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447 lines
13 KiB
JavaScript
447 lines
13 KiB
JavaScript
// Copyright 2014 Google Inc. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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(function(scope, testing) {
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var decomposeMatrix = (function() {
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function determinant(m) {
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return m[0][0] * m[1][1] * m[2][2] +
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m[1][0] * m[2][1] * m[0][2] +
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m[2][0] * m[0][1] * m[1][2] -
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m[0][2] * m[1][1] * m[2][0] -
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m[1][2] * m[2][1] * m[0][0] -
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m[2][2] * m[0][1] * m[1][0];
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}
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// from Wikipedia:
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//
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// [A B]^-1 = [A^-1 + A^-1B(D - CA^-1B)^-1CA^-1 -A^-1B(D - CA^-1B)^-1]
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// [C D] [-(D - CA^-1B)^-1CA^-1 (D - CA^-1B)^-1 ]
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//
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// Therefore
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//
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// [A [0]]^-1 = [A^-1 [0]]
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// [C 1 ] [ -CA^-1 1 ]
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function inverse(m) {
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var iDet = 1 / determinant(m);
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var a = m[0][0], b = m[0][1], c = m[0][2];
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var d = m[1][0], e = m[1][1], f = m[1][2];
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var g = m[2][0], h = m[2][1], k = m[2][2];
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var Ainv = [
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[(e * k - f * h) * iDet, (c * h - b * k) * iDet,
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(b * f - c * e) * iDet, 0],
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[(f * g - d * k) * iDet, (a * k - c * g) * iDet,
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(c * d - a * f) * iDet, 0],
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[(d * h - e * g) * iDet, (g * b - a * h) * iDet,
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(a * e - b * d) * iDet, 0]
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];
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var lastRow = [];
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for (var i = 0; i < 3; i++) {
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var val = 0;
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for (var j = 0; j < 3; j++) {
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val += m[3][j] * Ainv[j][i];
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}
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lastRow.push(val);
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}
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lastRow.push(1);
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Ainv.push(lastRow);
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return Ainv;
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}
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function transposeMatrix4(m) {
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return [[m[0][0], m[1][0], m[2][0], m[3][0]],
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[m[0][1], m[1][1], m[2][1], m[3][1]],
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[m[0][2], m[1][2], m[2][2], m[3][2]],
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[m[0][3], m[1][3], m[2][3], m[3][3]]];
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}
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function multVecMatrix(v, m) {
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var result = [];
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for (var i = 0; i < 4; i++) {
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var val = 0;
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for (var j = 0; j < 4; j++) {
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val += v[j] * m[j][i];
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}
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result.push(val);
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}
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return result;
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}
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function normalize(v) {
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var len = length(v);
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return [v[0] / len, v[1] / len, v[2] / len];
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}
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function length(v) {
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return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
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}
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function combine(v1, v2, v1s, v2s) {
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return [v1s * v1[0] + v2s * v2[0], v1s * v1[1] + v2s * v2[1],
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v1s * v1[2] + v2s * v2[2]];
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}
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function cross(v1, v2) {
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return [v1[1] * v2[2] - v1[2] * v2[1],
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v1[2] * v2[0] - v1[0] * v2[2],
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v1[0] * v2[1] - v1[1] * v2[0]];
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}
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function decomposeMatrix(matrix) {
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var m3d = [
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matrix.slice(0, 4),
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matrix.slice(4, 8),
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matrix.slice(8, 12),
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matrix.slice(12, 16)
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];
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// skip normalization step as m3d[3][3] should always be 1
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if (m3d[3][3] !== 1) {
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return null;
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}
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var perspectiveMatrix = [];
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for (var i = 0; i < 4; i++) {
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perspectiveMatrix.push(m3d[i].slice());
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}
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for (var i = 0; i < 3; i++) {
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perspectiveMatrix[i][3] = 0;
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}
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if (determinant(perspectiveMatrix) === 0) {
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return false;
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}
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var rhs = [];
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var perspective;
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if (m3d[0][3] || m3d[1][3] || m3d[2][3]) {
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rhs.push(m3d[0][3]);
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rhs.push(m3d[1][3]);
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rhs.push(m3d[2][3]);
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rhs.push(m3d[3][3]);
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var inversePerspectiveMatrix = inverse(perspectiveMatrix);
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var transposedInversePerspectiveMatrix =
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transposeMatrix4(inversePerspectiveMatrix);
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perspective = multVecMatrix(rhs, transposedInversePerspectiveMatrix);
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} else {
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perspective = [0, 0, 0, 1];
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}
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var translate = m3d[3].slice(0, 3);
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var row = [];
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row.push(m3d[0].slice(0, 3));
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var scale = [];
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scale.push(length(row[0]));
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row[0] = normalize(row[0]);
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var skew = [];
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row.push(m3d[1].slice(0, 3));
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skew.push(dot(row[0], row[1]));
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row[1] = combine(row[1], row[0], 1.0, -skew[0]);
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scale.push(length(row[1]));
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row[1] = normalize(row[1]);
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skew[0] /= scale[1];
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row.push(m3d[2].slice(0, 3));
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skew.push(dot(row[0], row[2]));
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row[2] = combine(row[2], row[0], 1.0, -skew[1]);
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skew.push(dot(row[1], row[2]));
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row[2] = combine(row[2], row[1], 1.0, -skew[2]);
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scale.push(length(row[2]));
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row[2] = normalize(row[2]);
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skew[1] /= scale[2];
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skew[2] /= scale[2];
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var pdum3 = cross(row[1], row[2]);
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if (dot(row[0], pdum3) < 0) {
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for (var i = 0; i < 3; i++) {
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scale[i] *= -1;
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row[i][0] *= -1;
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row[i][1] *= -1;
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row[i][2] *= -1;
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}
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}
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var t = row[0][0] + row[1][1] + row[2][2] + 1;
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var s;
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var quaternion;
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if (t > 1e-4) {
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s = 0.5 / Math.sqrt(t);
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quaternion = [
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(row[2][1] - row[1][2]) * s,
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(row[0][2] - row[2][0]) * s,
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(row[1][0] - row[0][1]) * s,
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0.25 / s
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];
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} else if (row[0][0] > row[1][1] && row[0][0] > row[2][2]) {
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s = Math.sqrt(1 + row[0][0] - row[1][1] - row[2][2]) * 2.0;
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quaternion = [
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0.25 * s,
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(row[0][1] + row[1][0]) / s,
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(row[0][2] + row[2][0]) / s,
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(row[2][1] - row[1][2]) / s
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];
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} else if (row[1][1] > row[2][2]) {
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s = Math.sqrt(1.0 + row[1][1] - row[0][0] - row[2][2]) * 2.0;
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quaternion = [
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(row[0][1] + row[1][0]) / s,
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0.25 * s,
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(row[1][2] + row[2][1]) / s,
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(row[0][2] - row[2][0]) / s
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];
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} else {
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s = Math.sqrt(1.0 + row[2][2] - row[0][0] - row[1][1]) * 2.0;
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quaternion = [
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(row[0][2] + row[2][0]) / s,
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(row[1][2] + row[2][1]) / s,
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0.25 * s,
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(row[1][0] - row[0][1]) / s
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];
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}
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return [translate, scale, skew, quaternion, perspective];
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}
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return decomposeMatrix;
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})();
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function dot(v1, v2) {
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var result = 0;
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for (var i = 0; i < v1.length; i++) {
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result += v1[i] * v2[i];
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}
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return result;
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}
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function multiplyMatrices(a, b) {
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return [
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a[0] * b[0] + a[4] * b[1] + a[8] * b[2] + a[12] * b[3],
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a[1] * b[0] + a[5] * b[1] + a[9] * b[2] + a[13] * b[3],
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a[2] * b[0] + a[6] * b[1] + a[10] * b[2] + a[14] * b[3],
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a[3] * b[0] + a[7] * b[1] + a[11] * b[2] + a[15] * b[3],
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a[0] * b[4] + a[4] * b[5] + a[8] * b[6] + a[12] * b[7],
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a[1] * b[4] + a[5] * b[5] + a[9] * b[6] + a[13] * b[7],
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a[2] * b[4] + a[6] * b[5] + a[10] * b[6] + a[14] * b[7],
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a[3] * b[4] + a[7] * b[5] + a[11] * b[6] + a[15] * b[7],
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a[0] * b[8] + a[4] * b[9] + a[8] * b[10] + a[12] * b[11],
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a[1] * b[8] + a[5] * b[9] + a[9] * b[10] + a[13] * b[11],
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a[2] * b[8] + a[6] * b[9] + a[10] * b[10] + a[14] * b[11],
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a[3] * b[8] + a[7] * b[9] + a[11] * b[10] + a[15] * b[11],
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a[0] * b[12] + a[4] * b[13] + a[8] * b[14] + a[12] * b[15],
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a[1] * b[12] + a[5] * b[13] + a[9] * b[14] + a[13] * b[15],
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a[2] * b[12] + a[6] * b[13] + a[10] * b[14] + a[14] * b[15],
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a[3] * b[12] + a[7] * b[13] + a[11] * b[14] + a[15] * b[15]
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];
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}
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function convertItemToMatrix(item) {
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switch (item.t) {
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case 'rotatex':
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var rads = item.d[0].rad || 0;
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var degs = item.d[0].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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return [1, 0, 0, 0,
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0, Math.cos(angle), Math.sin(angle), 0,
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0, -Math.sin(angle), Math.cos(angle), 0,
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0, 0, 0, 1];
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case 'rotatey':
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var rads = item.d[0].rad || 0;
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var degs = item.d[0].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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return [Math.cos(angle), 0, -Math.sin(angle), 0,
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0, 1, 0, 0,
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Math.sin(angle), 0, Math.cos(angle), 0,
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0, 0, 0, 1];
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case 'rotate':
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case 'rotatez':
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var rads = item.d[0].rad || 0;
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var degs = item.d[0].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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return [Math.cos(angle), Math.sin(angle), 0, 0,
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-Math.sin(angle), Math.cos(angle), 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1];
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case 'rotate3d':
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var x = item.d[0];
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var y = item.d[1];
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var z = item.d[2];
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var rads = item.d[3].rad || 0;
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var degs = item.d[3].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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var sqrLength = x * x + y * y + z * z;
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if (sqrLength === 0) {
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x = 1;
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y = 0;
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z = 0;
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} else if (sqrLength !== 1) {
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var length = Math.sqrt(sqrLength);
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x /= length;
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y /= length;
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z /= length;
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}
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var s = Math.sin(angle / 2);
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var sc = s * Math.cos(angle / 2);
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var sq = s * s;
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return [
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1 - 2 * (y * y + z * z) * sq,
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2 * (x * y * sq + z * sc),
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2 * (x * z * sq - y * sc),
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0,
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2 * (x * y * sq - z * sc),
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1 - 2 * (x * x + z * z) * sq,
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2 * (y * z * sq + x * sc),
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0,
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2 * (x * z * sq + y * sc),
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2 * (y * z * sq - x * sc),
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1 - 2 * (x * x + y * y) * sq,
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0,
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0, 0, 0, 1
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];
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case 'scale':
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return [item.d[0], 0, 0, 0,
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0, item.d[1], 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1];
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case 'scalex':
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return [item.d[0], 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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case 'scaley':
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return [1, 0, 0, 0,
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0, item.d[0], 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1];
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case 'scalez':
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return [1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, item.d[0], 0,
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0, 0, 0, 1];
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case 'scale3d':
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return [item.d[0], 0, 0, 0,
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0, item.d[1], 0, 0,
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0, 0, item.d[2], 0,
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0, 0, 0, 1];
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case 'skew':
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var xDegs = item.d[0].deg || 0;
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var xRads = item.d[0].rad || 0;
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var yDegs = item.d[1].deg || 0;
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var yRads = item.d[1].rad || 0;
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var xAngle = (xDegs * Math.PI / 180) + xRads;
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var yAngle = (yDegs * Math.PI / 180) + yRads;
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return [1, Math.tan(yAngle), 0, 0,
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Math.tan(xAngle), 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1];
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case 'skewx':
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var rads = item.d[0].rad || 0;
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var degs = item.d[0].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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return [1, 0, 0, 0,
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Math.tan(angle), 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1];
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case 'skewy':
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var rads = item.d[0].rad || 0;
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var degs = item.d[0].deg || 0;
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var angle = (degs * Math.PI / 180) + rads;
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return [1, Math.tan(angle), 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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case 'translate':
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var x = item.d[0].px || 0;
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var y = item.d[1].px || 0;
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return [1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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x, y, 0, 1];
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case 'translatex':
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var x = item.d[0].px || 0;
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return [1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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x, 0, 0, 1];
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case 'translatey':
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var y = item.d[0].px || 0;
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return [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, y, 0, 1];
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case 'translatez':
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var z = item.d[0].px || 0;
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return [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, z, 1];
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case 'translate3d':
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var x = item.d[0].px || 0;
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var y = item.d[1].px || 0;
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var z = item.d[2].px || 0;
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return [1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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x, y, z, 1];
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case 'perspective':
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var p = item.d[0].px ? (-1 / item.d[0].px) : 0;
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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, p,
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0, 0, 0, 1];
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case 'matrix':
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return [item.d[0], item.d[1], 0, 0,
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item.d[2], item.d[3], 0, 0,
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0, 0, 1, 0,
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item.d[4], item.d[5], 0, 1];
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case 'matrix3d':
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return item.d;
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default:
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WEB_ANIMATIONS_TESTING && console.assert(false, 'Transform item type ' + item.t +
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' conversion to matrix not yet implemented.');
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}
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}
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function convertToMatrix(transformList) {
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if (transformList.length === 0) {
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return [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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return transformList.map(convertItemToMatrix).reduce(multiplyMatrices);
|
|
}
|
|
|
|
function makeMatrixDecomposition(transformList) {
|
|
return [decomposeMatrix(convertToMatrix(transformList))];
|
|
}
|
|
|
|
scope.dot = dot;
|
|
scope.makeMatrixDecomposition = makeMatrixDecomposition;
|
|
|
|
})(webAnimations1, webAnimationsTesting);
|