aboutsummaryrefslogtreecommitdiffstats
path: root/colorspc.scm
blob: 3a887672d40671947916c33af84891eefff131ba (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
;;; "colorspc.scm" color-space conversions
;Copyright 2001, 2002 Aubrey Jaffer
;
;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 )))

;;; http://www.pima.net/standards/it10/PIMA7667/PIMA7667-2001.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 http://www.cs.rit.edu/~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 http://www.w3.org/Graphics/Color/sRGB.html

(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)))

;;;  http://www.pima.net/standards/it10/PIMA7667/PIMA7667-2001.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 http://www.cs.rit.edu/~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 Zn 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° 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)))

;;; http://www.inforamp.net/~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)))))

;;; http://www.colorpro.com/info/data/cie94.html

(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
			    (+ 1 (* .045 C*)) ; 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))))
;@
(define (XYZ:normalize-colors lst)
  (define sum (apply max (map (lambda (XYZ) (apply + XYZ)) lst)))
  (map (lambda (XYZ) (map (lambda (x) (/ x sum)) XYZ)) lst))
;@
(define (XYZ:normalize XYZ)
  (car (XYZ:normalize-colors (list XYZ))))

;;; 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)))

;;;  http://www.aim-dtp.net/aim/technology/cie_xyz/cie_xyz.htm:
;;;  Illuminant D65                           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)))

;;; http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.htm CIE 1931:
;@
(define CIEXYZ:A (chromaticity->whitepoint 0.44757 0.40745)) ; 2856.K
(define CIEXYZ:B (chromaticity->whitepoint 0.34842 0.35161)) ; 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 (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->CIEXYZ wl)
  (XYZ:normalize (wavelength->XYZ 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->CIEXYZ . args)
  (XYZ:normalize (apply spectrum->XYZ 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)
  (spectrum->XYZ (blackbody-spectrum temp 5.e-9)))
(define (temperature->CIEXYZ temp)
  (XYZ:normalize (temperature->XYZ temp)))
(define (temperature->chromaticity temp)
  (XYZ->chromaticity (temperature->XYZ temp)))