/**
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*
* @format
* @noflow
*/
/* eslint-disable space-infix-ops */
'use strict';
const invariant = require('invariant');
/**
* Memory conservative (mutative) matrix math utilities. Uses "command"
* matrices, which are reusable.
*/
const MatrixMath = {
createIdentityMatrix: function() {
return [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
},
createCopy: function(m) {
return [
m[0],
m[1],
m[2],
m[3],
m[4],
m[5],
m[6],
m[7],
m[8],
m[9],
m[10],
m[11],
m[12],
m[13],
m[14],
m[15],
];
},
createOrthographic: function(left, right, bottom, top, near, far) {
const a = 2 / (right - left);
const b = 2 / (top - bottom);
const c = -2 / (far - near);
const tx = -(right + left) / (right - left);
const ty = -(top + bottom) / (top - bottom);
const tz = -(far + near) / (far - near);
return [a, 0, 0, 0, 0, b, 0, 0, 0, 0, c, 0, tx, ty, tz, 1];
},
createFrustum: function(left, right, bottom, top, near, far) {
const r_width = 1 / (right - left);
const r_height = 1 / (top - bottom);
const r_depth = 1 / (near - far);
const x = 2 * (near * r_width);
const y = 2 * (near * r_height);
const A = (right + left) * r_width;
const B = (top + bottom) * r_height;
const C = (far + near) * r_depth;
const D = 2 * (far * near * r_depth);
return [x, 0, 0, 0, 0, y, 0, 0, A, B, C, -1, 0, 0, D, 0];
},
/**
* This create a perspective projection towards negative z
* Clipping the z range of [-near, -far]
*
* @param fovInRadians - field of view in randians
*/
createPerspective: function(fovInRadians, aspect, near, far) {
const h = 1 / Math.tan(fovInRadians / 2);
const r_depth = 1 / (near - far);
const C = (far + near) * r_depth;
const D = 2 * (far * near * r_depth);
return [h / aspect, 0, 0, 0, 0, h, 0, 0, 0, 0, C, -1, 0, 0, D, 0];
},
createTranslate2d: function(x, y) {
const mat = MatrixMath.createIdentityMatrix();
MatrixMath.reuseTranslate2dCommand(mat, x, y);
return mat;
},
reuseTranslate2dCommand: function(matrixCommand, x, y) {
matrixCommand[12] = x;
matrixCommand[13] = y;
},
reuseTranslate3dCommand: function(matrixCommand, x, y, z) {
matrixCommand[12] = x;
matrixCommand[13] = y;
matrixCommand[14] = z;
},
createScale: function(factor) {
const mat = MatrixMath.createIdentityMatrix();
MatrixMath.reuseScaleCommand(mat, factor);
return mat;
},
reuseScaleCommand: function(matrixCommand, factor) {
matrixCommand[0] = factor;
matrixCommand[5] = factor;
},
reuseScale3dCommand: function(matrixCommand, x, y, z) {
matrixCommand[0] = x;
matrixCommand[5] = y;
matrixCommand[10] = z;
},
reusePerspectiveCommand: function(matrixCommand, p) {
matrixCommand[11] = -1 / p;
},
reuseScaleXCommand(matrixCommand, factor) {
matrixCommand[0] = factor;
},
reuseScaleYCommand(matrixCommand, factor) {
matrixCommand[5] = factor;
},
reuseScaleZCommand(matrixCommand, factor) {
matrixCommand[10] = factor;
},
reuseRotateXCommand: function(matrixCommand, radians) {
matrixCommand[5] = Math.cos(radians);
matrixCommand[6] = Math.sin(radians);
matrixCommand[9] = -Math.sin(radians);
matrixCommand[10] = Math.cos(radians);
},
reuseRotateYCommand: function(matrixCommand, amount) {
matrixCommand[0] = Math.cos(amount);
matrixCommand[2] = -Math.sin(amount);
matrixCommand[8] = Math.sin(amount);
matrixCommand[10] = Math.cos(amount);
},
// http://www.w3.org/TR/css3-transforms/#recomposing-to-a-2d-matrix
reuseRotateZCommand: function(matrixCommand, radians) {
matrixCommand[0] = Math.cos(radians);
matrixCommand[1] = Math.sin(radians);
matrixCommand[4] = -Math.sin(radians);
matrixCommand[5] = Math.cos(radians);
},
createRotateZ: function(radians) {
const mat = MatrixMath.createIdentityMatrix();
MatrixMath.reuseRotateZCommand(mat, radians);
return mat;
},
reuseSkewXCommand: function(matrixCommand, radians) {
matrixCommand[4] = Math.tan(radians);
},
reuseSkewYCommand: function(matrixCommand, radians) {
matrixCommand[1] = Math.tan(radians);
},
multiplyInto: function(out, a, b) {
const 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];
let 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;
},
determinant(matrix: Array<number>): number {
const [
m00,
m01,
m02,
m03,
m10,
m11,
m12,
m13,
m20,
m21,
m22,
m23,
m30,
m31,
m32,
m33,
] = matrix;
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.
*
* Formula from:
* http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
*/
inverse(matrix: Array<number>): Array<number> {
const det = MatrixMath.determinant(matrix);
if (!det) {
return matrix;
}
const [
m00,
m01,
m02,
m03,
m10,
m11,
m12,
m13,
m20,
m21,
m22,
m23,
m30,
m31,
m32,
m33,
] = matrix;
return [
(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.
*/
transpose(m: Array<number>): Array<number> {
return [
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
*/
multiplyVectorByMatrix(v: Array<number>, m: Array<number>): Array<number> {
const [vx, vy, vz, vw] = v;
return [
vx * m[0] + vy * m[4] + vz * m[8] + vw * m[12],
vx * m[1] + vy * m[5] + vz * m[9] + vw * m[13],
vx * m[2] + vy * m[6] + vz * m[10] + vw * m[14],
vx * m[3] + vy * m[7] + vz * m[11] + vw * m[15],
];
},
/**
* From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
*/
v3Length(a: Array<number>): number {
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
*/
v3Normalize(vector: Array<number>, v3Length: number): Array<number> {
const im = 1 / (v3Length || MatrixMath.v3Length(vector));
return [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
*/
v3Dot(a, 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
*/
v3Combine(
a: Array<number>,
b: Array<number>,
aScale: number,
bScale: number,
): Array<number> {
return [
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
*/
v3Cross(a: Array<number>, b: Array<number>): Array<number> {
return [
a[1] * b[2] - a[2] * b[1],
a[2] * b[0] - a[0] * b[2],
a[0] * b[1] - a[1] * b[0],
];
},
/**
* Based on:
* http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
* and:
* http://quat.zachbennett.com/
*
* Note that this rounds degrees to the thousandth of a degree, due to
* floating point errors in the creation of the quaternion.
*
* Also note that this expects the qw value to be last, not first.
*
* Also, when researching this, remember that:
* yaw === heading === z-axis
* pitch === elevation/attitude === y-axis
* roll === bank === x-axis
*/
quaternionToDegreesXYZ(q: Array<number>, matrix, row): Array<number> {
const [qx, qy, qz, qw] = q;
const qw2 = qw * qw;
const qx2 = qx * qx;
const qy2 = qy * qy;
const qz2 = qz * qz;
const test = qx * qy + qz * qw;
const unit = qw2 + qx2 + qy2 + qz2;
const conv = 180 / Math.PI;
if (test > 0.49999 * unit) {
return [0, 2 * Math.atan2(qx, qw) * conv, 90];
}
if (test < -0.49999 * unit) {
return [0, -2 * Math.atan2(qx, qw) * conv, -90];
}
return [
MatrixMath.roundTo3Places(
Math.atan2(2 * qx * qw - 2 * qy * qz, 1 - 2 * qx2 - 2 * qz2) * conv,
),
MatrixMath.roundTo3Places(
Math.atan2(2 * qy * qw - 2 * qx * qz, 1 - 2 * qy2 - 2 * qz2) * conv,
),
MatrixMath.roundTo3Places(Math.asin(2 * qx * qy + 2 * qz * qw) * conv),
];
},
/**
* Based on:
* https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/round
*/
roundTo3Places(n: number): number {
const arr = n.toString().split('e');
return Math.round(arr[0] + 'e' + (arr[1] ? +arr[1] - 3 : 3)) * 0.001;
},
/**
* Decompose a matrix into separate transform values, for use on platforms
* where applying a precomposed matrix is not possible, and transforms are
* applied in an inflexible ordering (e.g. Android).
*
* Implementation based on
* http://www.w3.org/TR/css3-transforms/#decomposing-a-2d-matrix
* http://www.w3.org/TR/css3-transforms/#decomposing-a-3d-matrix
* which was based on
* http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c
*/
decomposeMatrix(transformMatrix: Array<number>): ?Object {
invariant(
transformMatrix.length === 16,
'Matrix decomposition needs a list of 3d matrix values, received %s',
transformMatrix,
);
// output values
let perspective = [];
const quaternion = [];
const scale = [];
const skew = [];
const translation = [];
// create normalized, 2d array matrix
// and normalized 1d array perspectiveMatrix with redefined 4th column
if (!transformMatrix[15]) {
return;
}
const matrix = [];
const perspectiveMatrix = [];
for (let i = 0; i < 4; i++) {
matrix.push([]);
for (let j = 0; j < 4; j++) {
const value = transformMatrix[i * 4 + j] / transformMatrix[15];
matrix[i].push(value);
perspectiveMatrix.push(j === 3 ? 0 : value);
}
}
perspectiveMatrix[15] = 1;
// test for singularity of upper 3x3 part of the perspective matrix
if (!MatrixMath.determinant(perspectiveMatrix)) {
return;
}
// isolate perspective
if (matrix[0][3] !== 0 || matrix[1][3] !== 0 || matrix[2][3] !== 0) {
// rightHandSide is the right hand side of the equation.
// rightHandSide is a vector, or point in 3d space relative to the origin.
const 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.
const inversePerspectiveMatrix = MatrixMath.inverse(perspectiveMatrix);
const transposedInversePerspectiveMatrix = MatrixMath.transpose(
inversePerspectiveMatrix,
);
perspective = MatrixMath.multiplyVectorByMatrix(
rightHandSide,
transposedInversePerspectiveMatrix,
);
} else {
// no perspective
perspective[0] = perspective[1] = perspective[2] = 0;
perspective[3] = 1;
}
// translation is simple
for (let 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
const row = [];
for (let i = 0; i < 3; i++) {
row[i] = [matrix[i][0], matrix[i][1], matrix[i][2]];
}
// Compute X scale factor and normalize first row.
scale[0] = MatrixMath.v3Length(row[0]);
row[0] = MatrixMath.v3Normalize(row[0], scale[0]);
// Compute XY shear factor and make 2nd row orthogonal to 1st.
skew[0] = MatrixMath.v3Dot(row[0], row[1]);
row[1] = MatrixMath.v3Combine(row[1], row[0], 1.0, -skew[0]);
// Compute XY shear factor and make 2nd row orthogonal to 1st.
skew[0] = MatrixMath.v3Dot(row[0], row[1]);
row[1] = MatrixMath.v3Combine(row[1], row[0], 1.0, -skew[0]);
// Now, compute Y scale and normalize 2nd row.
scale[1] = MatrixMath.v3Length(row[1]);
row[1] = MatrixMath.v3Normalize(row[1], scale[1]);
skew[0] /= scale[1];
// Compute XZ and YZ shears, orthogonalize 3rd row
skew[1] = MatrixMath.v3Dot(row[0], row[2]);
row[2] = MatrixMath.v3Combine(row[2], row[0], 1.0, -skew[1]);
skew[2] = MatrixMath.v3Dot(row[1], row[2]);
row[2] = MatrixMath.v3Combine(row[2], row[1], 1.0, -skew[2]);
// Next, get Z scale and normalize 3rd row.
scale[2] = MatrixMath.v3Length(row[2]);
row[2] = MatrixMath.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.
const pdum3 = MatrixMath.v3Cross(row[1], row[2]);
if (MatrixMath.v3Dot(row[0], pdum3) < 0) {
for (let 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
quaternion[0] =
0.5 * Math.sqrt(Math.max(1 + row[0][0] - row[1][1] - row[2][2], 0));
quaternion[1] =
0.5 * Math.sqrt(Math.max(1 - row[0][0] + row[1][1] - row[2][2], 0));
quaternion[2] =
0.5 * Math.sqrt(Math.max(1 - row[0][0] - row[1][1] + row[2][2], 0));
quaternion[3] =
0.5 * Math.sqrt(Math.max(1 + row[0][0] + row[1][1] + row[2][2], 0));
if (row[2][1] > row[1][2]) {
quaternion[0] = -quaternion[0];
}
if (row[0][2] > row[2][0]) {
quaternion[1] = -quaternion[1];
}
if (row[1][0] > row[0][1]) {
quaternion[2] = -quaternion[2];
}
// correct for occasional, weird Euler synonyms for 2d rotation
let rotationDegrees;
if (
quaternion[0] < 0.001 &&
quaternion[0] >= 0 &&
quaternion[1] < 0.001 &&
quaternion[1] >= 0
) {
// this is a 2d rotation on the z-axis
rotationDegrees = [
0,
0,
MatrixMath.roundTo3Places(
(Math.atan2(row[0][1], row[0][0]) * 180) / Math.PI,
),
];
} else {
rotationDegrees = MatrixMath.quaternionToDegreesXYZ(
quaternion,
matrix,
row,
);
}
// expose both base data and convenience names
return {
rotationDegrees,
perspective,
quaternion,
scale,
skew,
translation,
rotate: rotationDegrees[2],
rotateX: rotationDegrees[0],
rotateY: rotationDegrees[1],
scaleX: scale[0],
scaleY: scale[1],
translateX: translation[0],
translateY: translation[1],
};
},
};
module.exports = MatrixMath;