_ 345))
			    (+ 0.56 (abs (* 0.2 (cos (* (+ h_ 168) pi/180)))))
			    (+ 0.36 (abs (* 0.4 (cos (* (+ h_ 35) pi/180)))))))
		  (S_l  (if (< L* 16)
			    0.511
			    (/ (* 0.040975 L*) (+ 1 (* 0.01765 L*)))))
		  (S_c  (+ (/ (* 0.0638 C*) (+ 1 (* 0.0131 C*))) 0.638))
		  (S_h  (* S_c (+ (* (+ -1 T) f) 1))))
	     (sqrt (apply
		    + (map /
			   (map (lambda (x) (* x x)) (map - lch1 lch2))
			   (list S_l S_c S_h)
			   (or (color:process-params parametric-factors)
			       '(2 1 1)))))))
	 (map sqrt (map * lch1 lch2))))

(define (XYZ->chromaticity XYZ)
  (define sum (apply + XYZ))
  (list (/ (car XYZ) sum) (/ (cadr XYZ) sum)))
(define (chromaticity->CIEXYZ x y)
  (list x y (- 1 x y)))
(define (chromaticity->whitepoint x y)
  (list (/ x y) 1 (/ (- 1 x y) y)))
(define (XYZ->xyY XYZ)
  (define sum (apply + XYZ))
  (if (zero? sum)
      '(0 0 0)
      (list (/ (car XYZ) sum) (/ (cadr XYZ) sum) (cadr XYZ))))
(define (xyY->XYZ xyY)
  (define x (car xyY))
  (define y (cadr xyY))
  (if (zero? y)
      '(0 0 0)
      (let ((Y/y (/ (caddr xyY) y)))
	(list (* Y/y x) (caddr xyY) (* Y/y (- 1 x y))))))
(define (xyY:normalize-colors lst . n)
  (define (nthcdr n lst) (if (zero? n) lst (nthcdr (+ -1 n) (cdr lst))))
  (define Ys (map caddr lst))
  (set! n (if (null? n) 1 (car n)))
  (let ((max-Y (if (positive? n)
		   (* n (apply max Ys))
		   (let ()
		     (require 'sort)
		     (apply max (nthcdr (- n) (sort Ys >=)))))))
    (map (lambda (xyY)
	   (let ((x (max 0 (car xyY)))
		 (y (max 0 (cadr xyY))))
	     (define sum (max 1 (+ x y)))
	     (list (/ x sum)
		   (/ y sum)
		   (max 0 (min 1 (/ (caddr xyY) max-Y))))))
	 lst)))

      0.312713 0.329016
  ( define CIEXYZ : D65 ( chromaticity->whitepoint 0.312713 0.329016 ) )
  ( define CIEXYZ : D65 ( chromaticity->whitepoint 0.3127 0.3290 ) )
(define CIEXYZ:D50 (chromaticity->whitepoint 0.3457 0.3585))

  With its 16 - bit resolution , e - sRGB-16 is extremely sensitive to
  whitepoint .   Even the 6 digits of precision specified above is
  insufficient to make ( color->e - srgb 16 d65 ) = = > ( 57216 57216 57216 )
(define CIEXYZ:D65 (e-sRGB->CIEXYZ 16 '(57216 57216 57216)))

   CIE 1931 :
  2856.K
  4874.K

(define cie:x-bar #f)
(define cie:y-bar #f)
(define cie:z-bar #f)
(define (load-ciexyz . path)
  (let ((path (if (null? path)
		  (in-vicinity (library-vicinity) "cie1931.xyz")
		  (car path))))
    (set! cie:x-bar (make-vector 80))
    (set! cie:y-bar (make-vector 80))
    (set! cie:z-bar (make-vector 80))
    (call-with-input-file path
      (lambda (iprt)
	(do ((wlen 380 (+ 5 wlen))
	     (idx 0 (+ 1 idx)))
	    ((>= wlen 780))
	  (let ((rlen (read iprt)))
	    (if (not (eqv? wlen rlen))
		(slib:error path 'expected wlen 'not rlen))
	    (vector-set! cie:x-bar idx (read iprt))
	    (vector-set! cie:y-bar idx (read iprt))
	    (vector-set! cie:z-bar idx (read iprt))))))))
(define (read-cie-illuminant path)
  (define siv (make-vector 107))
  (call-with-input-file path
    (lambda (iprt)
      (do ((idx 0 (+ 1 idx)))
	  ((>= idx 107) siv)
	(vector-set! siv idx (read iprt))))))
(define (read-normalized-illuminant path)
  (define siv (read-cie-illuminant path))
  (let ((yw (/ (cadr (spectrum->XYZ siv 300e-9 830e-9)))))
    (illuminant-map (lambda (w x) (* x yw)) siv)))
(define (illuminant-map proc siv)
  (define prod (make-vector 107))
  (do ((idx 106 (+ -1 idx))
       (w 830e-9 (+ -5e-9 w)))
      ((negative? idx) prod)
    (vector-set! prod idx (proc w (vector-ref siv idx)))))
(define (illuminant-map->XYZ proc siv)
  (spectrum->XYZ (illuminant-map proc siv) 300e-9 830e-9))
(define (wavelength->XYZ wl)
  (if (not cie:y-bar) (require 'ciexyz))
  (set! wl (- (/ wl 5.e-9) 380/5))
  (if (<= 0 wl (+ -1 400/5))
      (let* ((wlf (inexact->exact (floor wl)))
	     (res (- wl wlf)))
	(define (interpolate vect idx res)
	  (+ (* res (vector-ref vect idx))
	     (* (- 1 res) (vector-ref vect (+ 1 idx)))))
	(list (interpolate cie:x-bar wlf res)
	      (interpolate cie:y-bar wlf res)
	      (interpolate cie:z-bar wlf res)))
      (slib:error 'wavelength->XYZ 'out-of-range wl)))
(define (wavelength->chromaticity wl)
  (XYZ->chromaticity (wavelength->XYZ wl)))
(define (spectrum->XYZ . args)
  (define x 0)
  (define y 0)
  (define z 0)
  (if (not cie:y-bar) (require 'ciexyz))
  (case (length args)
    ((1)
     (set! args (car args))
     (do ((wvln 380.e-9 (+ 5.e-9 wvln))
	  (idx 0 (+ 1 idx)))
	 ((>= idx 80) (map (lambda (x) (/ x 80)) (list x y z)))
       (let ((inten (args wvln)))
	 (set! x (+ x (* (vector-ref cie:x-bar idx) inten)))
	 (set! y (+ y (* (vector-ref cie:y-bar idx) inten)))
	 (set! z (+ z (* (vector-ref cie:z-bar idx) inten))))))
    ((3)
     (let* ((vect (if (list? (car args)) (list->vector (car args)) (car args)))
	    (vlen (vector-length vect))
	    (x1 (cadr args))
	    (x2 (caddr args))
	    (xinc (/ (- x2 x1) (+ -1 vlen)))
	    (x->j (lambda (x) (inexact->exact (round (/ (- x x1) xinc)))))
	    (x->k (lambda (x) (inexact->exact (round (/ (- x 380.e-9) 5.e-9)))))
	    (j->x (lambda (j) (+ x1 (* j xinc))))
	    (k->x (lambda (k) (+ 380.e-9 (* k 5.e-9))))
	    (xlo (max (min x1 x2) 380.e-9))
	    (xhi (min (max x1 x2) 780.e-9))
	    (jhi (x->j xhi))
	    (khi (x->k xhi))
	    (jinc (if (negative? xinc) -1 1)))
       (if (<= (abs xinc) 5.e-9)
	   (do ((wvln (j->x (x->j xlo)) (+ wvln (abs xinc)))
		(jdx (x->j xlo) (+ jdx jinc)))
	       ((>= jdx jhi)
		(let ((nsmps (abs (- jhi (x->j xlo)))))
		  (map (lambda (x) (/ x nsmps)) (list x y z))))
	     (let ((ciedex (min 79 (x->k wvln)))
		   (inten (vector-ref vect jdx)))
	       (set! x (+ x (* (vector-ref cie:x-bar ciedex) inten)))
	       (set! y (+ y (* (vector-ref cie:y-bar ciedex) inten)))
	       (set! z (+ z (* (vector-ref cie:z-bar ciedex) inten)))))
	   (do ((wvln (k->x (x->k xlo)) (+ wvln 5.e-9))
		(kdx (x->k xlo) (+ kdx 1)))
	       ((>= kdx khi)
		(let ((nsmps (abs (- khi (x->k xlo)))))
		  (map (lambda (x) (/ x nsmps)) (list x y z))))
	     (let ((inten (vector-ref vect (x->j wvln))))
	       (set! x (+ x (* (vector-ref cie:x-bar kdx) inten)))
	       (set! y (+ y (* (vector-ref cie:y-bar kdx) inten)))
	       (set! z (+ z (* (vector-ref cie:z-bar kdx) inten))))))))
    (else (slib:error 'spectrum->XYZ 'wna args))))
(define (spectrum->chromaticity . args)
  (XYZ->chromaticity (apply spectrum->XYZ args)))
(define blackbody-spectrum
  (let* ((c 2.998e8)
	 (h 6.626e-34)
	 (h*c (* h c))
	 (k 1.381e-23)
	 (pi*2*h*c*c (* 2 pi h*c c)))
    (lambda (temp . span)
      (define h*c/kT (/ h*c k temp))
      (define pi*2*h*c*c*span
	(* pi*2*h*c*c (if (null? span) 1.e-9 (car span))))
      (lambda (x)
	(/ pi*2*h*c*c*span
	   (expt x 5)
	   (- (exp (/ h*c/kT x)) 1))))))
(define (temperature->XYZ temp . span)
was .5e-9
(define (temperature->chromaticity temp)
  (XYZ->chromaticity (temperature->XYZ temp)))
