/*
* Copyright (c) Meta Platforms, Inc. and affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*/
package com.facebook.react.uimanager;
import com.facebook.infer.annotation.Assertions;
/**
* Provides helper methods for converting transform operations into a matrix and then into a list of
* translate, scale and rotate commands.
*/
public class MatrixMathHelper {
private static final double EPSILON = .00001d;
public static class MatrixDecompositionContext {
double[] perspective = new double[4];
double[] scale = new double[3];
double[] skew = new double[3];
double[] translation = new double[3];
double[] rotationDegrees = new double[3];
private static void resetArray(double[] arr) {
for (int i = 0; i < arr.length; i++) {
arr[i] = 0;
}
}
public void reset() {
MatrixDecompositionContext.resetArray(perspective);
MatrixDecompositionContext.resetArray(scale);
MatrixDecompositionContext.resetArray(skew);
MatrixDecompositionContext.resetArray(translation);
MatrixDecompositionContext.resetArray(rotationDegrees);
}
}
private static boolean isZero(double d) {
if (Double.isNaN(d)) {
return false;
}
return Math.abs(d) < EPSILON;
}
public static void multiplyInto(double[] out, double[] a, double[] b) {
double a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3],
a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7],
a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11],
a30 = a[12],
a31 = a[13],
a32 = a[14],
a33 = a[15];
double b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[4];
b1 = b[5];
b2 = b[6];
b3 = b[7];
out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[8];
b1 = b[9];
b2 = b[10];
b3 = b[11];
out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[12];
b1 = b[13];
b2 = b[14];
b3 = b[15];
out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
}
/** @param transformMatrix 16-element array of numbers representing 4x4 transform matrix */
public static void decomposeMatrix(double[] transformMatrix, MatrixDecompositionContext ctx) {
Assertions.assertCondition(transformMatrix.length == 16);
// output values
final double[] perspective = ctx.perspective;
final double[] scale = ctx.scale;
final double[] skew = ctx.skew;
final double[] translation = ctx.translation;
final double[] rotationDegrees = ctx.rotationDegrees;
// create normalized, 2d array matrix
// and normalized 1d array perspectiveMatrix with redefined 4th column
if (isZero(transformMatrix[15])) {
return;
}
double[][] matrix = new double[4][4];
double[] perspectiveMatrix = new double[16];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
double value = transformMatrix[(i * 4) + j] / transformMatrix[15];
matrix[i][j] = value;
perspectiveMatrix[(i * 4) + j] = j == 3 ? 0 : value;
}
}
perspectiveMatrix[15] = 1;
// test for singularity of upper 3x3 part of the perspective matrix
if (isZero(determinant(perspectiveMatrix))) {
return;
}
// isolate perspective
if (!isZero(matrix[0][3]) || !isZero(matrix[1][3]) || !isZero(matrix[2][3])) {
// rightHandSide is the right hand side of the equation.
// rightHandSide is a vector, or point in 3d space relative to the origin.
double[] rightHandSide = {matrix[0][3], matrix[1][3], matrix[2][3], matrix[3][3]};
// Solve the equation by inverting perspectiveMatrix and multiplying
// rightHandSide by the inverse.
double[] inversePerspectiveMatrix = inverse(perspectiveMatrix);
double[] transposedInversePerspectiveMatrix = transpose(inversePerspectiveMatrix);
multiplyVectorByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspective);
} else {
// no perspective
perspective[0] = perspective[1] = perspective[2] = 0d;
perspective[3] = 1d;
}
// translation is simple
for (int i = 0; i < 3; i++) {
translation[i] = matrix[3][i];
}
// Now get scale and shear.
// 'row' is a 3 element array of 3 component vectors
double[][] row = new double[3][3];
for (int i = 0; i < 3; i++) {
row[i][0] = matrix[i][0];
row[i][1] = matrix[i][1];
row[i][2] = matrix[i][2];
}
// Compute X scale factor and normalize first row.
scale[0] = v3Length(row[0]);
row[0] = v3Normalize(row[0], scale[0]);
// Compute XY shear factor and make 2nd row orthogonal to 1st.
skew[0] = v3Dot(row[0], row[1]);
row[1] = v3Combine(row[1], row[0], 1.0, -skew[0]);
// Now, compute Y scale and normalize 2nd row.
scale[1] = v3Length(row[1]);
row[1] = v3Normalize(row[1], scale[1]);
skew[0] /= scale[1];
// Compute XZ and YZ shears, orthogonalize 3rd row
skew[1] = v3Dot(row[0], row[2]);
row[2] = v3Combine(row[2], row[0], 1.0, -skew[1]);
skew[2] = v3Dot(row[1], row[2]);
row[2] = v3Combine(row[2], row[1], 1.0, -skew[2]);
// Next, get Z scale and normalize 3rd row.
scale[2] = v3Length(row[2]);
row[2] = v3Normalize(row[2], scale[2]);
skew[1] /= scale[2];
skew[2] /= scale[2];
// At this point, the matrix (in rows) is orthonormal.
// Check for a coordinate system flip. If the determinant
// is -1, then negate the matrix and the scaling factors.
double[] pdum3 = v3Cross(row[1], row[2]);
if (v3Dot(row[0], pdum3) < 0) {
for (int i = 0; i < 3; i++) {
scale[i] *= -1;
row[i][0] *= -1;
row[i][1] *= -1;
row[i][2] *= -1;
}
}
// Now, get the rotations out
// Based on: http://nghiaho.com/?page_id=846
double conv = 180 / Math.PI;
rotationDegrees[0] = roundTo3Places(-Math.atan2(row[2][1], row[2][2]) * conv);
rotationDegrees[1] =
roundTo3Places(
-Math.atan2(-row[2][0], Math.sqrt(row[2][1] * row[2][1] + row[2][2] * row[2][2]))
* conv);
rotationDegrees[2] = roundTo3Places(-Math.atan2(row[1][0], row[0][0]) * conv);
}
public static double determinant(double[] matrix) {
double m00 = matrix[0],
m01 = matrix[1],
m02 = matrix[2],
m03 = matrix[3],
m10 = matrix[4],
m11 = matrix[5],
m12 = matrix[6],
m13 = matrix[7],
m20 = matrix[8],
m21 = matrix[9],
m22 = matrix[10],
m23 = matrix[11],
m30 = matrix[12],
m31 = matrix[13],
m32 = matrix[14],
m33 = matrix[15];
return (m03 * m12 * m21 * m30
- m02 * m13 * m21 * m30
- m03 * m11 * m22 * m30
+ m01 * m13 * m22 * m30
+ m02 * m11 * m23 * m30
- m01 * m12 * m23 * m30
- m03 * m12 * m20 * m31
+ m02 * m13 * m20 * m31
+ m03 * m10 * m22 * m31
- m00 * m13 * m22 * m31
- m02 * m10 * m23 * m31
+ m00 * m12 * m23 * m31
+ m03 * m11 * m20 * m32
- m01 * m13 * m20 * m32
- m03 * m10 * m21 * m32
+ m00 * m13 * m21 * m32
+ m01 * m10 * m23 * m32
- m00 * m11 * m23 * m32
- m02 * m11 * m20 * m33
+ m01 * m12 * m20 * m33
+ m02 * m10 * m21 * m33
- m00 * m12 * m21 * m33
- m01 * m10 * m22 * m33
+ m00 * m11 * m22 * m33);
}
/**
* Inverse of a matrix. Multiplying by the inverse is used in matrix math instead of division.
*
* <p>Formula from:
* http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
*/
public static double[] inverse(double[] matrix) {
double det = determinant(matrix);
if (isZero(det)) {
return matrix;
}
double m00 = matrix[0],
m01 = matrix[1],
m02 = matrix[2],
m03 = matrix[3],
m10 = matrix[4],
m11 = matrix[5],
m12 = matrix[6],
m13 = matrix[7],
m20 = matrix[8],
m21 = matrix[9],
m22 = matrix[10],
m23 = matrix[11],
m30 = matrix[12],
m31 = matrix[13],
m32 = matrix[14],
m33 = matrix[15];
return new double[] {
(m12 * m23 * m31
- m13 * m22 * m31
+ m13 * m21 * m32
- m11 * m23 * m32
- m12 * m21 * m33
+ m11 * m22 * m33)
/ det,
(m03 * m22 * m31
- m02 * m23 * m31
- m03 * m21 * m32
+ m01 * m23 * m32
+ m02 * m21 * m33
- m01 * m22 * m33)
/ det,
(m02 * m13 * m31
- m03 * m12 * m31
+ m03 * m11 * m32
- m01 * m13 * m32
- m02 * m11 * m33
+ m01 * m12 * m33)
/ det,
(m03 * m12 * m21
- m02 * m13 * m21
- m03 * m11 * m22
+ m01 * m13 * m22
+ m02 * m11 * m23
- m01 * m12 * m23)
/ det,
(m13 * m22 * m30
- m12 * m23 * m30
- m13 * m20 * m32
+ m10 * m23 * m32
+ m12 * m20 * m33
- m10 * m22 * m33)
/ det,
(m02 * m23 * m30
- m03 * m22 * m30
+ m03 * m20 * m32
- m00 * m23 * m32
- m02 * m20 * m33
+ m00 * m22 * m33)
/ det,
(m03 * m12 * m30
- m02 * m13 * m30
- m03 * m10 * m32
+ m00 * m13 * m32
+ m02 * m10 * m33
- m00 * m12 * m33)
/ det,
(m02 * m13 * m20
- m03 * m12 * m20
+ m03 * m10 * m22
- m00 * m13 * m22
- m02 * m10 * m23
+ m00 * m12 * m23)
/ det,
(m11 * m23 * m30
- m13 * m21 * m30
+ m13 * m20 * m31
- m10 * m23 * m31
- m11 * m20 * m33
+ m10 * m21 * m33)
/ det,
(m03 * m21 * m30
- m01 * m23 * m30
- m03 * m20 * m31
+ m00 * m23 * m31
+ m01 * m20 * m33
- m00 * m21 * m33)
/ det,
(m01 * m13 * m30
- m03 * m11 * m30
+ m03 * m10 * m31
- m00 * m13 * m31
- m01 * m10 * m33
+ m00 * m11 * m33)
/ det,
(m03 * m11 * m20
- m01 * m13 * m20
- m03 * m10 * m21
+ m00 * m13 * m21
+ m01 * m10 * m23
- m00 * m11 * m23)
/ det,
(m12 * m21 * m30
- m11 * m22 * m30
- m12 * m20 * m31
+ m10 * m22 * m31
+ m11 * m20 * m32
- m10 * m21 * m32)
/ det,
(m01 * m22 * m30
- m02 * m21 * m30
+ m02 * m20 * m31
- m00 * m22 * m31
- m01 * m20 * m32
+ m00 * m21 * m32)
/ det,
(m02 * m11 * m30
- m01 * m12 * m30
- m02 * m10 * m31
+ m00 * m12 * m31
+ m01 * m10 * m32
- m00 * m11 * m32)
/ det,
(m01 * m12 * m20
- m02 * m11 * m20
+ m02 * m10 * m21
- m00 * m12 * m21
- m01 * m10 * m22
+ m00 * m11 * m22)
/ det
};
}
/** Turns columns into rows and rows into columns. */
public static double[] transpose(double[] m) {
return new double[] {
m[0], m[4], m[8], m[12],
m[1], m[5], m[9], m[13],
m[2], m[6], m[10], m[14],
m[3], m[7], m[11], m[15]
};
}
/** Based on: http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c */
public static void multiplyVectorByMatrix(double[] v, double[] m, double[] result) {
double vx = v[0], vy = v[1], vz = v[2], vw = v[3];
result[0] = vx * m[0] + vy * m[4] + vz * m[8] + vw * m[12];
result[1] = vx * m[1] + vy * m[5] + vz * m[9] + vw * m[13];
result[2] = vx * m[2] + vy * m[6] + vz * m[10] + vw * m[14];
result[3] = vx * m[3] + vy * m[7] + vz * m[11] + vw * m[15];
}
/** From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js */
public static double v3Length(double[] a) {
return Math.sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
}
/** Based on: https://code.google.com/p/webgl-mjs/source/browse/mjs.js */
public static double[] v3Normalize(double[] vector, double norm) {
double im = 1 / (isZero(norm) ? v3Length(vector) : norm);
return new double[] {vector[0] * im, vector[1] * im, vector[2] * im};
}
/**
* The dot product of a and b, two 3-element vectors. From:
* https://code.google.com/p/webgl-mjs/source/browse/mjs.js
*/
public static double v3Dot(double[] a, double[] b) {
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
/**
* From:
* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
*/
public static double[] v3Combine(double[] a, double[] b, double aScale, double bScale) {
return new double[] {
aScale * a[0] + bScale * b[0], aScale * a[1] + bScale * b[1], aScale * a[2] + bScale * b[2]
};
}
/**
* From:
* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
*/
public static double[] v3Cross(double[] a, double[] b) {
return new double[] {
a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]
};
}
public static double roundTo3Places(double n) {
return Math.round(n * 1000d) * 0.001;
}
public static double[] createIdentityMatrix() {
double[] res = new double[16];
resetIdentityMatrix(res);
return res;
}
public static double degreesToRadians(double degrees) {
return degrees * Math.PI / 180;
}
public static void resetIdentityMatrix(double[] matrix) {
matrix[1] =
matrix[2] =
matrix[3] =
matrix[4] =
matrix[6] =
matrix[7] =
matrix[8] =
matrix[9] = matrix[11] = matrix[12] = matrix[13] = matrix[14] = 0;
matrix[0] = matrix[5] = matrix[10] = matrix[15] = 1;
}
public static void applyPerspective(double[] m, double perspective) {
m[11] = -1 / perspective;
}
public static void applyScaleX(double[] m, double factor) {
m[0] = factor;
}
public static void applyScaleY(double[] m, double factor) {
m[5] = factor;
}
public static void applyScaleZ(double[] m, double factor) {
m[10] = factor;
}
public static void applyTranslate2D(double[] m, double x, double y) {
m[12] = x;
m[13] = y;
}
public static void applyTranslate3D(double[] m, double x, double y, double z) {
m[12] = x;
m[13] = y;
m[14] = z;
}
public static void applySkewX(double[] m, double radians) {
m[4] = Math.tan(radians);
}
public static void applySkewY(double[] m, double radians) {
m[1] = Math.tan(radians);
}
public static void applyRotateX(double[] m, double radians) {
m[5] = Math.cos(radians);
m[6] = Math.sin(radians);
m[9] = -Math.sin(radians);
m[10] = Math.cos(radians);
}
public static void applyRotateY(double[] m, double radians) {
m[0] = Math.cos(radians);
m[2] = -Math.sin(radians);
m[8] = Math.sin(radians);
m[10] = Math.cos(radians);
}
// http://www.w3.org/TR/css3-transforms/#recomposing-to-a-2d-matrix
public static void applyRotateZ(double[] m, double radians) {
m[0] = Math.cos(radians);
m[1] = Math.sin(radians);
m[4] = -Math.sin(radians);
m[5] = Math.cos(radians);
}
}