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/*************************************************************************
* Copyright (C) 2009 Tavian Barnes <tavianator@gmail.com> *
* *
* This file is part of The Dimension Library. *
* *
* The Dimension Library is free software; you can redistribute it and/ *
* or modify it under the terms of the GNU Lesser General Public License *
* as published by the Free Software Foundation; either version 3 of the *
* License, or (at your option) any later version. *
* *
* The Dimension Library is distributed in the hope that it will be *
* useful, but WITHOUT ANY WARRANTY; without even the implied warranty *
* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this program. If not, see *
* <http://www.gnu.org/licenses/>. *
*************************************************************************/
#include "dimension.h"
#include <math.h> /* For pow(), sqrt() */
/* sRGB white point (CIE D50) */
const dmnsn_CIE_XYZ dmnsn_whitepoint = { .X = 0.9504060171449392,
.Y = 0.9999085943425312,
.Z = 1.089062231497274 };
/* Standard colors */
const dmnsn_color dmnsn_black = { .X = 0.0, .Y = 0.0, .Z = 0.0 };
const dmnsn_color dmnsn_white = { .X = 0.9504060171449392,
.Y = 0.9999085943425312,
.Z = 1.089062231497274 };
/* Convert a CIE XYZ color to a dmnsn_color (actually a no-op) */
dmnsn_color
dmnsn_color_from_XYZ(dmnsn_CIE_XYZ XYZ)
{
dmnsn_color ret = { .X = XYZ.X, .Y = XYZ.Y, .Z = XYZ.Z,
.filter = 0.0, .trans = 0.0 };
return ret;
}
/* Convert a CIE xyY color to a dmnsn_color */
dmnsn_color
dmnsn_color_from_xyY(dmnsn_CIE_xyY xyY)
{
dmnsn_color ret = { .X = xyY.Y*xyY.x/xyY.y,
.Y = xyY.Y,
.Z = xyY.Y*(1.0 - xyY.x - xyY.y)/xyY.y,
.filter = 0.0,
.trans = 0.0 };
return ret;
}
/* Inverse function of CIE L*a*b*'s `f' function, for the reverse conversion */
static double dmnsn_Lab_finv(double t) {
if (t > 6.0/29.0) {
return t*t*t;
} else {
return 108.0*(t - 16.0/116.0)/841.0;
}
}
/* Convert a CIE L*a*b* color to a dmnsn_color, relative to the given
whitepoint. */
dmnsn_color
dmnsn_color_from_Lab(dmnsn_CIE_Lab Lab, dmnsn_CIE_XYZ white)
{
double fx, fy, fz;
dmnsn_color ret;
fy = (Lab.L + 16.0)/116.0;
fx = fy + Lab.a/500.0;
fz = fy - Lab.b/200.0;
ret.X = white.X*dmnsn_Lab_finv(fx);
ret.Y = white.Y*dmnsn_Lab_finv(fy);
ret.Z = white.Z*dmnsn_Lab_finv(fz);
ret.filter = 0.0;
ret.trans = 0.0;
return ret;
}
/* Convert a CIE L*u*v* color to a dmnsn_color, relative to the given
whitepoint. */
dmnsn_color
dmnsn_color_from_Luv(dmnsn_CIE_Luv Luv, dmnsn_CIE_XYZ white)
{
double fy;
double uprime, unprime, vprime, vnprime;
dmnsn_color ret;
fy = (Luv.L + 16.0)/116.0;
unprime = 4.0*white.X/(white.X + 15.0*white.Y + 3.0*white.Z);
uprime = Luv.u/Luv.L/13.0 + unprime;
vnprime = 9.0*white.Y/(white.X + 15.0*white.Y + 3.0*white.Z);
vprime = Luv.v/Luv.L/13.0 + vnprime;
ret.Y = white.Y*dmnsn_Lab_finv(fy);
ret.X = ret.Y*9.0*uprime/vprime/4.0;
ret.Z = ret.Y*(12.0 - 3*uprime - 20*vprime)/vprime/4.0;
ret.filter = 0.0;
ret.trans = 0.0;
return ret;
}
/* Inverse function of sRGB's `C' function, for the reverse conversion */
static double dmnsn_sRGB_Cinv(double CsRGB) {
/*
* If C represents R, G, and B, then the Clinear values are now found as
* follows:
*
* { Csrgb/12.92, Csrgb <= 0.04045
* Clinear = { 1/2.4
* { ((Csrgb + 0.055)/1.055) , Csrgb > 0.04045
*/
if (CsRGB <= 0.040449936) {
return CsRGB/12.92;
} else {
return pow((CsRGB + 0.055)/1.055, 2.4);
}
}
/* Convert an sRGB value to a dmnsn_color */
dmnsn_color
dmnsn_color_from_sRGB(dmnsn_sRGB sRGB)
{
double Rlinear, Glinear, Blinear; /* Linear RGB values - no gamma */
dmnsn_color ret;
Rlinear = dmnsn_sRGB_Cinv(sRGB.R);
Glinear = dmnsn_sRGB_Cinv(sRGB.G);
Blinear = dmnsn_sRGB_Cinv(sRGB.B);
/*
* Now, the linear conversion. Expressed as matrix multiplication, it looks
* like this:
*
* [X] [0.4124 0.3576 0.1805] [Rlinear]
* [Y] = [0.2126 0.7152 0.0722]*[Glinear]
* [X] [0.0193 0.1192 0.9505] [Blinear]
*/
ret.X = 0.4123808838268995*Rlinear + 0.3575728355732478*Glinear
+ 0.1804522977447919*Blinear;
ret.Y = 0.2126198631048975*Rlinear + 0.7151387878413206*Glinear
+ 0.0721499433963131*Blinear;
ret.Z = 0.0193434956789248*Rlinear + 0.1192121694056356*Glinear
+ 0.9505065664127130*Blinear;
ret.filter = 0.0;
ret.trans = 0.0;
return ret;
}
/* Convert a dmnsn_color to a CIE XYZ color (actually a no-op) */
dmnsn_CIE_XYZ
dmnsn_XYZ_from_color(dmnsn_color color)
{
dmnsn_CIE_XYZ ret = { .X = color.X, .Y = color.Y, .Z = color.Z };
return ret;
}
/* Convert a dmnsn_color to a CIE xyY color */
dmnsn_CIE_xyY
dmnsn_xyY_from_color(dmnsn_color color)
{
dmnsn_CIE_xyY ret = { .x = color.X/(color.X + color.Y + color.Z),
.y = color.Y/(color.X + color.Y + color.Z),
.Y = color.Y };
return ret;
}
/* CIE L*a*b*'s `f' function */
static double dmnsn_Lab_f(double t) {
if (t > 216.0/24389.0) {
return pow(t, 1.0/3.0);
} else {
return 841.0*t/108.0 + 4.0/29.0;
}
}
/* Convert a dmnsn_color to a CIE L*a*b* color, relative to the given
whitepoint */
dmnsn_CIE_Lab
dmnsn_Lab_from_color(dmnsn_color color, dmnsn_CIE_XYZ white)
{
dmnsn_CIE_Lab ret;
ret.L = 116.0*dmnsn_Lab_f(color.Y/white.Y) - 16.0;
ret.a = 500.0*(dmnsn_Lab_f(color.X/white.X) - dmnsn_Lab_f(color.Y/white.Y));
ret.b = 200.0*(dmnsn_Lab_f(color.Y/white.Y) - dmnsn_Lab_f(color.Z/white.Z));
return ret;
}
/* Convert a dmnsn_color to a CIE L*u*v* color, relative to the given
whitepoint */
dmnsn_CIE_Luv
dmnsn_Luv_from_color(dmnsn_color color, dmnsn_CIE_XYZ white)
{
double uprime, unprime, vprime, vnprime;
dmnsn_CIE_Luv ret;
uprime = 4.0*color.X/(color.X + 15.0*color.Y + 3.0*color.Z);
unprime = 4.0*white.X/(white.X + 15.0*white.Y + 3.0*white.Z);
vprime = 9.0*color.Y/(color.X + 15.0*color.Y + 3.0*color.Z);
vnprime = 9.0*white.Y/(white.X + 15.0*white.Y + 3.0*white.Z);
ret.L = 116.0*dmnsn_Lab_f(color.Y/white.Y) - 16.0;
ret.u = 13.0*ret.L*(uprime - unprime);
ret.v = 13.0*ret.L*(vprime - vnprime);
return ret;
}
/* sRGB's `C' function */
static double dmnsn_sRGB_C(double Clinear) {
/*
* If C represents R, G, and B, then the sRGB values are now found as follows:
*
* { 12.92*Clinear, Clinear <= 0.0031308
* Csrgb = { 1/2.4
* { (1.055)*Clinear - 0.055, Clinear > 0.0031308
*/
if (Clinear <= 0.0031308) {
return 12.92*Clinear;
} else {
return 1.055*pow(Clinear, 1.0/2.4) - 0.055;
}
}
/* Convert a dmnsn_color to an sRGB color */
dmnsn_sRGB
dmnsn_sRGB_from_color(dmnsn_color color)
{
double Rlinear, Glinear, Blinear; /* Linear RGB values - no gamma */
dmnsn_sRGB ret;
/*
* First, the linear conversion. Expressed as matrix multiplication, it looks
* like this:
*
* [Rlinear] [ 3.2410 -1.5374 -0.4986] [X]
* [Glinear] = [-0.9692 1.8760 0.0416]*[Y]
* [Blinear] [ 0.0556 -0.2040 1.0570] [Z]
*/
Rlinear = 3.2410*color.X - 1.5374*color.Y - 0.4986*color.Z;
Glinear = -0.9692*color.X + 1.8760*color.Y + 0.0416*color.Z;
Blinear = 0.0556*color.X - 0.2040*color.Y + 1.0570*color.Z;
ret.R = dmnsn_sRGB_C(Rlinear);
ret.G = dmnsn_sRGB_C(Glinear);
ret.B = dmnsn_sRGB_C(Blinear);
return ret;
}
/* Add two colors in a perceptually correct manner, using CIE L*a*b*. */
dmnsn_color
dmnsn_color_add(dmnsn_color color1, dmnsn_color color2)
{
dmnsn_CIE_Lab Lab, Lab1, Lab2;
dmnsn_color ret;
Lab1 = dmnsn_Lab_from_color(color1, dmnsn_whitepoint);
Lab2 = dmnsn_Lab_from_color(color2, dmnsn_whitepoint);
Lab.L = Lab1.L + Lab2.L;
Lab.a = Lab1.a + Lab2.a;
Lab.b = Lab1.b + Lab2.b;
ret = dmnsn_color_from_Lab(Lab, dmnsn_whitepoint);
/* Weighted average of transparencies by intensity */
ret.filter = (Lab1.L*color1.filter + Lab2.L*color2.filter)/Lab.L;
ret.trans = (Lab1.L*color1.trans + Lab2.L*color2.trans)/Lab.L;
return ret;
}
/* Find the perceptual difference between two colors, using CIE L*a*b*. */
double
dmnsn_color_difference(dmnsn_color color1, dmnsn_color color2)
{
dmnsn_CIE_Lab Lab1, Lab2;
Lab1 = dmnsn_Lab_from_color(color1, dmnsn_whitepoint);
Lab2 = dmnsn_Lab_from_color(color2, dmnsn_whitepoint);
return sqrt((Lab1.L - Lab2.L)*(Lab1.L - Lab2.L)
+ (Lab1.a - Lab2.a)*(Lab1.a - Lab2.a)
+ (Lab1.b - Lab2.b)*(Lab1.b - Lab2.b));
}
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