com.vaadin.polymer.public.bower_components.web-animations-js.src.matrix-decomposition.js Maven / Gradle / Ivy
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// Copyright 2014 Google Inc. All rights reserved.
//
// 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.
(function(scope, testing) {
var decomposeMatrix = (function() {
function determinant(m) {
return m[0][0] * m[1][1] * m[2][2] +
m[1][0] * m[2][1] * m[0][2] +
m[2][0] * m[0][1] * m[1][2] -
m[0][2] * m[1][1] * m[2][0] -
m[1][2] * m[2][1] * m[0][0] -
m[2][2] * m[0][1] * m[1][0];
}
// from Wikipedia:
//
// [A B]^-1 = [A^-1 + A^-1B(D - CA^-1B)^-1CA^-1 -A^-1B(D - CA^-1B)^-1]
// [C D] [-(D - CA^-1B)^-1CA^-1 (D - CA^-1B)^-1 ]
//
// Therefore
//
// [A [0]]^-1 = [A^-1 [0]]
// [C 1 ] [ -CA^-1 1 ]
function inverse(m) {
var iDet = 1 / determinant(m);
var a = m[0][0], b = m[0][1], c = m[0][2];
var d = m[1][0], e = m[1][1], f = m[1][2];
var g = m[2][0], h = m[2][1], k = m[2][2];
var Ainv = [
[(e * k - f * h) * iDet, (c * h - b * k) * iDet,
(b * f - c * e) * iDet, 0],
[(f * g - d * k) * iDet, (a * k - c * g) * iDet,
(c * d - a * f) * iDet, 0],
[(d * h - e * g) * iDet, (g * b - a * h) * iDet,
(a * e - b * d) * iDet, 0]
];
var lastRow = [];
for (var i = 0; i < 3; i++) {
var val = 0;
for (var j = 0; j < 3; j++) {
val += m[3][j] * Ainv[j][i];
}
lastRow.push(val);
}
lastRow.push(1);
Ainv.push(lastRow);
return Ainv;
}
function transposeMatrix4(m) {
return [[m[0][0], m[1][0], m[2][0], m[3][0]],
[m[0][1], m[1][1], m[2][1], m[3][1]],
[m[0][2], m[1][2], m[2][2], m[3][2]],
[m[0][3], m[1][3], m[2][3], m[3][3]]];
}
function multVecMatrix(v, m) {
var result = [];
for (var i = 0; i < 4; i++) {
var val = 0;
for (var j = 0; j < 4; j++) {
val += v[j] * m[j][i];
}
result.push(val);
}
return result;
}
function normalize(v) {
var len = length(v);
return [v[0] / len, v[1] / len, v[2] / len];
}
function length(v) {
return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
}
function combine(v1, v2, v1s, v2s) {
return [v1s * v1[0] + v2s * v2[0], v1s * v1[1] + v2s * v2[1],
v1s * v1[2] + v2s * v2[2]];
}
function cross(v1, v2) {
return [v1[1] * v2[2] - v1[2] * v2[1],
v1[2] * v2[0] - v1[0] * v2[2],
v1[0] * v2[1] - v1[1] * v2[0]];
}
function decomposeMatrix(matrix) {
var m3d = [
matrix.slice(0, 4),
matrix.slice(4, 8),
matrix.slice(8, 12),
matrix.slice(12, 16)
];
// skip normalization step as m3d[3][3] should always be 1
if (m3d[3][3] !== 1) {
return null;
}
var perspectiveMatrix = [];
for (var i = 0; i < 4; i++) {
perspectiveMatrix.push(m3d[i].slice());
}
for (var i = 0; i < 3; i++) {
perspectiveMatrix[i][3] = 0;
}
if (determinant(perspectiveMatrix) === 0) {
return null;
}
var rhs = [];
var perspective;
if (m3d[0][3] || m3d[1][3] || m3d[2][3]) {
rhs.push(m3d[0][3]);
rhs.push(m3d[1][3]);
rhs.push(m3d[2][3]);
rhs.push(m3d[3][3]);
var inversePerspectiveMatrix = inverse(perspectiveMatrix);
var transposedInversePerspectiveMatrix =
transposeMatrix4(inversePerspectiveMatrix);
perspective = multVecMatrix(rhs, transposedInversePerspectiveMatrix);
} else {
perspective = [0, 0, 0, 1];
}
var translate = m3d[3].slice(0, 3);
var row = [];
row.push(m3d[0].slice(0, 3));
var scale = [];
scale.push(length(row[0]));
row[0] = normalize(row[0]);
var skew = [];
row.push(m3d[1].slice(0, 3));
skew.push(dot(row[0], row[1]));
row[1] = combine(row[1], row[0], 1.0, -skew[0]);
scale.push(length(row[1]));
row[1] = normalize(row[1]);
skew[0] /= scale[1];
row.push(m3d[2].slice(0, 3));
skew.push(dot(row[0], row[2]));
row[2] = combine(row[2], row[0], 1.0, -skew[1]);
skew.push(dot(row[1], row[2]));
row[2] = combine(row[2], row[1], 1.0, -skew[2]);
scale.push(length(row[2]));
row[2] = normalize(row[2]);
skew[1] /= scale[2];
skew[2] /= scale[2];
var pdum3 = cross(row[1], row[2]);
if (dot(row[0], pdum3) < 0) {
for (var i = 0; i < 3; i++) {
scale[i] *= -1;
row[i][0] *= -1;
row[i][1] *= -1;
row[i][2] *= -1;
}
}
var t = row[0][0] + row[1][1] + row[2][2] + 1;
var s;
var quaternion;
if (t > 1e-4) {
s = 0.5 / Math.sqrt(t);
quaternion = [
(row[2][1] - row[1][2]) * s,
(row[0][2] - row[2][0]) * s,
(row[1][0] - row[0][1]) * s,
0.25 / s
];
} else if (row[0][0] > row[1][1] && row[0][0] > row[2][2]) {
s = Math.sqrt(1 + row[0][0] - row[1][1] - row[2][2]) * 2.0;
quaternion = [
0.25 * s,
(row[0][1] + row[1][0]) / s,
(row[0][2] + row[2][0]) / s,
(row[2][1] - row[1][2]) / s
];
} else if (row[1][1] > row[2][2]) {
s = Math.sqrt(1.0 + row[1][1] - row[0][0] - row[2][2]) * 2.0;
quaternion = [
(row[0][1] + row[1][0]) / s,
0.25 * s,
(row[1][2] + row[2][1]) / s,
(row[0][2] - row[2][0]) / s
];
} else {
s = Math.sqrt(1.0 + row[2][2] - row[0][0] - row[1][1]) * 2.0;
quaternion = [
(row[0][2] + row[2][0]) / s,
(row[1][2] + row[2][1]) / s,
0.25 * s,
(row[1][0] - row[0][1]) / s
];
}
return [translate, scale, skew, quaternion, perspective];
}
return decomposeMatrix;
})();
function dot(v1, v2) {
var result = 0;
for (var i = 0; i < v1.length; i++) {
result += v1[i] * v2[i];
}
return result;
}
function multiplyMatrices(a, b) {
return [
a[0] * b[0] + a[4] * b[1] + a[8] * b[2] + a[12] * b[3],
a[1] * b[0] + a[5] * b[1] + a[9] * b[2] + a[13] * b[3],
a[2] * b[0] + a[6] * b[1] + a[10] * b[2] + a[14] * b[3],
a[3] * b[0] + a[7] * b[1] + a[11] * b[2] + a[15] * b[3],
a[0] * b[4] + a[4] * b[5] + a[8] * b[6] + a[12] * b[7],
a[1] * b[4] + a[5] * b[5] + a[9] * b[6] + a[13] * b[7],
a[2] * b[4] + a[6] * b[5] + a[10] * b[6] + a[14] * b[7],
a[3] * b[4] + a[7] * b[5] + a[11] * b[6] + a[15] * b[7],
a[0] * b[8] + a[4] * b[9] + a[8] * b[10] + a[12] * b[11],
a[1] * b[8] + a[5] * b[9] + a[9] * b[10] + a[13] * b[11],
a[2] * b[8] + a[6] * b[9] + a[10] * b[10] + a[14] * b[11],
a[3] * b[8] + a[7] * b[9] + a[11] * b[10] + a[15] * b[11],
a[0] * b[12] + a[4] * b[13] + a[8] * b[14] + a[12] * b[15],
a[1] * b[12] + a[5] * b[13] + a[9] * b[14] + a[13] * b[15],
a[2] * b[12] + a[6] * b[13] + a[10] * b[14] + a[14] * b[15],
a[3] * b[12] + a[7] * b[13] + a[11] * b[14] + a[15] * b[15]
];
}
function toRadians(arg) {
var rads = arg.rad || 0;
var degs = arg.deg || 0;
var grads = arg.grad || 0;
var turns = arg.turn || 0;
var angle = (degs / 360 + grads / 400 + turns) * (2 * Math.PI) + rads;
return angle;
}
function convertItemToMatrix(item) {
switch (item.t) {
case 'rotatex':
var angle = toRadians(item.d[0]);
return [1, 0, 0, 0,
0, Math.cos(angle), Math.sin(angle), 0,
0, -Math.sin(angle), Math.cos(angle), 0,
0, 0, 0, 1];
case 'rotatey':
var angle = toRadians(item.d[0]);
return [Math.cos(angle), 0, -Math.sin(angle), 0,
0, 1, 0, 0,
Math.sin(angle), 0, Math.cos(angle), 0,
0, 0, 0, 1];
case 'rotate':
case 'rotatez':
var angle = toRadians(item.d[0]);
return [Math.cos(angle), Math.sin(angle), 0, 0,
-Math.sin(angle), Math.cos(angle), 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'rotate3d':
var x = item.d[0];
var y = item.d[1];
var z = item.d[2];
var angle = toRadians(item.d[3]);
var sqrLength = x * x + y * y + z * z;
if (sqrLength === 0) {
x = 1;
y = 0;
z = 0;
} else if (sqrLength !== 1) {
var length = Math.sqrt(sqrLength);
x /= length;
y /= length;
z /= length;
}
var s = Math.sin(angle / 2);
var sc = s * Math.cos(angle / 2);
var sq = s * s;
return [
1 - 2 * (y * y + z * z) * sq,
2 * (x * y * sq + z * sc),
2 * (x * z * sq - y * sc),
0,
2 * (x * y * sq - z * sc),
1 - 2 * (x * x + z * z) * sq,
2 * (y * z * sq + x * sc),
0,
2 * (x * z * sq + y * sc),
2 * (y * z * sq - x * sc),
1 - 2 * (x * x + y * y) * sq,
0,
0, 0, 0, 1
];
case 'scale':
return [item.d[0], 0, 0, 0,
0, item.d[1], 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'scalex':
return [item.d[0], 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'scaley':
return [1, 0, 0, 0,
0, item.d[0], 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'scalez':
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, item.d[0], 0,
0, 0, 0, 1];
case 'scale3d':
return [item.d[0], 0, 0, 0,
0, item.d[1], 0, 0,
0, 0, item.d[2], 0,
0, 0, 0, 1];
case 'skew':
var xAngle = toRadians(item.d[0]);
var yAngle = toRadians(item.d[1]);
return [1, Math.tan(yAngle), 0, 0,
Math.tan(xAngle), 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'skewx':
var angle = toRadians(item.d[0]);
return [1, 0, 0, 0,
Math.tan(angle), 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'skewy':
var angle = toRadians(item.d[0]);
return [1, Math.tan(angle), 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
case 'translate':
var x = item.d[0].px || 0;
var y = item.d[1].px || 0;
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
x, y, 0, 1];
case 'translatex':
var x = item.d[0].px || 0;
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
x, 0, 0, 1];
case 'translatey':
var y = item.d[0].px || 0;
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, y, 0, 1];
case 'translatez':
var z = item.d[0].px || 0;
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, z, 1];
case 'translate3d':
var x = item.d[0].px || 0;
var y = item.d[1].px || 0;
var z = item.d[2].px || 0;
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
x, y, z, 1];
case 'perspective':
var p = item.d[0].px ? (-1 / item.d[0].px) : 0;
return [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, p,
0, 0, 0, 1];
case 'matrix':
return [item.d[0], item.d[1], 0, 0,
item.d[2], item.d[3], 0, 0,
0, 0, 1, 0,
item.d[4], item.d[5], 0, 1];
case 'matrix3d':
return item.d;
default:
WEB_ANIMATIONS_TESTING && console.assert(false, 'Transform item type ' + item.t +
' conversion to matrix not yet implemented.');
}
}
function convertToMatrix(transformList) {
if (transformList.length === 0) {
return [1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1];
}
return transformList.map(convertItemToMatrix).reduce(multiplyMatrices);
}
function makeMatrixDecomposition(transformList) {
return [decomposeMatrix(convertToMatrix(transformList))];
}
scope.dot = dot;
scope.makeMatrixDecomposition = makeMatrixDecomposition;
scope.transformListToMatrix = convertToMatrix;
})(webAnimations1, webAnimationsTesting);
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