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pico-launcher/arm9/source/material/cam/hct_solver.cpp
Gericom 5d6f67c612 Initial commit
2025-11-25 17:41:31 +01:00

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/*
* Copyright 2022 Google LLC
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "material/cam/hct_solver.h"
#include <math.h>
#include "material/cam/viewing_conditions.h"
#include "material/utils/utils.h"
namespace material_color_utilities {
constexpr double kScaledDiscountFromLinrgb[3][3] = {
{
0.001200833568784504,
0.002389694492170889,
0.0002795742885861124,
},
{
0.0005891086651375999,
0.0029785502573438758,
0.0003270666104008398,
},
{
0.00010146692491640572,
0.0005364214359186694,
0.0032979401770712076,
},
};
constexpr double kLinrgbFromScaledDiscount[3][3] = {
{
1373.2198709594231,
-1100.4251190754821,
-7.278681089101213,
},
{
-271.815969077903,
559.6580465940733,
-32.46047482791194,
},
{
1.9622899599665666,
-57.173814538844006,
308.7233197812385,
},
};
constexpr double kYFromLinrgb[3] = {0.2126, 0.7152, 0.0722};
constexpr double kCriticalPlanes[255] = {
0.015176349177441876, 0.045529047532325624, 0.07588174588720938,
0.10623444424209313, 0.13658714259697685, 0.16693984095186062,
0.19729253930674434, 0.2276452376616281, 0.2579979360165119,
0.28835063437139563, 0.3188300904430532, 0.350925934958123,
0.3848314933096426, 0.42057480301049466, 0.458183274052838,
0.4976837250274023, 0.5391024159806381, 0.5824650784040898,
0.6277969426914107, 0.6751227633498623, 0.7244668422128921,
0.775853049866786, 0.829304845476233, 0.8848452951698498,
0.942497089126609, 1.0022825574869039, 1.0642236851973577,
1.1283421258858297, 1.1946592148522128, 1.2631959812511864,
1.3339731595349034, 1.407011200216447, 1.4823302800086415,
1.5599503113873272, 1.6398909516233677, 1.7221716113234105,
1.8068114625156377, 1.8938294463134073, 1.9832442801866852,
2.075074464868551, 2.1693382909216234, 2.2660538449872063,
2.36523901573795, 2.4669114995532007, 2.5710888059345764,
2.6777882626779785, 2.7870270208169257, 2.898822059350997,
3.0131901897720907, 3.1301480604002863, 3.2497121605402226,
3.3718988244681087, 3.4967242352587946, 3.624204428461639,
3.754355295633311, 3.887192587735158, 4.022731918402185,
4.160988767090289, 4.301978482107941, 4.445716283538092,
4.592217266055746, 4.741496401646282, 4.893568542229298,
5.048448422192488, 5.20615066083972, 5.3666897647573375,
5.5300801301023865, 5.696336044816294, 5.865471690767354,
6.037501145825082, 6.212438385869475, 6.390297286737924,
6.571091626112461, 6.7548350853498045, 6.941541251256611,
7.131223617812143, 7.323895587840543, 7.5195704746346665,
7.7182615035334345, 7.919981813454504, 8.124744458384042,
8.332562408825165, 8.543448553206703, 8.757415699253682,
8.974476575321063, 9.194643831691977, 9.417930041841839,
9.644347703669503, 9.873909240696694, 10.106627003236781,
10.342513269534024, 10.58158024687427, 10.8238400726681,
11.069304815507364, 11.317986476196008, 11.569896988756009,
11.825048221409341, 12.083451977536606, 12.345119996613247,
12.610063955123938, 12.878295467455942, 13.149826086772048,
13.42466730586372, 13.702830557985108, 13.984327217668513,
14.269168601521828, 14.55736596900856, 14.848930523210871,
15.143873411576273, 15.44220572664832, 15.743938506781891,
16.04908273684337, 16.35764934889634, 16.66964922287304,
16.985093187232053, 17.30399201960269, 17.62635644741625,
17.95219714852476, 18.281524751807332, 18.614349837764564,
18.95068293910138, 19.290534541298456, 19.633915083172692,
19.98083495742689, 20.331304511189067, 20.685334046541502,
21.042933821039977, 21.404114048223256, 21.76888489811322,
22.137256497705877, 22.50923893145328, 22.884842241736916,
23.264076429332462, 23.6469514538663, 24.033477234264016,
24.42366364919083, 24.817520537484558, 25.21505769858089,
25.61628489293138, 26.021211842414342, 26.429848230738664,
26.842203703840827, 27.258287870275353, 27.678110301598522,
28.10168053274597, 28.529008062403893, 28.96010235337422,
29.39497283293396, 29.83362889318845, 30.276079891419332,
30.722335150426627, 31.172403958865512, 31.62629557157785,
32.08401920991837, 32.54558406207592, 33.010999283389665,
33.4802739966603, 33.953417292456834, 34.430438229418264,
34.911345834551085, 35.39614910352207, 35.88485700094671,
36.37747846067349, 36.87402238606382, 37.37449765026789,
37.87891309649659, 38.38727753828926, 38.89959975977785,
39.41588851594697, 39.93615253289054, 40.460400508064545,
40.98864111053629, 41.520882981230194, 42.05713473317016,
42.597404951718396, 43.141702194811224, 43.6900349931913,
44.24241185063697, 44.798841244188324, 45.35933162437017,
45.92389141541209, 46.49252901546552, 47.065252796817916,
47.64207110610409, 48.22299226451468, 48.808024568002054,
49.3971762874833, 49.9904556690408, 50.587870934119984,
51.189430279724725, 51.79514187861014, 52.40501387947288,
53.0190544071392, 53.637271562750364, 54.259673423945976,
54.88626804504493, 55.517063457223934, 56.15206766869424,
56.79128866487574, 57.43473440856916, 58.08241284012621,
58.734331877617365, 59.39049941699807, 60.05092333227251,
60.715611475655585, 61.38457167773311, 62.057811747619894,
62.7353394731159, 63.417162620860914, 64.10328893648692,
64.79372614476921, 65.48848194977529, 66.18756403501224,
66.89098006357258, 67.59873767827808, 68.31084450182222,
69.02730813691093, 69.74813616640164, 70.47333615344107,
71.20291564160104, 71.93688215501312, 72.67524319850172,
73.41800625771542, 74.16517879925733, 74.9167682708136,
75.67278210128072, 76.43322770089146, 77.1981124613393,
77.96744375590167, 78.74122893956174, 79.51947534912904,
80.30219030335869, 81.08938110306934, 81.88105503125999,
82.67721935322541, 83.4778813166706, 84.28304815182372,
85.09272707154808, 85.90692527145302, 86.72564993000343,
87.54890820862819, 88.3767072518277, 89.2090541872801,
90.04595612594655, 90.88742016217518, 91.73345337380438,
92.58406282226491, 93.43925555268066, 94.29903859396902,
95.16341895893969, 96.03240364439274, 96.9059996312159,
97.78421388448044, 98.6670533535366, 99.55452497210776,
};
/**
* Sanitizes a small enough angle in radians.
*
* @param angle An angle in radians; must not deviate too much from 0.
* @return A coterminal angle between 0 and 2pi.
*/
double SanitizeRadians(double angle) { return fmod(angle + kPi * 8, kPi * 2); }
/**
* Delinearizes an RGB component, returning a floating-point number.
*
* @param rgb_component 0.0 <= rgb_component <= 100.0, represents linear R/G/B
* channel
* @return 0.0 <= output <= 255.0, color channel converted to regular RGB space
*/
double TrueDelinearized(double rgb_component) {
double normalized = rgb_component / 100.0;
double delinearized = 0.0;
if (normalized <= 0.0031308) {
delinearized = normalized * 12.92;
} else {
delinearized = 1.055 * pow(normalized, 1.0 / 2.4) - 0.055;
}
return delinearized * 255.0;
}
double ChromaticAdaptation(double component) {
double af = pow(abs(component), 0.42);
return Signum(component) * 400.0 * af / (af + 27.13);
}
/**
* Returns the hue of a linear RGB color in CAM16.
*
* @param linrgb The linear RGB coordinates of a color.
* @return The hue of the color in CAM16, in radians.
*/
double HueOf(Vec3 linrgb) {
Vec3 scaledDiscount = MatrixMultiply(linrgb, kScaledDiscountFromLinrgb);
double r_a = ChromaticAdaptation(scaledDiscount.a);
double g_a = ChromaticAdaptation(scaledDiscount.b);
double b_a = ChromaticAdaptation(scaledDiscount.c);
// redness-greenness
double a = (11.0 * r_a + -12.0 * g_a + b_a) / 11.0;
// yellowness-blueness
double b = (r_a + g_a - 2.0 * b_a) / 9.0;
return atan2(b, a);
}
bool AreInCyclicOrder(double a, double b, double c) {
double delta_a_b = SanitizeRadians(b - a);
double delta_a_c = SanitizeRadians(c - a);
return delta_a_b < delta_a_c;
}
/**
* Solves the lerp equation.
*
* @param source The starting number.
* @param mid The number in the middle.
* @param target The ending number.
* @return A number t such that lerp(source, target, t) = mid.
*/
double Intercept(double source, double mid, double target) {
return (mid - source) / (target - source);
}
Vec3 LerpPoint(Vec3 source, double t, Vec3 target) {
return (Vec3){
source.a + (target.a - source.a) * t,
source.b + (target.b - source.b) * t,
source.c + (target.c - source.c) * t,
};
}
double GetAxis(Vec3 vector, int axis) {
switch (axis) {
case 0:
return vector.a;
case 1:
return vector.b;
case 2:
return vector.c;
default:
return -1.0;
}
}
/**
* Intersects a segment with a plane.
*
* @param source The coordinates of point A.
* @param coordinate The R-, G-, or B-coordinate of the plane.
* @param target The coordinates of point B.
* @param axis The axis the plane is perpendicular with. (0: R, 1: G, 2: B)
* @return The intersection point of the segment AB with the plane R=coordinate,
* G=coordinate, or B=coordinate
*/
Vec3 SetCoordinate(Vec3 source, double coordinate, Vec3 target, int axis) {
double t =
Intercept(GetAxis(source, axis), coordinate, GetAxis(target, axis));
return LerpPoint(source, t, target);
}
bool IsBounded(double x) { return 0.0 <= x && x <= 100.0; }
/**
* Returns the nth possible vertex of the polygonal intersection.
*
* @param y The Y value of the plane.
* @param n The zero-based index of the point. 0 <= n <= 11.
* @return The nth possible vertex of the polygonal intersection of the y plane
* and the RGB cube, in linear RGB coordinates, if it exists. If this possible
* vertex lies outside of the cube,
* [-1.0, -1.0, -1.0] is returned.
*/
Vec3 NthVertex(double y, int n) {
double k_r = kYFromLinrgb[0];
double k_g = kYFromLinrgb[1];
double k_b = kYFromLinrgb[2];
double coord_a = n % 4 <= 1 ? 0.0 : 100.0;
double coord_b = n % 2 == 0 ? 0.0 : 100.0;
if (n < 4) {
double g = coord_a;
double b = coord_b;
double r = (y - g * k_g - b * k_b) / k_r;
if (IsBounded(r)) {
return (Vec3){r, g, b};
} else {
return (Vec3){-1.0, -1.0, -1.0};
}
} else if (n < 8) {
double b = coord_a;
double r = coord_b;
double g = (y - r * k_r - b * k_b) / k_g;
if (IsBounded(g)) {
return (Vec3){r, g, b};
} else {
return (Vec3){-1.0, -1.0, -1.0};
}
} else {
double r = coord_a;
double g = coord_b;
double b = (y - r * k_r - g * k_g) / k_b;
if (IsBounded(b)) {
return (Vec3){r, g, b};
} else {
return (Vec3){-1.0, -1.0, -1.0};
}
}
}
/**
* Finds the segment containing the desired color.
*
* @param y The Y value of the color.
* @param target_hue The hue of the color.
* @return A list of two sets of linear RGB coordinates, each corresponding to
* an endpoint of the segment containing the desired color.
*/
void BisectToSegment(double y, double target_hue, Vec3 out[2]) {
Vec3 left = (Vec3){-1.0, -1.0, -1.0};
Vec3 right = left;
double left_hue = 0.0;
double right_hue = 0.0;
bool initialized = false;
bool uncut = true;
for (int n = 0; n < 12; n++) {
Vec3 mid = NthVertex(y, n);
if (mid.a < 0) {
continue;
}
double mid_hue = HueOf(mid);
if (!initialized) {
left = mid;
right = mid;
left_hue = mid_hue;
right_hue = mid_hue;
initialized = true;
continue;
}
if (uncut || AreInCyclicOrder(left_hue, mid_hue, right_hue)) {
uncut = false;
if (AreInCyclicOrder(left_hue, target_hue, mid_hue)) {
right = mid;
right_hue = mid_hue;
} else {
left = mid;
left_hue = mid_hue;
}
}
}
out[0] = left;
out[1] = right;
}
Vec3 Midpoint(Vec3 a, Vec3 b) {
return (Vec3){
(a.a + b.a) / 2,
(a.b + b.b) / 2,
(a.c + b.c) / 2,
};
}
int CriticalPlaneBelow(double x) { return (int)floor(x - 0.5); }
int CriticalPlaneAbove(double x) { return (int)ceil(x - 0.5); }
/**
* Finds a color with the given Y and hue on the boundary of the cube.
*
* @param y The Y value of the color.
* @param target_hue The hue of the color.
* @return The desired color, in linear RGB coordinates.
*/
Vec3 BisectToLimit(double y, double target_hue) {
Vec3 segment[2];
BisectToSegment(y, target_hue, segment);
Vec3 left = segment[0];
double left_hue = HueOf(left);
Vec3 right = segment[1];
for (int axis = 0; axis < 3; axis++) {
if (GetAxis(left, axis) != GetAxis(right, axis)) {
int l_plane = -1;
int r_plane = 255;
if (GetAxis(left, axis) < GetAxis(right, axis)) {
l_plane = CriticalPlaneBelow(TrueDelinearized(GetAxis(left, axis)));
r_plane = CriticalPlaneAbove(TrueDelinearized(GetAxis(right, axis)));
} else {
l_plane = CriticalPlaneAbove(TrueDelinearized(GetAxis(left, axis)));
r_plane = CriticalPlaneBelow(TrueDelinearized(GetAxis(right, axis)));
}
for (int i = 0; i < 8; i++) {
if (abs(r_plane - l_plane) <= 1) {
break;
} else {
int m_plane = (int)floor((l_plane + r_plane) / 2.0);
double mid_plane_coordinate = kCriticalPlanes[m_plane];
Vec3 mid = SetCoordinate(left, mid_plane_coordinate, right, axis);
double mid_hue = HueOf(mid);
if (AreInCyclicOrder(left_hue, target_hue, mid_hue)) {
right = mid;
r_plane = m_plane;
} else {
left = mid;
left_hue = mid_hue;
l_plane = m_plane;
}
}
}
}
}
return Midpoint(left, right);
}
double InverseChromaticAdaptation(double adapted) {
double adapted_abs = abs(adapted);
double base = fmax(0, 27.13 * adapted_abs / (400.0 - adapted_abs));
return Signum(adapted) * pow(base, 1.0 / 0.42);
}
/**
* Finds a color with the given hue, chroma, and Y.
*
* @param hue_radians The desired hue in radians.
* @param chroma The desired chroma.
* @param y The desired Y.
* @return The desired color as a hexadecimal integer, if found; 0 otherwise.
*/
Argb FindResultByJ(double hue_radians, double chroma, double y) {
// Initial estimate of j.
double j = sqrt(y) * 11.0;
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
ViewingConditions viewing_conditions = kDefaultViewingConditions;
double t_inner_coeff =
1 /
pow(1.64 - pow(0.29, viewing_conditions.background_y_to_white_point_y),
0.73);
double e_hue = 0.25 * (cos(hue_radians + 2.0) + 3.8);
double p1 = e_hue * (50000.0 / 13.0) * viewing_conditions.n_c *
viewing_conditions.ncb;
double h_sin = sin(hue_radians);
double h_cos = cos(hue_radians);
for (int iteration_round = 0; iteration_round < 5; iteration_round++) {
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
double j_normalized = j / 100.0;
double alpha =
chroma == 0.0 || j == 0.0 ? 0.0 : chroma / sqrt(j_normalized);
double t = pow(alpha * t_inner_coeff, 1.0 / 0.9);
double ac =
viewing_conditions.aw *
pow(j_normalized, 1.0 / viewing_conditions.c / viewing_conditions.z);
double p2 = ac / viewing_conditions.nbb;
double gamma = 23.0 * (p2 + 0.305) * t /
(23.0 * p1 + 11 * t * h_cos + 108.0 * t * h_sin);
double a = gamma * h_cos;
double b = gamma * h_sin;
double r_a = (460.0 * p2 + 451.0 * a + 288.0 * b) / 1403.0;
double g_a = (460.0 * p2 - 891.0 * a - 261.0 * b) / 1403.0;
double b_a = (460.0 * p2 - 220.0 * a - 6300.0 * b) / 1403.0;
double r_c_scaled = InverseChromaticAdaptation(r_a);
double g_c_scaled = InverseChromaticAdaptation(g_a);
double b_c_scaled = InverseChromaticAdaptation(b_a);
Vec3 scaled = (Vec3){r_c_scaled, g_c_scaled, b_c_scaled};
Vec3 linrgb = MatrixMultiply(scaled, kLinrgbFromScaledDiscount);
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
if (linrgb.a < 0 || linrgb.b < 0 || linrgb.c < 0) {
return 0;
}
double k_r = kYFromLinrgb[0];
double k_g = kYFromLinrgb[1];
double k_b = kYFromLinrgb[2];
double fnj = k_r * linrgb.a + k_g * linrgb.b + k_b * linrgb.c;
if (fnj <= 0) {
return 0;
}
if (iteration_round == 4 || abs(fnj - y) < 0.002) {
if (linrgb.a > 100.01 || linrgb.b > 100.01 || linrgb.c > 100.01) {
return 0;
}
return ArgbFromLinrgb(linrgb);
}
// Iterates with Newton method,
// Using 2 * fn(j) / j as the approximation of fn'(j)
j = j - (fnj - y) * j / (2 * fnj);
}
return 0;
}
/**
* Finds an sRGB color with the given hue, chroma, and L*, if possible.
*
* @param hue_degrees The desired hue, in degrees.
* @param chroma The desired chroma.
* @param lstar The desired L*.
* @return A hexadecimal representing the sRGB color. The color has sufficiently
* close hue, chroma, and L* to the desired values, if possible; otherwise, the
* hue and L* will be sufficiently close, and chroma will be maximized.
*/
Argb SolveToInt(double hue_degrees, double chroma, double lstar) {
if (chroma < 0.0001 || lstar < 0.0001 || lstar > 99.9999) {
return IntFromLstar(lstar);
}
hue_degrees = SanitizeDegreesDouble(hue_degrees);
double hue_radians = hue_degrees / 180 * kPi;
double y = YFromLstar(lstar);
Argb exact_answer = FindResultByJ(hue_radians, chroma, y);
if (exact_answer != 0) {
return exact_answer;
}
Vec3 linrgb = BisectToLimit(y, hue_radians);
return ArgbFromLinrgb(linrgb);
}
/**
* Finds an sRGB color with the given hue, chroma, and L*, if possible.
*
* @param hue_degrees The desired hue, in degrees.
* @param chroma The desired chroma.
* @param lstar The desired L*.
* @return An CAM16 object representing the sRGB color. The color has
* sufficiently close hue, chroma, and L* to the desired values, if possible;
* otherwise, the hue and L* will be sufficiently close, and chroma will be
* maximized.
*/
Cam SolveToCam(double hue_degrees, double chroma, double lstar) {
return CamFromInt(SolveToInt(hue_degrees, chroma, lstar));
}
} // namespace material_color_utilities
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