// Title: CIE Color Conversion Formulas // Authors: Michael Horvath, Christoph Lipka // Website: http://isometricland.net // Created: 2016-11-20 // Updated: 2017-03-07 // This file is licensed under the terms of the CC-GNU LGPL. // http://www.gnu.org/licenses/lgpl-2.1.html // Illuminant = D65 // Observer = 2° (1931) // +kfi0 +kff15 +kc // I still need to create a function that converts to xyY color space, then figure out how to render the spectral locus/cone. #declare XYZWhiteReference1 = 95.047; #declare XYZWhiteReference2 = 100.000; #declare XYZWhiteReference3 = 108.883; #declare XYZEpsilon = 0.008856; #declare XYZKappa = 903.3; // input L = between 0 and 100 // input C = between 0 and 128 // input H = between 0 and 360 // output L = between 0 and 100 // output A = between -128 and +128 // output B = between -128 and +128 #declare funcLCH2LABa1 = function(L,C,H) {L} #declare funcLCH2LABa2 = function(L,C,H) {cosd(H) * C} #declare funcLCH2LABa3 = function(L,C,H) {sind(H) * C} // input L = between 0 and 100 // input A = between -128 and +128 // input B = between -128 and +128 // output X: between 0 and 100 // output Y: between 0 and 100 // output Z: between 0 and 100 // Note that some of these functions are out of order. #declare funcLAB2XYZa2 = function(L,A,B) {(L + 16) / 116} #declare funcLAB2XYZa1 = function(L,A,B) {funcLAB2XYZa2(L,A,B) + A / 500} #declare funcLAB2XYZa3 = function(L,A,B) {funcLAB2XYZa2(L,A,B) - B / 200} #declare funcLAB2XYZb1 = function(L,A,B) {XYZWhiteReference1 * select(pow(funcLAB2XYZa1(L,A,B), 3) - XYZEpsilon, (funcLAB2XYZa1(L,A,B) - 16.0 / 116.0) / 7.787, (funcLAB2XYZa1(L,A,B) - 16.0 / 116.0) / 7.787, pow(funcLAB2XYZa1(L,A,B), 3))} #declare funcLAB2XYZb2 = function(L,A,B) {XYZWhiteReference2 * select(L - XYZKappa * XYZEpsilon, L / XYZKappa, L / XYZKappa, pow(((L + 16) / 116), 3))} #declare funcLAB2XYZb3 = function(L,A,B) {XYZWhiteReference3 * select(pow(funcLAB2XYZa3(L,A,B), 3) - XYZEpsilon, (funcLAB2XYZa3(L,A,B) - 16.0 / 116.0) / 7.787, (funcLAB2XYZa3(L,A,B) - 16.0 / 116.0) / 7.787, pow(funcLAB2XYZa3(L,A,B), 3))} // input X: between 0 and 100 // input Y: between 0 and 100 // input Z: between 0 and 100 // output R: between 0 and 1 // output G: between 0 and 1 // output B: between 0 and 1 // Note that out-of-range colors are *NOT* corrected. You will have to do this yourself. #declare funcXYZ2RGBa1 = function(X,Y,Z) {X/100 * 3.2406 + Y/100 * -1.5372 + Z/100 * -0.4986} #declare funcXYZ2RGBa2 = function(X,Y,Z) {X/100 * -0.9689 + Y/100 * 1.8758 + Z/100 * 0.0415} #declare funcXYZ2RGBa3 = function(X,Y,Z) {X/100 * 0.0557 + Y/100 * -0.2040 + Z/100 * 1.0570} #declare funcXYZ2RGBb1 = function(X,Y,Z) {select(funcXYZ2RGBa1(X,Y,Z) - 0.0031308, 12.92 * funcXYZ2RGBa1(X,Y,Z), 12.92 * funcXYZ2RGBa1(X,Y,Z), 1.055 * pow(funcXYZ2RGBa1(X,Y,Z), 1 / 2.4) - 0.055)} #declare funcXYZ2RGBb2 = function(X,Y,Z) {select(funcXYZ2RGBa2(X,Y,Z) - 0.0031308, 12.92 * funcXYZ2RGBa2(X,Y,Z), 12.92 * funcXYZ2RGBa2(X,Y,Z), 1.055 * pow(funcXYZ2RGBa2(X,Y,Z), 1 / 2.4) - 0.055)} #declare funcXYZ2RGBb3 = function(X,Y,Z) {select(funcXYZ2RGBa3(X,Y,Z) - 0.0031308, 12.92 * funcXYZ2RGBa3(X,Y,Z), 12.92 * funcXYZ2RGBa3(X,Y,Z), 1.055 * pow(funcXYZ2RGBa3(X,Y,Z), 1 / 2.4) - 0.055)} // utility #declare selectRGBa = function(C,D) {select(C,-1,D)} #declare selectRGBb = function(C,D) {select(C-1,D,D,-1)} #declare linearRGBa = function(C) {C/12.92} #declare linearRGBb = function(C) {pow((C + 0.055)/(1 + 0.055), 2.4)} #declare linearRGBc = function(C) {select(C-0.04045,linearRGBa(C),linearRGBa(C),linearRGBb(C))} #declare fD = function(C) {abs(C-0.5)-0.5} #declare fDist = function(Dr,Dg,Db) {max(Dr,Dg,Db)} // input R: between 0 and 1 // input G: between 0 and 1 // input B: between 0 and 1 // output R: between 0 and 1 // output G: between 0 and 1 // output B: between 0 and 1 // only uses these when converting individual values, not inside isosurfaces or function patterns #declare correctRGBa1 = function(R,G,B) {selectRGBa(R,selectRGBa(G,selectRGBa(B,R)))} #declare correctRGBa2 = function(R,G,B) {selectRGBa(R,selectRGBa(G,selectRGBa(B,G)))} #declare correctRGBa3 = function(R,G,B) {selectRGBa(R,selectRGBa(G,selectRGBa(B,B)))} #declare correctRGBb1 = function(R,G,B) {selectRGBb(R,selectRGBb(G,selectRGBb(B,correctRGBa1(R,G,B))))} #declare correctRGBb2 = function(R,G,B) {selectRGBb(R,selectRGBb(G,selectRGBb(B,correctRGBa2(R,G,B))))} #declare correctRGBb3 = function(R,G,B) {selectRGBb(R,selectRGBb(G,selectRGBb(B,correctRGBa3(R,G,B))))} // input L = between 0 and 100 // input C = between 0 and 100 // input H = between 0 and 360 // output R: between 0 and 1 // output G: between 0 and 1 // output B: between 0 and 1 #declare funcLAB2RGBa1 = function(L,A,B) {funcXYZ2RGBb1(funcLAB2XYZb1(L,A,B),funcLAB2XYZb2(L,A,B),funcLAB2XYZb3(L,A,B))} #declare funcLAB2RGBa2 = function(L,A,B) {funcXYZ2RGBb2(funcLAB2XYZb1(L,A,B),funcLAB2XYZb2(L,A,B),funcLAB2XYZb3(L,A,B))} #declare funcLAB2RGBa3 = function(L,A,B) {funcXYZ2RGBb3(funcLAB2XYZb1(L,A,B),funcLAB2XYZb2(L,A,B),funcLAB2XYZb3(L,A,B))} // testing #local VLCH = <25, 50, 270>; #local VLAB = ; #local VXYZ = ; #local VRGB = ; #local VCOR = < correctRGBb1(VRGB.x,VRGB.y,VRGB.z), correctRGBb2(VRGB.x,VRGB.y,VRGB.z), correctRGBb3(VRGB.x,VRGB.y,VRGB.z)>; #debug concat("\nVLCH = ", vstr(3, VLCH, ", ", 0, 5), "\n") #debug concat("\nVLAB = ", vstr(3, VLAB, ", ", 0, 5), "\n") #debug concat("\nVXYZ = ", vstr(3, VXYZ, ", ", 0, 5), "\n") #debug concat("\nVRGB = ", vstr(3, VRGB, ", ", 0, 5), "\n") #debug concat("\nVCOR = ", vstr(3, VCOR, ", ", 0, 5), "\n")