607 lines
18 KiB
JavaScript
Executable File
607 lines
18 KiB
JavaScript
Executable File
/**
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* Copyright (c) 2015-present, Facebook, Inc.
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* All rights reserved.
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*
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* This source code is licensed under the BSD-style license found in the
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* LICENSE file in the root directory of this source tree. An additional grant
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* of patent rights can be found in the PATENTS file in the same directory.
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*
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* @providesModule MatrixMath
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* @noflow
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*/
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/* eslint-disable space-infix-ops */
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'use strict';
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var invariant = require('fbjs/lib/invariant');
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/**
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* Memory conservative (mutative) matrix math utilities. Uses "command"
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* matrices, which are reusable.
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*/
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var MatrixMath = {
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createIdentityMatrix: function() {
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return [
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1,0,0,0,
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0,1,0,0,
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0,0,1,0,
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0,0,0,1
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];
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},
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createCopy: function(m) {
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return [
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m[0], m[1], m[2], m[3],
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m[4], m[5], m[6], m[7],
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m[8], m[9], m[10], m[11],
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m[12], m[13], m[14], m[15],
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];
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},
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createOrthographic: function(left, right, bottom, top, near, far) {
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var a = 2 / (right - left);
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var b = 2 / (top - bottom);
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var c = -2 / (far - near);
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var tx = -(right + left) / (right - left);
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var ty = -(top + bottom) / (top - bottom);
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var tz = -(far + near) / (far - near);
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return [
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a, 0, 0, 0,
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0, b, 0, 0,
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0, 0, c, 0,
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tx, ty, tz, 1
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];
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},
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createFrustum: function(left, right, bottom, top, near, far) {
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var r_width = 1 / (right - left);
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var r_height = 1 / (top - bottom);
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var r_depth = 1 / (near - far);
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var x = 2 * (near * r_width);
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var y = 2 * (near * r_height);
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var A = (right + left) * r_width;
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var B = (top + bottom) * r_height;
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var C = (far + near) * r_depth;
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var D = 2 * (far * near * r_depth);
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return [
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x, 0, 0, 0,
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0, y, 0, 0,
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A, B, C,-1,
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0, 0, D, 0,
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];
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},
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/**
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* This create a perspective projection towards negative z
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* Clipping the z range of [-near, -far]
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*
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* @param fovInRadians - field of view in randians
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*/
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createPerspective: function(fovInRadians, aspect, near, far) {
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var h = 1 / Math.tan(fovInRadians / 2);
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var r_depth = 1 / (near - far);
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var C = (far + near) * r_depth;
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var D = 2 * (far * near * r_depth);
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return [
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h/aspect, 0, 0, 0,
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0, h, 0, 0,
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0, 0, C,-1,
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0, 0, D, 0,
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];
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},
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createTranslate2d: function(x, y) {
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var mat = MatrixMath.createIdentityMatrix();
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MatrixMath.reuseTranslate2dCommand(mat, x, y);
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return mat;
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},
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reuseTranslate2dCommand: function(matrixCommand, x, y) {
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matrixCommand[12] = x;
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matrixCommand[13] = y;
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},
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reuseTranslate3dCommand: function(matrixCommand, x, y, z) {
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matrixCommand[12] = x;
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matrixCommand[13] = y;
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matrixCommand[14] = z;
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},
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createScale: function(factor) {
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var mat = MatrixMath.createIdentityMatrix();
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MatrixMath.reuseScaleCommand(mat, factor);
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return mat;
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},
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reuseScaleCommand: function(matrixCommand, factor) {
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matrixCommand[0] = factor;
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matrixCommand[5] = factor;
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},
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reuseScale3dCommand: function(matrixCommand, x, y, z) {
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matrixCommand[0] = x;
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matrixCommand[5] = y;
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matrixCommand[10] = z;
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},
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reusePerspectiveCommand: function(matrixCommand, p) {
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matrixCommand[11] = -1 / p;
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},
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reuseScaleXCommand(matrixCommand, factor) {
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matrixCommand[0] = factor;
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},
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reuseScaleYCommand(matrixCommand, factor) {
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matrixCommand[5] = factor;
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},
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reuseScaleZCommand(matrixCommand, factor) {
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matrixCommand[10] = factor;
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},
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reuseRotateXCommand: function(matrixCommand, radians) {
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matrixCommand[5] = Math.cos(radians);
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matrixCommand[6] = Math.sin(radians);
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matrixCommand[9] = -Math.sin(radians);
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matrixCommand[10] = Math.cos(radians);
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},
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reuseRotateYCommand: function(matrixCommand, amount) {
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matrixCommand[0] = Math.cos(amount);
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matrixCommand[2] = -Math.sin(amount);
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matrixCommand[8] = Math.sin(amount);
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matrixCommand[10] = Math.cos(amount);
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},
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// http://www.w3.org/TR/css3-transforms/#recomposing-to-a-2d-matrix
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reuseRotateZCommand: function(matrixCommand, radians) {
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matrixCommand[0] = Math.cos(radians);
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matrixCommand[1] = Math.sin(radians);
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matrixCommand[4] = -Math.sin(radians);
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matrixCommand[5] = Math.cos(radians);
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},
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createRotateZ: function(radians) {
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var mat = MatrixMath.createIdentityMatrix();
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MatrixMath.reuseRotateZCommand(mat, radians);
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return mat;
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},
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reuseSkewXCommand: function(matrixCommand, radians) {
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matrixCommand[4] = Math.tan(radians);
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},
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reuseSkewYCommand: function(matrixCommand, radians) {
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matrixCommand[1] = Math.tan(radians);
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},
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multiplyInto: function(out, a, b) {
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var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
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var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
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out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
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out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
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out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
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out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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},
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determinant(matrix: Array<number>): number {
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var [
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m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33
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] = matrix;
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return (
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m03 * m12 * m21 * m30 - m02 * m13 * m21 * m30 -
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m03 * m11 * m22 * m30 + m01 * m13 * m22 * m30 +
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m02 * m11 * m23 * m30 - m01 * m12 * m23 * m30 -
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m03 * m12 * m20 * m31 + m02 * m13 * m20 * m31 +
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m03 * m10 * m22 * m31 - m00 * m13 * m22 * m31 -
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m02 * m10 * m23 * m31 + m00 * m12 * m23 * m31 +
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m03 * m11 * m20 * m32 - m01 * m13 * m20 * m32 -
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m03 * m10 * m21 * m32 + m00 * m13 * m21 * m32 +
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m01 * m10 * m23 * m32 - m00 * m11 * m23 * m32 -
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m02 * m11 * m20 * m33 + m01 * m12 * m20 * m33 +
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m02 * m10 * m21 * m33 - m00 * m12 * m21 * m33 -
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m01 * m10 * m22 * m33 + m00 * m11 * m22 * m33
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);
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},
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/**
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* Inverse of a matrix. Multiplying by the inverse is used in matrix math
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* instead of division.
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*
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* Formula from:
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* http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
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*/
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inverse(matrix: Array<number>): Array<number> {
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var det = MatrixMath.determinant(matrix);
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if (!det) {
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return matrix;
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}
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var [
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m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33
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] = matrix;
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return [
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(m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33) / det,
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(m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33) / det,
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(m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33) / det,
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(m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23) / det,
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(m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33) / det,
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(m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33) / det,
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(m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33) / det,
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(m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23) / det,
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(m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33) / det,
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(m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33) / det,
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(m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33) / det,
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(m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23) / det,
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(m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32) / det,
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(m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32) / det,
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(m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32) / det,
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(m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22) / det
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];
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},
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/**
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* Turns columns into rows and rows into columns.
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*/
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transpose(m: Array<number>): Array<number> {
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return [
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m[0], m[4], m[8], m[12],
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m[1], m[5], m[9], m[13],
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m[2], m[6], m[10], m[14],
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m[3], m[7], m[11], m[15]
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];
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},
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/**
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* Based on: http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c
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*/
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multiplyVectorByMatrix(
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v: Array<number>,
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m: Array<number>
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): Array<number> {
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var [vx, vy, vz, vw] = v;
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return [
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vx * m[0] + vy * m[4] + vz * m[8] + vw * m[12],
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vx * m[1] + vy * m[5] + vz * m[9] + vw * m[13],
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vx * m[2] + vy * m[6] + vz * m[10] + vw * m[14],
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vx * m[3] + vy * m[7] + vz * m[11] + vw * m[15]
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];
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},
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/**
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* From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
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*/
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v3Length(a: Array<number>): number {
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return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
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},
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/**
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* Based on: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
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*/
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v3Normalize(
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vector: Array<number>,
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v3Length: number
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): Array<number> {
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var im = 1 / (v3Length || MatrixMath.v3Length(vector));
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return [
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vector[0] * im,
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vector[1] * im,
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vector[2] * im
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];
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},
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/**
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* The dot product of a and b, two 3-element vectors.
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* From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
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*/
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v3Dot(a, b) {
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return a[0] * b[0] +
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a[1] * b[1] +
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a[2] * b[2];
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},
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/**
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* From:
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* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
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*/
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v3Combine(
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a: Array<number>,
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b: Array<number>,
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aScale: number,
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bScale: number
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): Array<number> {
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return [
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aScale * a[0] + bScale * b[0],
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aScale * a[1] + bScale * b[1],
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aScale * a[2] + bScale * b[2]
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];
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},
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/**
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* From:
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* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
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*/
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v3Cross(a: Array<number>, b: Array<number>): Array<number> {
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return [
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a[1] * b[2] - a[2] * b[1],
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a[2] * b[0] - a[0] * b[2],
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a[0] * b[1] - a[1] * b[0]
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];
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},
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/**
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* Based on:
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* http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
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* and:
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* http://quat.zachbennett.com/
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*
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* Note that this rounds degrees to the thousandth of a degree, due to
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* floating point errors in the creation of the quaternion.
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*
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* Also note that this expects the qw value to be last, not first.
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*
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* Also, when researching this, remember that:
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* yaw === heading === z-axis
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* pitch === elevation/attitude === y-axis
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* roll === bank === x-axis
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*/
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quaternionToDegreesXYZ(q: Array<number>, matrix, row): Array<number> {
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var [qx, qy, qz, qw] = q;
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var qw2 = qw * qw;
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var qx2 = qx * qx;
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var qy2 = qy * qy;
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var qz2 = qz * qz;
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var test = qx * qy + qz * qw;
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var unit = qw2 + qx2 + qy2 + qz2;
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var conv = 180 / Math.PI;
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if (test > 0.49999 * unit) {
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return [0, 2 * Math.atan2(qx, qw) * conv, 90];
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}
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if (test < -0.49999 * unit) {
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return [0, -2 * Math.atan2(qx, qw) * conv, -90];
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}
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return [
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MatrixMath.roundTo3Places(
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Math.atan2(2*qx*qw-2*qy*qz,1-2*qx2-2*qz2) * conv
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),
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MatrixMath.roundTo3Places(
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Math.atan2(2*qy*qw-2*qx*qz,1-2*qy2-2*qz2) * conv
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),
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MatrixMath.roundTo3Places(
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Math.asin(2*qx*qy+2*qz*qw) * conv
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)
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];
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},
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/**
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* Based on:
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* https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/round
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*/
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roundTo3Places(n: number): number {
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var arr = n.toString().split('e');
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return Math.round(arr[0] + 'e' + (arr[1] ? (+arr[1] - 3) : 3)) * 0.001;
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},
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/**
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* Decompose a matrix into separate transform values, for use on platforms
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* where applying a precomposed matrix is not possible, and transforms are
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* applied in an inflexible ordering (e.g. Android).
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*
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* Implementation based on
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* http://www.w3.org/TR/css3-transforms/#decomposing-a-2d-matrix
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* http://www.w3.org/TR/css3-transforms/#decomposing-a-3d-matrix
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* which was based on
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* http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c
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*/
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decomposeMatrix(transformMatrix: Array<number>): ?Object {
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invariant(
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transformMatrix.length === 16,
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'Matrix decomposition needs a list of 3d matrix values, received %s',
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transformMatrix
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);
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// output values
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var perspective = [];
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var quaternion = [];
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var scale = [];
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var skew = [];
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var translation = [];
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|
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// create normalized, 2d array matrix
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// and normalized 1d array perspectiveMatrix with redefined 4th column
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if (!transformMatrix[15]) {
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return;
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}
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var matrix = [];
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var perspectiveMatrix = [];
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for (var i = 0; i < 4; i++) {
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matrix.push([]);
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for (var j = 0; j < 4; j++) {
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var value = transformMatrix[(i * 4) + j] / transformMatrix[15];
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matrix[i].push(value);
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perspectiveMatrix.push(j === 3 ? 0 : value);
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}
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}
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perspectiveMatrix[15] = 1;
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|
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// test for singularity of upper 3x3 part of the perspective matrix
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if (!MatrixMath.determinant(perspectiveMatrix)) {
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return;
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}
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|
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// isolate perspective
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if (matrix[0][3] !== 0 || matrix[1][3] !== 0 || matrix[2][3] !== 0) {
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// rightHandSide is the right hand side of the equation.
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// rightHandSide is a vector, or point in 3d space relative to the origin.
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var rightHandSide = [
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|
matrix[0][3],
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matrix[1][3],
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|
matrix[2][3],
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matrix[3][3]
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|
];
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|
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// Solve the equation by inverting perspectiveMatrix and multiplying
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// rightHandSide by the inverse.
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var inversePerspectiveMatrix = MatrixMath.inverse(
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|
perspectiveMatrix
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|
);
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var transposedInversePerspectiveMatrix = MatrixMath.transpose(
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|
inversePerspectiveMatrix
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|
);
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var perspective = MatrixMath.multiplyVectorByMatrix(
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|
rightHandSide,
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|
transposedInversePerspectiveMatrix
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|
);
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} else {
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// no perspective
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|
perspective[0] = perspective[1] = perspective[2] = 0;
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|
perspective[3] = 1;
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|
}
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|
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|
// translation is simple
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|
for (var i = 0; i < 3; i++) {
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translation[i] = matrix[3][i];
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|
}
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|
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|
// Now get scale and shear.
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|
// 'row' is a 3 element array of 3 component vectors
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|
var row = [];
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|
for (i = 0; i < 3; i++) {
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|
row[i] = [
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|
matrix[i][0],
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|
matrix[i][1],
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|
matrix[i][2]
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|
];
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|
}
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|
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// Compute X scale factor and normalize first row.
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scale[0] = MatrixMath.v3Length(row[0]);
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|
row[0] = MatrixMath.v3Normalize(row[0], scale[0]);
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|
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// Compute XY shear factor and make 2nd row orthogonal to 1st.
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|
skew[0] = MatrixMath.v3Dot(row[0], row[1]);
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|
row[1] = MatrixMath.v3Combine(row[1], row[0], 1.0, -skew[0]);
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|
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// Compute XY shear factor and make 2nd row orthogonal to 1st.
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|
skew[0] = MatrixMath.v3Dot(row[0], row[1]);
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|
row[1] = MatrixMath.v3Combine(row[1], row[0], 1.0, -skew[0]);
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|
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|
// Now, compute Y scale and normalize 2nd row.
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|
scale[1] = MatrixMath.v3Length(row[1]);
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|
row[1] = MatrixMath.v3Normalize(row[1], scale[1]);
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|
skew[0] /= scale[1];
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|
|
|
// Compute XZ and YZ shears, orthogonalize 3rd row
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|
skew[1] = MatrixMath.v3Dot(row[0], row[2]);
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|
row[2] = MatrixMath.v3Combine(row[2], row[0], 1.0, -skew[1]);
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|
skew[2] = MatrixMath.v3Dot(row[1], row[2]);
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|
row[2] = MatrixMath.v3Combine(row[2], row[1], 1.0, -skew[2]);
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|
|
|
// Next, get Z scale and normalize 3rd row.
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|
scale[2] = MatrixMath.v3Length(row[2]);
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|
row[2] = MatrixMath.v3Normalize(row[2], scale[2]);
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|
skew[1] /= scale[2];
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|
skew[2] /= scale[2];
|
|
|
|
// At this point, the matrix (in rows) is orthonormal.
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|
// Check for a coordinate system flip. If the determinant
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|
// is -1, then negate the matrix and the scaling factors.
|
|
var pdum3 = MatrixMath.v3Cross(row[1], row[2]);
|
|
if (MatrixMath.v3Dot(row[0], pdum3) < 0) {
|
|
for (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
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|
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));
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|
quaternion[2] =
|
|
0.5 * Math.sqrt(Math.max(1 - row[0][0] - row[1][1] + row[2][2], 0));
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|
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
|
|
var 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;
|