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/*
* Copyright (c) 2024, Google LLC, OpenSavvy and contributors.
*
* 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.
*/
package opensavvy.material3.colors.hct
import opensavvy.material3.colors.utils.Color
import opensavvy.material3.colors.utils.Color.Companion.fromLinrgb
import opensavvy.material3.colors.utils.Color.Companion.fromLstar
import opensavvy.material3.colors.utils.Color.Companion.yFromLstar
import opensavvy.material3.colors.utils.matrixMultiply
import opensavvy.material3.colors.utils.sanitizeDegreesDouble
import opensavvy.material3.colors.utils.signum
import kotlin.math.*
/** A class that solves the HCT equation. */
object HctSolver {
val SCALED_DISCOUNT_FROM_LINRGB: Array = arrayOf(
doubleArrayOf(
0.001200833568784504, 0.002389694492170889, 0.0002795742885861124,
),
doubleArrayOf(
0.0005891086651375999, 0.0029785502573438758, 0.0003270666104008398,
),
doubleArrayOf(
0.00010146692491640572, 0.0005364214359186694, 0.0032979401770712076,
),
)
val LINRGB_FROM_SCALED_DISCOUNT: Array = arrayOf(
doubleArrayOf(
1373.2198709594231, -1100.4251190754821, -7.278681089101213,
),
doubleArrayOf(
-271.815969077903, 559.6580465940733, -32.46047482791194,
),
doubleArrayOf(
1.9622899599665666, -57.173814538844006, 308.7233197812385,
),
)
val Y_FROM_LINRGB: DoubleArray = doubleArrayOf(0.2126, 0.7152, 0.0722)
val CRITICAL_PLANES: DoubleArray = doubleArrayOf(
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.
*/
fun sanitizeRadians(angle: Double): Double {
return (angle + PI * 8) % (PI * 2)
}
/**
* Delinearizes an RGB component, returning a floating-point number.
*
* @param rgbComponent 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
*/
fun trueDelinearized(rgbComponent: Double): Double {
val normalized = rgbComponent / 100.0
var delinearized = 0.0
delinearized = if (normalized <= 0.0031308) {
normalized * 12.92
} else {
1.055 * normalized.pow(1.0 / 2.4) - 0.055
}
return delinearized * 255.0
}
fun chromaticAdaptation(component: Double): Double {
val af = abs(component).pow(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.
*/
fun hueOf(linrgb: DoubleArray?): Double {
val scaledDiscount = matrixMultiply(linrgb!!, SCALED_DISCOUNT_FROM_LINRGB)
val rA = chromaticAdaptation(scaledDiscount[0])
val gA = chromaticAdaptation(scaledDiscount[1])
val bA = chromaticAdaptation(scaledDiscount[2])
// redness-greenness
val a = (11.0 * rA + -12.0 * gA + bA) / 11.0
// yellowness-blueness
val b = (rA + gA - 2.0 * bA) / 9.0
return atan2(b, a)
}
fun areInCyclicOrder(a: Double, b: Double, c: Double): Boolean {
val deltaAB = sanitizeRadians(b - a)
val deltaAC = sanitizeRadians(c - a)
return deltaAB < deltaAC
}
/**
* 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.
*/
fun intercept(source: Double, mid: Double, target: Double): Double {
return (mid - source) / (target - source)
}
fun lerpPoint(source: DoubleArray, t: Double, target: DoubleArray): DoubleArray {
return doubleArrayOf(
source[0] + (target[0] - source[0]) * t,
source[1] + (target[1] - source[1]) * t,
source[2] + (target[2] - source[2]) * t,
)
}
/**
* 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
*/
fun setCoordinate(source: DoubleArray, coordinate: Double, target: DoubleArray, axis: Int): DoubleArray {
val t = intercept(source[axis], coordinate, target[axis])
return lerpPoint(source, t, target)
}
fun isBounded(x: Double): Boolean {
return x in 0.0..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.
*/
fun nthVertex(y: Double, n: Int): DoubleArray {
val kR = Y_FROM_LINRGB[0]
val kG = Y_FROM_LINRGB[1]
val kB = Y_FROM_LINRGB[2]
val coordA = if (n % 4 <= 1) 0.0 else 100.0
val coordB = if (n % 2 == 0) 0.0 else 100.0
if (n < 4) {
val r = (y - coordA * kG - coordB * kB) / kR
return if (isBounded(r)) {
doubleArrayOf(r, coordA, coordB)
} else {
doubleArrayOf(-1.0, -1.0, -1.0)
}
} else if (n < 8) {
val g = (y - coordB * kR - coordA * kB) / kG
return if (isBounded(g)) {
doubleArrayOf(coordB, g, coordA)
} else {
doubleArrayOf(-1.0, -1.0, -1.0)
}
} else {
val b = (y - coordA * kR - coordB * kG) / kB
return if (isBounded(b)) {
doubleArrayOf(coordA, coordB, b)
} else {
doubleArrayOf(-1.0, -1.0, -1.0)
}
}
}
/**
* Finds the segment containing the desired color.
*
* @param y The Y value of the color.
* @param targetHue 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.
*/
fun bisectToSegment(y: Double, targetHue: Double): Array {
var left = doubleArrayOf(-1.0, -1.0, -1.0)
var right = left
var leftHue = 0.0
var rightHue = 0.0
var initialized = false
var uncut = true
for (n in 0..11) {
val mid = nthVertex(y, n)
if (mid[0] < 0) {
continue
}
val midHue = hueOf(mid)
if (!initialized) {
left = mid
right = mid
leftHue = midHue
rightHue = midHue
initialized = true
continue
}
if (uncut || areInCyclicOrder(leftHue, midHue, rightHue)) {
uncut = false
if (areInCyclicOrder(leftHue, targetHue, midHue)) {
right = mid
rightHue = midHue
} else {
left = mid
leftHue = midHue
}
}
}
return arrayOf(left, right)
}
fun midpoint(a: DoubleArray, b: DoubleArray): DoubleArray {
return doubleArrayOf(
(a[0] + b[0]) / 2, (a[1] + b[1]) / 2, (a[2] + b[2]) / 2,
)
}
fun criticalPlaneBelow(x: Double): Int {
return floor(x - 0.5).toInt()
}
fun criticalPlaneAbove(x: Double): Int {
return ceil(x - 0.5).toInt()
}
/**
* Finds a color with the given Y and hue on the boundary of the cube.
*
* @param y The Y value of the color.
* @param targetHue The hue of the color.
* @return The desired color, in linear RGB coordinates.
*/
fun bisectToLimit(y: Double, targetHue: Double): DoubleArray {
val segment = bisectToSegment(y, targetHue)
var left = segment[0]
var leftHue = hueOf(left)
var right = segment[1]
for (axis in 0..2) {
if (left[axis] != right[axis]) {
var lPlane = -1
var rPlane = 255
if (left[axis] < right[axis]) {
lPlane = criticalPlaneBelow(trueDelinearized(left[axis]))
rPlane = criticalPlaneAbove(trueDelinearized(right[axis]))
} else {
lPlane = criticalPlaneAbove(trueDelinearized(left[axis]))
rPlane = criticalPlaneBelow(trueDelinearized(right[axis]))
}
for (i in 0..7) {
if (abs((rPlane - lPlane).toDouble()) <= 1) {
break
} else {
val mPlane = floor((lPlane + rPlane) / 2.0).toInt()
val midPlaneCoordinate = CRITICAL_PLANES[mPlane]
val mid = setCoordinate(left, midPlaneCoordinate, right, axis)
val midHue = hueOf(mid)
if (areInCyclicOrder(leftHue, targetHue, midHue)) {
right = mid
rPlane = mPlane
} else {
left = mid
leftHue = midHue
lPlane = mPlane
}
}
}
}
}
return midpoint(left, right)
}
fun inverseChromaticAdaptation(adapted: Double): Double {
val adaptedAbs = abs(adapted)
val base = max(0.0, 27.13 * adaptedAbs / (400.0 - adaptedAbs))
return signum(adapted) * base.pow(1.0 / 0.42)
}
/**
* Finds a color with the given hue, chroma, and Y.
*
* @param hueRadians 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; [Color.BLACK] otherwise.
*/
fun findResultByJ(hueRadians: Double, chroma: Double, y: Double): Color {
// Initial estimate of j.
var j = sqrt(y) * 11.0
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
val viewingConditions: ViewingConditions = ViewingConditions.DEFAULT
val tInnerCoeff: Double = 1 / (1.64 - 0.29.pow(viewingConditions.n)).pow(0.73)
val eHue = 0.25 * (cos(hueRadians + 2.0) + 3.8)
val p1: Double = eHue * (50000.0 / 13.0) * viewingConditions.nc * viewingConditions.ncb
val hSin = sin(hueRadians)
val hCos = cos(hueRadians)
for (iterationRound in 0..4) {
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
val jNormalized = j / 100.0
val alpha = if (chroma == 0.0 || j == 0.0) 0.0 else chroma / sqrt(jNormalized)
val t = (alpha * tInnerCoeff).pow(1.0 / 0.9)
val ac: Double =
(viewingConditions.aw
* jNormalized.pow(1.0 / viewingConditions.c / viewingConditions.z))
val p2: Double = ac / viewingConditions.nbb
val gamma = 23.0 * (p2 + 0.305) * t / (23.0 * p1 + 11 * t * hCos + 108.0 * t * hSin)
val a = gamma * hCos
val b = gamma * hSin
val rA = (460.0 * p2 + 451.0 * a + 288.0 * b) / 1403.0
val gA = (460.0 * p2 - 891.0 * a - 261.0 * b) / 1403.0
val bA = (460.0 * p2 - 220.0 * a - 6300.0 * b) / 1403.0
val rCScaled = inverseChromaticAdaptation(rA)
val gCScaled = inverseChromaticAdaptation(gA)
val bCScaled = inverseChromaticAdaptation(bA)
val linrgb =
matrixMultiply(
doubleArrayOf(rCScaled, gCScaled, bCScaled), LINRGB_FROM_SCALED_DISCOUNT)
// ===========================================================
// Operations inlined from Cam16 to avoid repeated calculation
// ===========================================================
if (linrgb[0] < 0 || linrgb[1] < 0 || linrgb[2] < 0) {
return Color.BLACK
}
val kR = Y_FROM_LINRGB[0]
val kG = Y_FROM_LINRGB[1]
val kB = Y_FROM_LINRGB[2]
val fnj = kR * linrgb[0] + kG * linrgb[1] + kB * linrgb[2]
if (fnj <= 0) {
return Color.BLACK
}
if (iterationRound == 4 || abs(fnj - y) < 0.002) {
if (linrgb[0] > 100.01 || linrgb[1] > 100.01 || linrgb[2] > 100.01) {
return Color.BLACK
}
return fromLinrgb(linrgb)
}
// Iterates with Newton method,
// Using 2 * fn(j) / j as the approximation of fn'(j)
j -= (fnj - y) * j / (2 * fnj)
}
return Color.BLACK
}
/**
* Finds an sRGB color with the given hue, chroma, and L*, if possible.
*
* @param hueDegrees 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.
*/
fun solveToColor(hueDegrees: Double, chroma: Double, lstar: Double): Color {
var hueDegrees = hueDegrees
if (chroma < 0.0001 || lstar < 0.0001 || lstar > 99.9999) {
return fromLstar(lstar)
}
hueDegrees = sanitizeDegreesDouble(hueDegrees)
val hueRadians: Double = hueDegrees / 180 * PI
val y = yFromLstar(lstar)
val exactAnswer = findResultByJ(hueRadians, chroma, y)
if (exactAnswer != Color.BLACK) {
return exactAnswer
}
val linrgb = bisectToLimit(y, hueRadians)
return fromLinrgb(linrgb)
}
/**
* Finds an sRGB color with the given hue, chroma, and L*, if possible.
*
* @param hueDegrees The desired hue, in degrees.
* @param chroma The desired chroma.
* @param lstar The desired L*.
* @return A 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.
*/
fun solveToCam(hueDegrees: Double, chroma: Double, lstar: Double): Cam16 {
return Cam16.fromColor(solveToColor(hueDegrees, chroma, lstar))
}
}
