1 ;;; color-lab.el --- Color manipulation laboratory routines
3 ;; Copyright (C) 2010 Free Software Foundation, Inc.
5 ;; Author: Julien Danjou <julien@danjou.info>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is free software: you can redistribute it and/or modify
11 ;; it under the terms of the GNU General Public License as published by
12 ;; the Free Software Foundation, either version 3 of the License, or
13 ;; (at your option) any later version.
15 ;; GNU Emacs is distributed in the hope that it will be useful,
16 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
17 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 ;; GNU General Public License for more details.
20 ;; You should have received a copy of the GNU General Public License
21 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
25 ;; This package provides color manipulation functions.
30 (unless (boundp 'float-pi)
31 (defconst float-pi (* 4 (atan 1)) "The value of Pi (3.1415926...)."))
33 (defun rgb->hsv (red green blue)
34 "Convert RED GREEN BLUE values to HSV representation.
35 Hue is in radian. Saturation and values are between 0 and 1."
36 (let* ((r (float red))
43 (cond ((and (= r g) (= g b)) 0)
46 (* 60 (/ (- g b) (- max min))))
49 (+ 360 (* 60 (/ (- g b) (- max min)))))
51 (+ 120 (* 60 (/ (- b r) (- max min)))))
53 (+ 240 (* 60 (/ (- r g) (- max min)))))))
60 (defun rgb->hsl (red green blue)
61 "Convert RED GREEN BLUE colors to their HSL representation.
62 RED, GREEN and BLUE must be between 0 and 255."
63 (let* ((r (/ red 255.0))
69 (l (/ (+ max min) 2.0)))
75 (+ (/ (- g b) delta) (if (< g b) 6 0)))
77 (+ (/ (- b r) delta) 2))
79 (+ (/ (- r g) delta) 4)))
84 (/ delta (- 2 (+ max min)))
85 (/ delta (+ max min))))
88 (defun rgb->xyz (red green blue)
89 "Converts RED GREEN BLUE colors to CIE XYZ representation.
90 RED, BLUE and GREEN must be between 0 and 1."
91 (let ((r (if (<= red 0.04045)
93 (expt (/ (+ red 0.055) 1.055) 2.4)))
94 (g (if (<= green 0.04045)
96 (expt (/ (+ green 0.055) 1.055) 2.4)))
97 (b (if (<= blue 0.04045)
99 (expt (/ (+ blue 0.055) 1.055) 2.4))))
100 (list (+ (* 0.4124564 r) (* 0.3575761 g) (* 0.1804375 b))
101 (+ (* 0.21266729 r) (* 0.7151522 g) (* 0.0721750 b))
102 (+ (* 0.0193339 r) (* 0.1191920 g) (* 0.9503041 b)))))
104 (defun xyz->rgb (X Y Z)
105 "Converts CIE XYZ colors to RGB."
106 (let ((r (+ (* 3.2404542 X) (* -1.5371385 Y) (* -0.4985314 Z)))
107 (g (+ (* -0.9692660 X) (* 1.8760108 Y) (* 0.0415560 Z)))
108 (b (+ (* 0.0556434 X) (* -0.2040259 Y) (* 1.0572252 Z))))
109 (list (if (<= r 0.0031308)
111 (- (* 1.055 (expt r (/ 1 2.4))) 0.055))
114 (- (* 1.055 (expt g (/ 1 2.4))) 0.055))
117 (- (* 1.055 (expt b (/ 1 2.4))) 0.055)))))
119 (defconst color-lab-d65-xyz '(0.950455 1.0 1.088753)
120 "D65 white point in CIE XYZ.")
122 (defconst color-lab-ε (/ 216 24389.0))
123 (defconst color-lab-κ (/ 24389 27.0))
125 (defun xyz->lab (X Y Z &optional white-point)
126 "Converts CIE XYZ to CIE L*a*b*.
127 WHITE-POINT can be specified as (X Y Z) white point to use. If
128 none is set, `color-lab-d65-xyz' is used."
129 (destructuring-bind (Xr Yr Zr) (or white-point color-lab-d65-xyz)
133 (fx (if (> xr color-lab-ε)
135 (/ (+ (* color-lab-κ xr) 16) 116.0)))
136 (fy (if (> yr color-lab-ε)
138 (/ (+ (* color-lab-κ yr) 16) 116.0)))
139 (fz (if (> zr color-lab-ε)
141 (/ (+ (* color-lab-κ zr) 16) 116.0))))
143 (- (* 116 fy) 16) ; L
144 (* 500 (- fx fy)) ; a
145 (* 200 (- fy fz)))))) ; b
147 (defun lab->xyz (L a b &optional white-point)
148 "Converts CIE L*a*b* to CIE XYZ.
149 WHITE-POINT can be specified as (X Y Z) white point to use. If
150 none is set, `color-lab-d65-xyz' is used."
151 (destructuring-bind (Xr Yr Zr) (or white-point color-lab-d65-xyz)
152 (let* ((fy (/ (+ L 16) 116.0))
153 (fz (- fy (/ b 200.0)))
154 (fx (+ (/ a 500.0) fy))
155 (xr (if (> (expt fx 3) color-lab-ε)
157 (/ (- (* fx 116) 16) color-lab-κ)))
158 (yr (if (> L (* color-lab-κ color-lab-ε))
159 (expt (/ (+ L 16) 116.0) 3)
161 (zr (if (> (expt fz 3) color-lab-ε)
163 (/ (- (* 116 fz) 16) color-lab-κ))))
168 (defun rgb->lab (red green blue)
169 "Converts RGB to CIE L*a*b*."
170 (apply 'xyz->lab (rgb->xyz red green blue)))
172 (defun rgb->normalize (color)
173 "Normalize a RGB color to values between [0,1]."
174 (mapcar (lambda (x) (/ x 65535.0)) (x-color-values color)))
176 (defun lab->rgb (L a b)
177 "Converts CIE L*a*b* to RGB."
178 (apply 'xyz->rgb (lab->xyz L a b)))
180 (defun color-lab-ciede2000 (color1 color2 &optional kL kC kH)
181 "Computes the CIEDE2000 color distance between COLOR1 and COLOR2.
182 Colors must be in CIE L*a*b* format."
183 (destructuring-bind (L₁ a₁ b₁) color1
184 (destructuring-bind (L₂ a₂ b₂) color2
185 (let* ((kL (or kL 1))
188 (C₁ (sqrt (+ (expt a₁ 2) (expt b₁ 2))))
189 (C₂ (sqrt (+ (expt a₂ 2) (expt b₂ 2))))
190 (C̄ (/ (+ C₁ C₂) 2.0))
191 (G (* 0.5 (- 1 (sqrt (/ (expt C̄ 7) (+ (expt C̄ 7) (expt 25 7)))))))
194 (C′₁ (sqrt (+ (expt a′₁ 2) (expt b₁ 2))))
195 (C′₂ (sqrt (+ (expt a′₂ 2) (expt b₂ 2))))
196 (h′₁ (if (and (= b₁ 0) (= a′₁ 0))
198 (let ((v (atan b₁ a′₁)))
202 (h′₂ (if (and (= b₂ 0) (= a′₂ 0))
204 (let ((v (atan b₂ a′₂)))
210 (Δh′ (cond ((= (* C′₁ C′₂) 0)
212 ((<= (abs (- h′₂ h′₁)) float-pi)
214 ((> (- h′₂ h′₁) float-pi)
215 (- (- h′₂ h′₁) (* 2 float-pi)))
216 ((< (- h′₂ h′₁) (- float-pi))
217 (+ (- h′₂ h′₁) (* 2 float-pi)))))
218 (ΔH′ (* 2 (sqrt (* C′₁ C′₂)) (sin (/ Δh′ 2.0))))
219 (L̄′ (/ (+ L₁ L₂) 2.0))
220 (C̄′ (/ (+ C′₁ C′₂) 2.0))
221 (h̄′ (cond ((= (* C′₁ C′₂) 0)
223 ((<= (abs (- h′₁ h′₂)) float-pi)
225 ((< (+ h′₁ h′₂) (* 2 float-pi))
226 (/ (+ h′₁ h′₂ (* 2 float-pi)) 2.0))
227 ((>= (+ h′₁ h′₂) (* 2 float-pi))
228 (/ (+ h′₁ h′₂ (* -2 float-pi)) 2.0))))
230 (- (* 0.17 (cos (- h̄′ (degrees-to-radians 30)))))
231 (* 0.24 (cos (* h̄′ 2)))
232 (* 0.32 (cos (+ (* h̄′ 3) (degrees-to-radians 6))))
233 (- (* 0.20 (cos (- (* h̄′ 4) (degrees-to-radians 63)))))))
234 (Δθ (* (degrees-to-radians 30) (exp (- (expt (/ (- h̄′ (degrees-to-radians 275)) (degrees-to-radians 25)) 2)))))
235 (Rc (* 2 (sqrt (/ (expt C̄′ 7) (+ (expt C̄′ 7) (expt 25 7))))))
236 (Sl (+ 1 (/ (* 0.015 (expt (- L̄′ 50) 2)) (sqrt (+ 20 (expt (- L̄′ 50) 2))))))
237 (Sc (+ 1 (* C̄′ 0.045)))
238 (Sh (+ 1 (* 0.015 C̄′ T)))
239 (Rt (- (* (sin (* Δθ 2)) Rc))))
240 (sqrt (+ (expt (/ ΔL′ (* Sl kL)) 2)
241 (expt (/ ΔC′ (* Sc kC)) 2)
242 (expt (/ ΔH′ (* Sh kH)) 2)
243 (* Rt (/ ΔC′ (* Sc kC)) (/ ΔH′ (* Sh kH)))))))))