/************************************************************************* * Copyright (C) 2008 Tavian Barnes * * * * 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 * * . * *************************************************************************/ #include "dimension.h" #include /* For pow(), sqrt() */ /* sRGB white point (CIE D50) */ const dmnsn_CIE_XYZ dmnsn_whitepoint = { .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); /* Waited 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)); }