hct.Cam16 Maven / Gradle / Ivy
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/*
* Copyright 2021 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.
*/
package hct;
import static java.lang.Math.max;
import utils.ColorUtils;
/**
* CAM16, a color appearance model. Colors are not just defined by their hex code, but rather, a hex
* code and viewing conditions.
*
* CAM16 instances also have coordinates in the CAM16-UCS space, called J*, a*, b*, or jstar,
* astar, bstar in code. CAM16-UCS is included in the CAM16 specification, and should be used when
* measuring distances between colors.
*
*
In traditional color spaces, a color can be identified solely by the observer's measurement of
* the color. Color appearance models such as CAM16 also use information about the environment where
* the color was observed, known as the viewing conditions.
*
*
For example, white under the traditional assumption of a midday sun white point is accurately
* measured as a slightly chromatic blue by CAM16. (roughly, hue 203, chroma 3, lightness 100)
*/
public final class Cam16 {
// Transforms XYZ color space coordinates to 'cone'/'RGB' responses in CAM16.
static final double[][] XYZ_TO_CAM16RGB = {
{0.401288, 0.650173, -0.051461},
{-0.250268, 1.204414, 0.045854},
{-0.002079, 0.048952, 0.953127}
};
// Transforms 'cone'/'RGB' responses in CAM16 to XYZ color space coordinates.
static final double[][] CAM16RGB_TO_XYZ = {
{1.8620678, -1.0112547, 0.14918678},
{0.38752654, 0.62144744, -0.00897398},
{-0.01584150, -0.03412294, 1.0499644}
};
// CAM16 color dimensions, see getters for documentation.
private final double hue;
private final double chroma;
private final double j;
private final double q;
private final double m;
private final double s;
// Coordinates in UCS space. Used to determine color distance, like delta E equations in L*a*b*.
private final double jstar;
private final double astar;
private final double bstar;
// Avoid allocations during conversion by pre-allocating an array.
private final double[] tempArray = new double[] {0.0, 0.0, 0.0};
/**
* CAM16 instances also have coordinates in the CAM16-UCS space, called J*, a*, b*, or jstar,
* astar, bstar in code. CAM16-UCS is included in the CAM16 specification, and is used to measure
* distances between colors.
*/
public double distance(Cam16 other) {
double dJ = getJstar() - other.getJstar();
double dA = getAstar() - other.getAstar();
double dB = getBstar() - other.getBstar();
double dEPrime = Math.sqrt(dJ * dJ + dA * dA + dB * dB);
double dE = 1.41 * Math.pow(dEPrime, 0.63);
return dE;
}
/** Hue in CAM16 */
public double getHue() {
return hue;
}
/** Chroma in CAM16 */
public double getChroma() {
return chroma;
}
/** Lightness in CAM16 */
public double getJ() {
return j;
}
/**
* Brightness in CAM16.
*
*
Prefer lightness, brightness is an absolute quantity. For example, a sheet of white paper is
* much brighter viewed in sunlight than in indoor light, but it is the lightest object under any
* lighting.
*/
public double getQ() {
return q;
}
/**
* Colorfulness in CAM16.
*
*
Prefer chroma, colorfulness is an absolute quantity. For example, a yellow toy car is much
* more colorful outside than inside, but it has the same chroma in both environments.
*/
public double getM() {
return m;
}
/**
* Saturation in CAM16.
*
*
Colorfulness in proportion to brightness. Prefer chroma, saturation measures colorfulness
* relative to the color's own brightness, where chroma is colorfulness relative to white.
*/
public double getS() {
return s;
}
/** Lightness coordinate in CAM16-UCS */
public double getJstar() {
return jstar;
}
/** a* coordinate in CAM16-UCS */
public double getAstar() {
return astar;
}
/** b* coordinate in CAM16-UCS */
public double getBstar() {
return bstar;
}
/**
* All of the CAM16 dimensions can be calculated from 3 of the dimensions, in the following
* combinations: - {j or q} and {c, m, or s} and hue - jstar, astar, bstar Prefer using a static
* method that constructs from 3 of those dimensions. This constructor is intended for those
* methods to use to return all possible dimensions.
*
* @param hue for example, red, orange, yellow, green, etc.
* @param chroma informally, colorfulness / color intensity. like saturation in HSL, except
* perceptually accurate.
* @param j lightness
* @param q brightness; ratio of lightness to white point's lightness
* @param m colorfulness
* @param s saturation; ratio of chroma to white point's chroma
* @param jstar CAM16-UCS J coordinate
* @param astar CAM16-UCS a coordinate
* @param bstar CAM16-UCS b coordinate
*/
private Cam16(
double hue,
double chroma,
double j,
double q,
double m,
double s,
double jstar,
double astar,
double bstar) {
this.hue = hue;
this.chroma = chroma;
this.j = j;
this.q = q;
this.m = m;
this.s = s;
this.jstar = jstar;
this.astar = astar;
this.bstar = bstar;
}
/**
* Create a CAM16 color from a color, assuming the color was viewed in default viewing conditions.
*
* @param argb ARGB representation of a color.
*/
public static Cam16 fromInt(int argb) {
return fromIntInViewingConditions(argb, ViewingConditions.DEFAULT);
}
/**
* Create a CAM16 color from a color in defined viewing conditions.
*
* @param argb ARGB representation of a color.
* @param viewingConditions Information about the environment where the color was observed.
*/
// The RGB => XYZ conversion matrix elements are derived scientific constants. While the values
// may differ at runtime due to floating point imprecision, keeping the values the same, and
// accurate, across implementations takes precedence.
@SuppressWarnings("FloatingPointLiteralPrecision")
static Cam16 fromIntInViewingConditions(int argb, ViewingConditions viewingConditions) {
// Transform ARGB int to XYZ
int red = (argb & 0x00ff0000) >> 16;
int green = (argb & 0x0000ff00) >> 8;
int blue = (argb & 0x000000ff);
double redL = ColorUtils.linearized(red);
double greenL = ColorUtils.linearized(green);
double blueL = ColorUtils.linearized(blue);
double x = 0.41233895 * redL + 0.35762064 * greenL + 0.18051042 * blueL;
double y = 0.2126 * redL + 0.7152 * greenL + 0.0722 * blueL;
double z = 0.01932141 * redL + 0.11916382 * greenL + 0.95034478 * blueL;
return fromXyzInViewingConditions(x, y, z, viewingConditions);
}
static Cam16 fromXyzInViewingConditions(
double x, double y, double z, ViewingConditions viewingConditions) {
// Transform XYZ to 'cone'/'rgb' responses
double[][] matrix = XYZ_TO_CAM16RGB;
double rT = (x * matrix[0][0]) + (y * matrix[0][1]) + (z * matrix[0][2]);
double gT = (x * matrix[1][0]) + (y * matrix[1][1]) + (z * matrix[1][2]);
double bT = (x * matrix[2][0]) + (y * matrix[2][1]) + (z * matrix[2][2]);
// Discount illuminant
double rD = viewingConditions.getRgbD()[0] * rT;
double gD = viewingConditions.getRgbD()[1] * gT;
double bD = viewingConditions.getRgbD()[2] * bT;
// Chromatic adaptation
double rAF = Math.pow(viewingConditions.getFl() * Math.abs(rD) / 100.0, 0.42);
double gAF = Math.pow(viewingConditions.getFl() * Math.abs(gD) / 100.0, 0.42);
double bAF = Math.pow(viewingConditions.getFl() * Math.abs(bD) / 100.0, 0.42);
double rA = Math.signum(rD) * 400.0 * rAF / (rAF + 27.13);
double gA = Math.signum(gD) * 400.0 * gAF / (gAF + 27.13);
double bA = Math.signum(bD) * 400.0 * bAF / (bAF + 27.13);
// redness-greenness
double a = (11.0 * rA + -12.0 * gA + bA) / 11.0;
// yellowness-blueness
double b = (rA + gA - 2.0 * bA) / 9.0;
// auxiliary components
double u = (20.0 * rA + 20.0 * gA + 21.0 * bA) / 20.0;
double p2 = (40.0 * rA + 20.0 * gA + bA) / 20.0;
// hue
double atan2 = Math.atan2(b, a);
double atanDegrees = Math.toDegrees(atan2);
double hue =
atanDegrees < 0
? atanDegrees + 360.0
: atanDegrees >= 360 ? atanDegrees - 360.0 : atanDegrees;
double hueRadians = Math.toRadians(hue);
// achromatic response to color
double ac = p2 * viewingConditions.getNbb();
// CAM16 lightness and brightness
double j =
100.0
* Math.pow(
ac / viewingConditions.getAw(),
viewingConditions.getC() * viewingConditions.getZ());
double q =
4.0
/ viewingConditions.getC()
* Math.sqrt(j / 100.0)
* (viewingConditions.getAw() + 4.0)
* viewingConditions.getFlRoot();
// CAM16 chroma, colorfulness, and saturation.
double huePrime = (hue < 20.14) ? hue + 360 : hue;
double eHue = 0.25 * (Math.cos(Math.toRadians(huePrime) + 2.0) + 3.8);
double p1 = 50000.0 / 13.0 * eHue * viewingConditions.getNc() * viewingConditions.getNcb();
double t = p1 * Math.hypot(a, b) / (u + 0.305);
double alpha =
Math.pow(1.64 - Math.pow(0.29, viewingConditions.getN()), 0.73) * Math.pow(t, 0.9);
// CAM16 chroma, colorfulness, saturation
double c = alpha * Math.sqrt(j / 100.0);
double m = c * viewingConditions.getFlRoot();
double s =
50.0 * Math.sqrt((alpha * viewingConditions.getC()) / (viewingConditions.getAw() + 4.0));
// CAM16-UCS components
double jstar = (1.0 + 100.0 * 0.007) * j / (1.0 + 0.007 * j);
double mstar = 1.0 / 0.0228 * Math.log1p(0.0228 * m);
double astar = mstar * Math.cos(hueRadians);
double bstar = mstar * Math.sin(hueRadians);
return new Cam16(hue, c, j, q, m, s, jstar, astar, bstar);
}
/**
* @param j CAM16 lightness
* @param c CAM16 chroma
* @param h CAM16 hue
*/
static Cam16 fromJch(double j, double c, double h) {
return fromJchInViewingConditions(j, c, h, ViewingConditions.DEFAULT);
}
/**
* @param j CAM16 lightness
* @param c CAM16 chroma
* @param h CAM16 hue
* @param viewingConditions Information about the environment where the color was observed.
*/
private static Cam16 fromJchInViewingConditions(
double j, double c, double h, ViewingConditions viewingConditions) {
double q =
4.0
/ viewingConditions.getC()
* Math.sqrt(j / 100.0)
* (viewingConditions.getAw() + 4.0)
* viewingConditions.getFlRoot();
double m = c * viewingConditions.getFlRoot();
double alpha = c / Math.sqrt(j / 100.0);
double s =
50.0 * Math.sqrt((alpha * viewingConditions.getC()) / (viewingConditions.getAw() + 4.0));
double hueRadians = Math.toRadians(h);
double jstar = (1.0 + 100.0 * 0.007) * j / (1.0 + 0.007 * j);
double mstar = 1.0 / 0.0228 * Math.log1p(0.0228 * m);
double astar = mstar * Math.cos(hueRadians);
double bstar = mstar * Math.sin(hueRadians);
return new Cam16(h, c, j, q, m, s, jstar, astar, bstar);
}
/**
* Create a CAM16 color from CAM16-UCS coordinates.
*
* @param jstar CAM16-UCS lightness.
* @param astar CAM16-UCS a dimension. Like a* in L*a*b*, it is a Cartesian coordinate on the Y
* axis.
* @param bstar CAM16-UCS b dimension. Like a* in L*a*b*, it is a Cartesian coordinate on the X
* axis.
*/
public static Cam16 fromUcs(double jstar, double astar, double bstar) {
return fromUcsInViewingConditions(jstar, astar, bstar, ViewingConditions.DEFAULT);
}
/**
* Create a CAM16 color from CAM16-UCS coordinates in defined viewing conditions.
*
* @param jstar CAM16-UCS lightness.
* @param astar CAM16-UCS a dimension. Like a* in L*a*b*, it is a Cartesian coordinate on the Y
* axis.
* @param bstar CAM16-UCS b dimension. Like a* in L*a*b*, it is a Cartesian coordinate on the X
* axis.
* @param viewingConditions Information about the environment where the color was observed.
*/
public static Cam16 fromUcsInViewingConditions(
double jstar, double astar, double bstar, ViewingConditions viewingConditions) {
double m = Math.hypot(astar, bstar);
double m2 = Math.expm1(m * 0.0228) / 0.0228;
double c = m2 / viewingConditions.getFlRoot();
double h = Math.atan2(bstar, astar) * (180.0 / Math.PI);
if (h < 0.0) {
h += 360.0;
}
double j = jstar / (1. - (jstar - 100.) * 0.007);
return fromJchInViewingConditions(j, c, h, viewingConditions);
}
/**
* ARGB representation of the color. Assumes the color was viewed in default viewing conditions,
* which are near-identical to the default viewing conditions for sRGB.
*/
public int toInt() {
return viewed(ViewingConditions.DEFAULT);
}
/**
* ARGB representation of the color, in defined viewing conditions.
*
* @param viewingConditions Information about the environment where the color will be viewed.
* @return ARGB representation of color
*/
int viewed(ViewingConditions viewingConditions) {
double[] xyz = xyzInViewingConditions(viewingConditions, tempArray);
return ColorUtils.argbFromXyz(xyz[0], xyz[1], xyz[2]);
}
double[] xyzInViewingConditions(ViewingConditions viewingConditions, double[] returnArray) {
double alpha =
(getChroma() == 0.0 || getJ() == 0.0) ? 0.0 : getChroma() / Math.sqrt(getJ() / 100.0);
double t =
Math.pow(
alpha / Math.pow(1.64 - Math.pow(0.29, viewingConditions.getN()), 0.73), 1.0 / 0.9);
double hRad = Math.toRadians(getHue());
double eHue = 0.25 * (Math.cos(hRad + 2.0) + 3.8);
double ac =
viewingConditions.getAw()
* Math.pow(getJ() / 100.0, 1.0 / viewingConditions.getC() / viewingConditions.getZ());
double p1 = eHue * (50000.0 / 13.0) * viewingConditions.getNc() * viewingConditions.getNcb();
double p2 = (ac / viewingConditions.getNbb());
double hSin = Math.sin(hRad);
double hCos = Math.cos(hRad);
double gamma = 23.0 * (p2 + 0.305) * t / (23.0 * p1 + 11.0 * t * hCos + 108.0 * t * hSin);
double a = gamma * hCos;
double b = gamma * hSin;
double rA = (460.0 * p2 + 451.0 * a + 288.0 * b) / 1403.0;
double gA = (460.0 * p2 - 891.0 * a - 261.0 * b) / 1403.0;
double bA = (460.0 * p2 - 220.0 * a - 6300.0 * b) / 1403.0;
double rCBase = max(0, (27.13 * Math.abs(rA)) / (400.0 - Math.abs(rA)));
double rC =
Math.signum(rA) * (100.0 / viewingConditions.getFl()) * Math.pow(rCBase, 1.0 / 0.42);
double gCBase = max(0, (27.13 * Math.abs(gA)) / (400.0 - Math.abs(gA)));
double gC =
Math.signum(gA) * (100.0 / viewingConditions.getFl()) * Math.pow(gCBase, 1.0 / 0.42);
double bCBase = max(0, (27.13 * Math.abs(bA)) / (400.0 - Math.abs(bA)));
double bC =
Math.signum(bA) * (100.0 / viewingConditions.getFl()) * Math.pow(bCBase, 1.0 / 0.42);
double rF = rC / viewingConditions.getRgbD()[0];
double gF = gC / viewingConditions.getRgbD()[1];
double bF = bC / viewingConditions.getRgbD()[2];
double[][] matrix = CAM16RGB_TO_XYZ;
double x = (rF * matrix[0][0]) + (gF * matrix[0][1]) + (bF * matrix[0][2]);
double y = (rF * matrix[1][0]) + (gF * matrix[1][1]) + (bF * matrix[1][2]);
double z = (rF * matrix[2][0]) + (gF * matrix[2][1]) + (bF * matrix[2][2]);
if (returnArray != null) {
returnArray[0] = x;
returnArray[1] = y;
returnArray[2] = z;
return returnArray;
} else {
return new double[] {x, y, z};
}
}
}