| // Copyright 2013 The Closure Library Authors. 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. |
| |
| |
| ////////////////////////// NOTE ABOUT EDITING THIS FILE /////////////////////// |
| // // |
| // Any edits to this file must be applied to mat4f.js by running: // |
| // swap_type.sh mat4d.js > mat4f.js // |
| // // |
| ////////////////////////// NOTE ABOUT EDITING THIS FILE /////////////////////// |
| |
| |
| /** |
| * @fileoverview Provides functions for operating on 4x4 double (64bit) |
| * matrices. The matrices are stored in column-major order. |
| * |
| * The last parameter will typically be the output matrix and an |
| * object can be both an input and output parameter to all methods except |
| * where noted. |
| * |
| * See the README for notes about the design and structure of the API |
| * (especially related to performance). |
| * |
| */ |
| goog.provide('goog.vec.mat4d'); |
| goog.provide('goog.vec.mat4d.Type'); |
| |
| goog.require('goog.vec'); |
| goog.require('goog.vec.vec3d'); |
| goog.require('goog.vec.vec4d'); |
| |
| |
| /** @typedef {goog.vec.Float64} */ goog.vec.mat4d.Type; |
| |
| |
| /** |
| * Creates a mat4d with all elements initialized to zero. |
| * |
| * @return {!goog.vec.mat4d.Type} The new mat4d. |
| */ |
| goog.vec.mat4d.create = function() { |
| return new Float64Array(16); |
| }; |
| |
| |
| /** |
| * Initializes the matrix from the set of values. Note the values supplied are |
| * in column major order. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the |
| * values. |
| * @param {number} v00 The values at (0, 0). |
| * @param {number} v10 The values at (1, 0). |
| * @param {number} v20 The values at (2, 0). |
| * @param {number} v30 The values at (3, 0). |
| * @param {number} v01 The values at (0, 1). |
| * @param {number} v11 The values at (1, 1). |
| * @param {number} v21 The values at (2, 1). |
| * @param {number} v31 The values at (3, 1). |
| * @param {number} v02 The values at (0, 2). |
| * @param {number} v12 The values at (1, 2). |
| * @param {number} v22 The values at (2, 2). |
| * @param {number} v32 The values at (3, 2). |
| * @param {number} v03 The values at (0, 3). |
| * @param {number} v13 The values at (1, 3). |
| * @param {number} v23 The values at (2, 3). |
| * @param {number} v33 The values at (3, 3). |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setFromValues = function( |
| mat, v00, v10, v20, v30, v01, v11, v21, v31, v02, v12, v22, v32, |
| v03, v13, v23, v33) { |
| mat[0] = v00; |
| mat[1] = v10; |
| mat[2] = v20; |
| mat[3] = v30; |
| mat[4] = v01; |
| mat[5] = v11; |
| mat[6] = v21; |
| mat[7] = v31; |
| mat[8] = v02; |
| mat[9] = v12; |
| mat[10] = v22; |
| mat[11] = v32; |
| mat[12] = v03; |
| mat[13] = v13; |
| mat[14] = v23; |
| mat[15] = v33; |
| return mat; |
| }; |
| |
| |
| /** |
| * Initializes mat4d mat from mat4d src. |
| * |
| * @param {goog.vec.mat4d.Type} mat The destination matrix. |
| * @param {goog.vec.mat4d.Type} src The source matrix. |
| * @return {!goog.vec.mat4d.Type} Return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setFromMat4d = function(mat, src) { |
| mat[0] = src[0]; |
| mat[1] = src[1]; |
| mat[2] = src[2]; |
| mat[3] = src[3]; |
| mat[4] = src[4]; |
| mat[5] = src[5]; |
| mat[6] = src[6]; |
| mat[7] = src[7]; |
| mat[8] = src[8]; |
| mat[9] = src[9]; |
| mat[10] = src[10]; |
| mat[11] = src[11]; |
| mat[12] = src[12]; |
| mat[13] = src[13]; |
| mat[14] = src[14]; |
| mat[15] = src[15]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Initializes mat4d mat from mat4f src (typed as a Float32Array to |
| * avoid circular goog.requires). |
| * |
| * @param {goog.vec.mat4d.Type} mat The destination matrix. |
| * @param {Float32Array} src The source matrix. |
| * @return {!goog.vec.mat4d.Type} Return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setFromMat4f = function(mat, src) { |
| mat[0] = src[0]; |
| mat[1] = src[1]; |
| mat[2] = src[2]; |
| mat[3] = src[3]; |
| mat[4] = src[4]; |
| mat[5] = src[5]; |
| mat[6] = src[6]; |
| mat[7] = src[7]; |
| mat[8] = src[8]; |
| mat[9] = src[9]; |
| mat[10] = src[10]; |
| mat[11] = src[11]; |
| mat[12] = src[12]; |
| mat[13] = src[13]; |
| mat[14] = src[14]; |
| mat[15] = src[15]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Initializes mat4d mat from Array src. |
| * |
| * @param {goog.vec.mat4d.Type} mat The destination matrix. |
| * @param {Array<number>} src The source matrix. |
| * @return {!goog.vec.mat4d.Type} Return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setFromArray = function(mat, src) { |
| mat[0] = src[0]; |
| mat[1] = src[1]; |
| mat[2] = src[2]; |
| mat[3] = src[3]; |
| mat[4] = src[4]; |
| mat[5] = src[5]; |
| mat[6] = src[6]; |
| mat[7] = src[7]; |
| mat[8] = src[8]; |
| mat[9] = src[9]; |
| mat[10] = src[10]; |
| mat[11] = src[11]; |
| mat[12] = src[12]; |
| mat[13] = src[13]; |
| mat[14] = src[14]; |
| mat[15] = src[15]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the element at the requested row and column. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix containing the value to |
| * retrieve. |
| * @param {number} row The row index. |
| * @param {number} column The column index. |
| * @return {number} The element value at the requested row, column indices. |
| */ |
| goog.vec.mat4d.getElement = function(mat, row, column) { |
| return mat[row + column * 4]; |
| }; |
| |
| |
| /** |
| * Sets the element at the requested row and column. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix containing the value to |
| * retrieve. |
| * @param {number} row The row index. |
| * @param {number} column The column index. |
| * @param {number} value The value to set at the requested row, column. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setElement = function(mat, row, column, value) { |
| mat[row + column * 4] = value; |
| return mat; |
| }; |
| |
| |
| /** |
| * Sets the diagonal values of the matrix from the given values. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {number} v00 The values for (0, 0). |
| * @param {number} v11 The values for (1, 1). |
| * @param {number} v22 The values for (2, 2). |
| * @param {number} v33 The values for (3, 3). |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setDiagonalValues = function(mat, v00, v11, v22, v33) { |
| mat[0] = v00; |
| mat[5] = v11; |
| mat[10] = v22; |
| mat[15] = v33; |
| return mat; |
| }; |
| |
| |
| /** |
| * Sets the diagonal values of the matrix from the given vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {goog.vec.vec4d.Type} vec The vector containing the values. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setDiagonal = function(mat, vec) { |
| mat[0] = vec[0]; |
| mat[5] = vec[1]; |
| mat[10] = vec[2]; |
| mat[15] = vec[3]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Gets the diagonal values of the matrix into the given vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix containing the values. |
| * @param {goog.vec.vec4d.Type} vec The vector to receive the values. |
| * @param {number=} opt_diagonal Which diagonal to get. A value of 0 selects the |
| * main diagonal, a positive number selects a super diagonal and a negative |
| * number selects a sub diagonal. |
| * @return {goog.vec.vec4d.Type} return vec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.getDiagonal = function(mat, vec, opt_diagonal) { |
| if (!opt_diagonal) { |
| // This is the most common case, so we avoid the for loop. |
| vec[0] = mat[0]; |
| vec[1] = mat[5]; |
| vec[2] = mat[10]; |
| vec[3] = mat[15]; |
| } else { |
| var offset = opt_diagonal > 0 ? 4 * opt_diagonal : -opt_diagonal; |
| for (var i = 0; i < 4 - Math.abs(opt_diagonal); i++) { |
| vec[i] = mat[offset + 5 * i]; |
| } |
| } |
| return vec; |
| }; |
| |
| |
| /** |
| * Sets the specified column with the supplied values. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to recieve the values. |
| * @param {number} column The column index to set the values on. |
| * @param {number} v0 The value for row 0. |
| * @param {number} v1 The value for row 1. |
| * @param {number} v2 The value for row 2. |
| * @param {number} v3 The value for row 3. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setColumnValues = function(mat, column, v0, v1, v2, v3) { |
| var i = column * 4; |
| mat[i] = v0; |
| mat[i + 1] = v1; |
| mat[i + 2] = v2; |
| mat[i + 3] = v3; |
| return mat; |
| }; |
| |
| |
| /** |
| * Sets the specified column with the value from the supplied vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {number} column The column index to set the values on. |
| * @param {goog.vec.vec4d.Type} vec The vector of elements for the column. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setColumn = function(mat, column, vec) { |
| var i = column * 4; |
| mat[i] = vec[0]; |
| mat[i + 1] = vec[1]; |
| mat[i + 2] = vec[2]; |
| mat[i + 3] = vec[3]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the specified column from the matrix into the given vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the values. |
| * @param {number} column The column to get the values from. |
| * @param {goog.vec.vec4d.Type} vec The vector of elements to |
| * receive the column. |
| * @return {!goog.vec.vec4d.Type} return vec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.getColumn = function(mat, column, vec) { |
| var i = column * 4; |
| vec[0] = mat[i]; |
| vec[1] = mat[i + 1]; |
| vec[2] = mat[i + 2]; |
| vec[3] = mat[i + 3]; |
| return vec; |
| }; |
| |
| |
| /** |
| * Sets the columns of the matrix from the given vectors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {goog.vec.vec4d.Type} vec0 The values for column 0. |
| * @param {goog.vec.vec4d.Type} vec1 The values for column 1. |
| * @param {goog.vec.vec4d.Type} vec2 The values for column 2. |
| * @param {goog.vec.vec4d.Type} vec3 The values for column 3. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setColumns = function(mat, vec0, vec1, vec2, vec3) { |
| mat[0] = vec0[0]; |
| mat[1] = vec0[1]; |
| mat[2] = vec0[2]; |
| mat[3] = vec0[3]; |
| mat[4] = vec1[0]; |
| mat[5] = vec1[1]; |
| mat[6] = vec1[2]; |
| mat[7] = vec1[3]; |
| mat[8] = vec2[0]; |
| mat[9] = vec2[1]; |
| mat[10] = vec2[2]; |
| mat[11] = vec2[3]; |
| mat[12] = vec3[0]; |
| mat[13] = vec3[1]; |
| mat[14] = vec3[2]; |
| mat[15] = vec3[3]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the column values from the given matrix into the given vectors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the columns. |
| * @param {goog.vec.vec4d.Type} vec0 The vector to receive column 0. |
| * @param {goog.vec.vec4d.Type} vec1 The vector to receive column 1. |
| * @param {goog.vec.vec4d.Type} vec2 The vector to receive column 2. |
| * @param {goog.vec.vec4d.Type} vec3 The vector to receive column 3. |
| */ |
| goog.vec.mat4d.getColumns = function(mat, vec0, vec1, vec2, vec3) { |
| vec0[0] = mat[0]; |
| vec0[1] = mat[1]; |
| vec0[2] = mat[2]; |
| vec0[3] = mat[3]; |
| vec1[0] = mat[4]; |
| vec1[1] = mat[5]; |
| vec1[2] = mat[6]; |
| vec1[3] = mat[7]; |
| vec2[0] = mat[8]; |
| vec2[1] = mat[9]; |
| vec2[2] = mat[10]; |
| vec2[3] = mat[11]; |
| vec3[0] = mat[12]; |
| vec3[1] = mat[13]; |
| vec3[2] = mat[14]; |
| vec3[3] = mat[15]; |
| }; |
| |
| |
| /** |
| * Sets the row values from the supplied values. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {number} row The index of the row to receive the values. |
| * @param {number} v0 The value for column 0. |
| * @param {number} v1 The value for column 1. |
| * @param {number} v2 The value for column 2. |
| * @param {number} v3 The value for column 3. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setRowValues = function(mat, row, v0, v1, v2, v3) { |
| mat[row] = v0; |
| mat[row + 4] = v1; |
| mat[row + 8] = v2; |
| mat[row + 12] = v3; |
| return mat; |
| }; |
| |
| |
| /** |
| * Sets the row values from the supplied vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the row values. |
| * @param {number} row The index of the row. |
| * @param {goog.vec.vec4d.Type} vec The vector containing the values. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setRow = function(mat, row, vec) { |
| mat[row] = vec[0]; |
| mat[row + 4] = vec[1]; |
| mat[row + 8] = vec[2]; |
| mat[row + 12] = vec[3]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the row values into the given vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the values. |
| * @param {number} row The index of the row supplying the values. |
| * @param {goog.vec.vec4d.Type} vec The vector to receive the row. |
| * @return {!goog.vec.vec4d.Type} return vec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.getRow = function(mat, row, vec) { |
| vec[0] = mat[row]; |
| vec[1] = mat[row + 4]; |
| vec[2] = mat[row + 8]; |
| vec[3] = mat[row + 12]; |
| return vec; |
| }; |
| |
| |
| /** |
| * Sets the rows of the matrix from the supplied vectors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to receive the values. |
| * @param {goog.vec.vec4d.Type} vec0 The values for row 0. |
| * @param {goog.vec.vec4d.Type} vec1 The values for row 1. |
| * @param {goog.vec.vec4d.Type} vec2 The values for row 2. |
| * @param {goog.vec.vec4d.Type} vec3 The values for row 3. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.setRows = function(mat, vec0, vec1, vec2, vec3) { |
| mat[0] = vec0[0]; |
| mat[1] = vec1[0]; |
| mat[2] = vec2[0]; |
| mat[3] = vec3[0]; |
| mat[4] = vec0[1]; |
| mat[5] = vec1[1]; |
| mat[6] = vec2[1]; |
| mat[7] = vec3[1]; |
| mat[8] = vec0[2]; |
| mat[9] = vec1[2]; |
| mat[10] = vec2[2]; |
| mat[11] = vec3[2]; |
| mat[12] = vec0[3]; |
| mat[13] = vec1[3]; |
| mat[14] = vec2[3]; |
| mat[15] = vec3[3]; |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the rows of the matrix into the supplied vectors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to supply the values. |
| * @param {goog.vec.vec4d.Type} vec0 The vector to receive row 0. |
| * @param {goog.vec.vec4d.Type} vec1 The vector to receive row 1. |
| * @param {goog.vec.vec4d.Type} vec2 The vector to receive row 2. |
| * @param {goog.vec.vec4d.Type} vec3 The vector to receive row 3. |
| */ |
| goog.vec.mat4d.getRows = function(mat, vec0, vec1, vec2, vec3) { |
| vec0[0] = mat[0]; |
| vec1[0] = mat[1]; |
| vec2[0] = mat[2]; |
| vec3[0] = mat[3]; |
| vec0[1] = mat[4]; |
| vec1[1] = mat[5]; |
| vec2[1] = mat[6]; |
| vec3[1] = mat[7]; |
| vec0[2] = mat[8]; |
| vec1[2] = mat[9]; |
| vec2[2] = mat[10]; |
| vec3[2] = mat[11]; |
| vec0[3] = mat[12]; |
| vec1[3] = mat[13]; |
| vec2[3] = mat[14]; |
| vec3[3] = mat[15]; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix the zero matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @return {!goog.vec.mat4d.Type} return mat so operations can be chained. |
| */ |
| goog.vec.mat4d.makeZero = function(mat) { |
| mat[0] = 0; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = 0; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = 0; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 0; |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix the identity matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @return {!goog.vec.mat4d.Type} return mat so operations can be chained. |
| */ |
| goog.vec.mat4d.makeIdentity = function(mat) { |
| mat[0] = 1; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = 1; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = 1; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| return mat; |
| }; |
| |
| |
| /** |
| * Performs a per-component addition of the matrix mat0 and mat1, storing |
| * the result into resultMat. |
| * |
| * @param {goog.vec.mat4d.Type} mat0 The first addend. |
| * @param {goog.vec.mat4d.Type} mat1 The second addend. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to |
| * receive the results (may be either mat0 or mat1). |
| * @return {!goog.vec.mat4d.Type} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.addMat = function(mat0, mat1, resultMat) { |
| resultMat[0] = mat0[0] + mat1[0]; |
| resultMat[1] = mat0[1] + mat1[1]; |
| resultMat[2] = mat0[2] + mat1[2]; |
| resultMat[3] = mat0[3] + mat1[3]; |
| resultMat[4] = mat0[4] + mat1[4]; |
| resultMat[5] = mat0[5] + mat1[5]; |
| resultMat[6] = mat0[6] + mat1[6]; |
| resultMat[7] = mat0[7] + mat1[7]; |
| resultMat[8] = mat0[8] + mat1[8]; |
| resultMat[9] = mat0[9] + mat1[9]; |
| resultMat[10] = mat0[10] + mat1[10]; |
| resultMat[11] = mat0[11] + mat1[11]; |
| resultMat[12] = mat0[12] + mat1[12]; |
| resultMat[13] = mat0[13] + mat1[13]; |
| resultMat[14] = mat0[14] + mat1[14]; |
| resultMat[15] = mat0[15] + mat1[15]; |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Performs a per-component subtraction of the matrix mat0 and mat1, |
| * storing the result into resultMat. |
| * |
| * @param {goog.vec.mat4d.Type} mat0 The minuend. |
| * @param {goog.vec.mat4d.Type} mat1 The subtrahend. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to receive |
| * the results (may be either mat0 or mat1). |
| * @return {!goog.vec.mat4d.Type} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.subMat = function(mat0, mat1, resultMat) { |
| resultMat[0] = mat0[0] - mat1[0]; |
| resultMat[1] = mat0[1] - mat1[1]; |
| resultMat[2] = mat0[2] - mat1[2]; |
| resultMat[3] = mat0[3] - mat1[3]; |
| resultMat[4] = mat0[4] - mat1[4]; |
| resultMat[5] = mat0[5] - mat1[5]; |
| resultMat[6] = mat0[6] - mat1[6]; |
| resultMat[7] = mat0[7] - mat1[7]; |
| resultMat[8] = mat0[8] - mat1[8]; |
| resultMat[9] = mat0[9] - mat1[9]; |
| resultMat[10] = mat0[10] - mat1[10]; |
| resultMat[11] = mat0[11] - mat1[11]; |
| resultMat[12] = mat0[12] - mat1[12]; |
| resultMat[13] = mat0[13] - mat1[13]; |
| resultMat[14] = mat0[14] - mat1[14]; |
| resultMat[15] = mat0[15] - mat1[15]; |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Multiplies matrix mat with the given scalar, storing the result |
| * into resultMat. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} scalar The scalar value to multiply to each element of mat. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to receive |
| * the results (may be mat). |
| * @return {!goog.vec.mat4d.Type} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multScalar = function(mat, scalar, resultMat) { |
| resultMat[0] = mat[0] * scalar; |
| resultMat[1] = mat[1] * scalar; |
| resultMat[2] = mat[2] * scalar; |
| resultMat[3] = mat[3] * scalar; |
| resultMat[4] = mat[4] * scalar; |
| resultMat[5] = mat[5] * scalar; |
| resultMat[6] = mat[6] * scalar; |
| resultMat[7] = mat[7] * scalar; |
| resultMat[8] = mat[8] * scalar; |
| resultMat[9] = mat[9] * scalar; |
| resultMat[10] = mat[10] * scalar; |
| resultMat[11] = mat[11] * scalar; |
| resultMat[12] = mat[12] * scalar; |
| resultMat[13] = mat[13] * scalar; |
| resultMat[14] = mat[14] * scalar; |
| resultMat[15] = mat[15] * scalar; |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Multiplies the two matrices mat0 and mat1 using matrix multiplication, |
| * storing the result into resultMat. |
| * |
| * @param {goog.vec.mat4d.Type} mat0 The first (left hand) matrix. |
| * @param {goog.vec.mat4d.Type} mat1 The second (right hand) matrix. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to receive |
| * the results (may be either mat0 or mat1). |
| * @return {!goog.vec.mat4d.Type} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multMat = function(mat0, mat1, resultMat) { |
| var a00 = mat0[0], a10 = mat0[1], a20 = mat0[2], a30 = mat0[3]; |
| var a01 = mat0[4], a11 = mat0[5], a21 = mat0[6], a31 = mat0[7]; |
| var a02 = mat0[8], a12 = mat0[9], a22 = mat0[10], a32 = mat0[11]; |
| var a03 = mat0[12], a13 = mat0[13], a23 = mat0[14], a33 = mat0[15]; |
| |
| var b00 = mat1[0], b10 = mat1[1], b20 = mat1[2], b30 = mat1[3]; |
| var b01 = mat1[4], b11 = mat1[5], b21 = mat1[6], b31 = mat1[7]; |
| var b02 = mat1[8], b12 = mat1[9], b22 = mat1[10], b32 = mat1[11]; |
| var b03 = mat1[12], b13 = mat1[13], b23 = mat1[14], b33 = mat1[15]; |
| |
| resultMat[0] = a00 * b00 + a01 * b10 + a02 * b20 + a03 * b30; |
| resultMat[1] = a10 * b00 + a11 * b10 + a12 * b20 + a13 * b30; |
| resultMat[2] = a20 * b00 + a21 * b10 + a22 * b20 + a23 * b30; |
| resultMat[3] = a30 * b00 + a31 * b10 + a32 * b20 + a33 * b30; |
| |
| resultMat[4] = a00 * b01 + a01 * b11 + a02 * b21 + a03 * b31; |
| resultMat[5] = a10 * b01 + a11 * b11 + a12 * b21 + a13 * b31; |
| resultMat[6] = a20 * b01 + a21 * b11 + a22 * b21 + a23 * b31; |
| resultMat[7] = a30 * b01 + a31 * b11 + a32 * b21 + a33 * b31; |
| |
| resultMat[8] = a00 * b02 + a01 * b12 + a02 * b22 + a03 * b32; |
| resultMat[9] = a10 * b02 + a11 * b12 + a12 * b22 + a13 * b32; |
| resultMat[10] = a20 * b02 + a21 * b12 + a22 * b22 + a23 * b32; |
| resultMat[11] = a30 * b02 + a31 * b12 + a32 * b22 + a33 * b32; |
| |
| resultMat[12] = a00 * b03 + a01 * b13 + a02 * b23 + a03 * b33; |
| resultMat[13] = a10 * b03 + a11 * b13 + a12 * b23 + a13 * b33; |
| resultMat[14] = a20 * b03 + a21 * b13 + a22 * b23 + a23 * b33; |
| resultMat[15] = a30 * b03 + a31 * b13 + a32 * b23 + a33 * b33; |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Transposes the given matrix mat storing the result into resultMat. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to transpose. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to receive |
| * the results (may be mat). |
| * @return {!goog.vec.mat4d.Type} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.transpose = function(mat, resultMat) { |
| if (resultMat == mat) { |
| var a10 = mat[1], a20 = mat[2], a30 = mat[3]; |
| var a21 = mat[6], a31 = mat[7]; |
| var a32 = mat[11]; |
| resultMat[1] = mat[4]; |
| resultMat[2] = mat[8]; |
| resultMat[3] = mat[12]; |
| resultMat[4] = a10; |
| resultMat[6] = mat[9]; |
| resultMat[7] = mat[13]; |
| resultMat[8] = a20; |
| resultMat[9] = a21; |
| resultMat[11] = mat[14]; |
| resultMat[12] = a30; |
| resultMat[13] = a31; |
| resultMat[14] = a32; |
| } else { |
| resultMat[0] = mat[0]; |
| resultMat[1] = mat[4]; |
| resultMat[2] = mat[8]; |
| resultMat[3] = mat[12]; |
| |
| resultMat[4] = mat[1]; |
| resultMat[5] = mat[5]; |
| resultMat[6] = mat[9]; |
| resultMat[7] = mat[13]; |
| |
| resultMat[8] = mat[2]; |
| resultMat[9] = mat[6]; |
| resultMat[10] = mat[10]; |
| resultMat[11] = mat[14]; |
| |
| resultMat[12] = mat[3]; |
| resultMat[13] = mat[7]; |
| resultMat[14] = mat[11]; |
| resultMat[15] = mat[15]; |
| } |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Computes the determinant of the matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to compute the matrix for. |
| * @return {number} The determinant of the matrix. |
| */ |
| goog.vec.mat4d.determinant = function(mat) { |
| var m00 = mat[0], m10 = mat[1], m20 = mat[2], m30 = mat[3]; |
| var m01 = mat[4], m11 = mat[5], m21 = mat[6], m31 = mat[7]; |
| var m02 = mat[8], m12 = mat[9], m22 = mat[10], m32 = mat[11]; |
| var m03 = mat[12], m13 = mat[13], m23 = mat[14], m33 = mat[15]; |
| |
| var a0 = m00 * m11 - m10 * m01; |
| var a1 = m00 * m21 - m20 * m01; |
| var a2 = m00 * m31 - m30 * m01; |
| var a3 = m10 * m21 - m20 * m11; |
| var a4 = m10 * m31 - m30 * m11; |
| var a5 = m20 * m31 - m30 * m21; |
| var b0 = m02 * m13 - m12 * m03; |
| var b1 = m02 * m23 - m22 * m03; |
| var b2 = m02 * m33 - m32 * m03; |
| var b3 = m12 * m23 - m22 * m13; |
| var b4 = m12 * m33 - m32 * m13; |
| var b5 = m22 * m33 - m32 * m23; |
| |
| return a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0; |
| }; |
| |
| |
| /** |
| * Computes the inverse of mat storing the result into resultMat. If the |
| * inverse is defined, this function returns true, false otherwise. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix to invert. |
| * @param {goog.vec.mat4d.Type} resultMat The matrix to receive |
| * the result (may be mat). |
| * @return {boolean} True if the inverse is defined. If false is returned, |
| * resultMat is not modified. |
| */ |
| goog.vec.mat4d.invert = function(mat, resultMat) { |
| var m00 = mat[0], m10 = mat[1], m20 = mat[2], m30 = mat[3]; |
| var m01 = mat[4], m11 = mat[5], m21 = mat[6], m31 = mat[7]; |
| var m02 = mat[8], m12 = mat[9], m22 = mat[10], m32 = mat[11]; |
| var m03 = mat[12], m13 = mat[13], m23 = mat[14], m33 = mat[15]; |
| |
| var a0 = m00 * m11 - m10 * m01; |
| var a1 = m00 * m21 - m20 * m01; |
| var a2 = m00 * m31 - m30 * m01; |
| var a3 = m10 * m21 - m20 * m11; |
| var a4 = m10 * m31 - m30 * m11; |
| var a5 = m20 * m31 - m30 * m21; |
| var b0 = m02 * m13 - m12 * m03; |
| var b1 = m02 * m23 - m22 * m03; |
| var b2 = m02 * m33 - m32 * m03; |
| var b3 = m12 * m23 - m22 * m13; |
| var b4 = m12 * m33 - m32 * m13; |
| var b5 = m22 * m33 - m32 * m23; |
| |
| var det = a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0; |
| if (det == 0) { |
| return false; |
| } |
| |
| var idet = 1.0 / det; |
| resultMat[0] = (m11 * b5 - m21 * b4 + m31 * b3) * idet; |
| resultMat[1] = (-m10 * b5 + m20 * b4 - m30 * b3) * idet; |
| resultMat[2] = (m13 * a5 - m23 * a4 + m33 * a3) * idet; |
| resultMat[3] = (-m12 * a5 + m22 * a4 - m32 * a3) * idet; |
| resultMat[4] = (-m01 * b5 + m21 * b2 - m31 * b1) * idet; |
| resultMat[5] = (m00 * b5 - m20 * b2 + m30 * b1) * idet; |
| resultMat[6] = (-m03 * a5 + m23 * a2 - m33 * a1) * idet; |
| resultMat[7] = (m02 * a5 - m22 * a2 + m32 * a1) * idet; |
| resultMat[8] = (m01 * b4 - m11 * b2 + m31 * b0) * idet; |
| resultMat[9] = (-m00 * b4 + m10 * b2 - m30 * b0) * idet; |
| resultMat[10] = (m03 * a4 - m13 * a2 + m33 * a0) * idet; |
| resultMat[11] = (-m02 * a4 + m12 * a2 - m32 * a0) * idet; |
| resultMat[12] = (-m01 * b3 + m11 * b1 - m21 * b0) * idet; |
| resultMat[13] = (m00 * b3 - m10 * b1 + m20 * b0) * idet; |
| resultMat[14] = (-m03 * a3 + m13 * a1 - m23 * a0) * idet; |
| resultMat[15] = (m02 * a3 - m12 * a1 + m22 * a0) * idet; |
| return true; |
| }; |
| |
| |
| /** |
| * Returns true if the components of mat0 are equal to the components of mat1. |
| * |
| * @param {goog.vec.mat4d.Type} mat0 The first matrix. |
| * @param {goog.vec.mat4d.Type} mat1 The second matrix. |
| * @return {boolean} True if the the two matrices are equivalent. |
| */ |
| goog.vec.mat4d.equals = function(mat0, mat1) { |
| return mat0.length == mat1.length && |
| mat0[0] == mat1[0] && |
| mat0[1] == mat1[1] && |
| mat0[2] == mat1[2] && |
| mat0[3] == mat1[3] && |
| mat0[4] == mat1[4] && |
| mat0[5] == mat1[5] && |
| mat0[6] == mat1[6] && |
| mat0[7] == mat1[7] && |
| mat0[8] == mat1[8] && |
| mat0[9] == mat1[9] && |
| mat0[10] == mat1[10] && |
| mat0[11] == mat1[11] && |
| mat0[12] == mat1[12] && |
| mat0[13] == mat1[13] && |
| mat0[14] == mat1[14] && |
| mat0[15] == mat1[15]; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. The input vector is multiplied against the |
| * upper 3x4 matrix omitting the projective component. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the transformation. |
| * @param {goog.vec.vec3d.Type} vec The 3 element vector to transform. |
| * @param {goog.vec.vec3d.Type} resultVec The 3 element vector to |
| * receive the results (may be vec). |
| * @return {!goog.vec.vec3d.Type} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multVec3 = function(mat, vec, resultVec) { |
| var x = vec[0], y = vec[1], z = vec[2]; |
| resultVec[0] = x * mat[0] + y * mat[4] + z * mat[8] + mat[12]; |
| resultVec[1] = x * mat[1] + y * mat[5] + z * mat[9] + mat[13]; |
| resultVec[2] = x * mat[2] + y * mat[6] + z * mat[10] + mat[14]; |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. The input vector is multiplied against the |
| * upper 3x3 matrix omitting the projective component and translation |
| * components. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the transformation. |
| * @param {goog.vec.vec3d.Type} vec The 3 element vector to transform. |
| * @param {goog.vec.vec3d.Type} resultVec The 3 element vector to |
| * receive the results (may be vec). |
| * @return {!goog.vec.vec3d.Type} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multVec3NoTranslate = function(mat, vec, resultVec) { |
| var x = vec[0], y = vec[1], z = vec[2]; |
| resultVec[0] = x * mat[0] + y * mat[4] + z * mat[8]; |
| resultVec[1] = x * mat[1] + y * mat[5] + z * mat[9]; |
| resultVec[2] = x * mat[2] + y * mat[6] + z * mat[10]; |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. The input vector is multiplied against the |
| * full 4x4 matrix with the homogeneous divide applied to reduce the 4 element |
| * vector to a 3 element vector. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the transformation. |
| * @param {goog.vec.vec3d.Type} vec The 3 element vector to transform. |
| * @param {goog.vec.vec3d.Type} resultVec The 3 element vector |
| * to receive the results (may be vec). |
| * @return {!goog.vec.vec3d.Type} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multVec3Projective = function(mat, vec, resultVec) { |
| var x = vec[0], y = vec[1], z = vec[2]; |
| var invw = 1 / (x * mat[3] + y * mat[7] + z * mat[11] + mat[15]); |
| resultVec[0] = (x * mat[0] + y * mat[4] + z * mat[8] + mat[12]) * invw; |
| resultVec[1] = (x * mat[1] + y * mat[5] + z * mat[9] + mat[13]) * invw; |
| resultVec[2] = (x * mat[2] + y * mat[6] + z * mat[10] + mat[14]) * invw; |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix supplying the transformation. |
| * @param {goog.vec.vec4d.Type} vec The vector to transform. |
| * @param {goog.vec.vec4d.Type} resultVec The vector to |
| * receive the results (may be vec). |
| * @return {!goog.vec.vec4d.Type} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.multVec4 = function(mat, vec, resultVec) { |
| var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; |
| resultVec[0] = x * mat[0] + y * mat[4] + z * mat[8] + w * mat[12]; |
| resultVec[1] = x * mat[1] + y * mat[5] + z * mat[9] + w * mat[13]; |
| resultVec[2] = x * mat[2] + y * mat[6] + z * mat[10] + w * mat[14]; |
| resultVec[3] = x * mat[3] + y * mat[7] + z * mat[11] + w * mat[15]; |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a translation matrix with x, y and z |
| * translation factors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} x The translation along the x axis. |
| * @param {number} y The translation along the y axis. |
| * @param {number} z The translation along the z axis. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeTranslate = function(mat, x, y, z) { |
| mat[0] = 1; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = 1; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = 1; |
| mat[11] = 0; |
| mat[12] = x; |
| mat[13] = y; |
| mat[14] = z; |
| mat[15] = 1; |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix as a scale matrix with x, y and z scale factors. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} x The scale along the x axis. |
| * @param {number} y The scale along the y axis. |
| * @param {number} z The scale along the z axis. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeScale = function(mat, x, y, z) { |
| mat[0] = x; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = y; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = z; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a rotation matrix with the given rotation |
| * angle about the axis defined by the vector (ax, ay, az). |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The rotation angle in radians. |
| * @param {number} ax The x component of the rotation axis. |
| * @param {number} ay The y component of the rotation axis. |
| * @param {number} az The z component of the rotation axis. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeRotate = function(mat, angle, ax, ay, az) { |
| var c = Math.cos(angle); |
| var d = 1 - c; |
| var s = Math.sin(angle); |
| |
| mat[0] = ax * ax * d + c; |
| mat[1] = ax * ay * d + az * s; |
| mat[2] = ax * az * d - ay * s; |
| mat[3] = 0; |
| mat[4] = ax * ay * d - az * s; |
| mat[5] = ay * ay * d + c; |
| mat[6] = ay * az * d + ax * s; |
| mat[7] = 0; |
| mat[8] = ax * az * d + ay * s; |
| mat[9] = ay * az * d - ax * s; |
| mat[10] = az * az * d + c; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a rotation matrix with the given rotation |
| * angle about the X axis. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The rotation angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeRotateX = function(mat, angle) { |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[0] = 1; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = c; |
| mat[6] = s; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = -s; |
| mat[10] = c; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a rotation matrix with the given rotation |
| * angle about the Y axis. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The rotation angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeRotateY = function(mat, angle) { |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[0] = c; |
| mat[1] = 0; |
| mat[2] = -s; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = 1; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = s; |
| mat[9] = 0; |
| mat[10] = c; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a rotation matrix with the given rotation |
| * angle about the Z axis. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The rotation angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeRotateZ = function(mat, angle) { |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[0] = c; |
| mat[1] = s; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = -s; |
| mat[5] = c; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = 1; |
| mat[11] = 0; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a perspective projection matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} left The coordinate of the left clipping plane. |
| * @param {number} right The coordinate of the right clipping plane. |
| * @param {number} bottom The coordinate of the bottom clipping plane. |
| * @param {number} top The coordinate of the top clipping plane. |
| * @param {number} near The distance to the near clipping plane. |
| * @param {number} far The distance to the far clipping plane. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeFrustum = function( |
| mat, left, right, bottom, top, near, far) { |
| var x = (2 * near) / (right - left); |
| var y = (2 * near) / (top - bottom); |
| var a = (right + left) / (right - left); |
| var b = (top + bottom) / (top - bottom); |
| var c = -(far + near) / (far - near); |
| var d = -(2 * far * near) / (far - near); |
| |
| mat[0] = x; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = y; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = a; |
| mat[9] = b; |
| mat[10] = c; |
| mat[11] = -1; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = d; |
| mat[15] = 0; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makse the given 4x4 matrix perspective projection matrix given a |
| * field of view and aspect ratio. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} fovy The field of view along the y (vertical) axis in |
| * radians. |
| * @param {number} aspect The x (width) to y (height) aspect ratio. |
| * @param {number} near The distance to the near clipping plane. |
| * @param {number} far The distance to the far clipping plane. |
| * @return {goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makePerspective = function(mat, fovy, aspect, near, far) { |
| var angle = fovy / 2; |
| var dz = far - near; |
| var sinAngle = Math.sin(angle); |
| if (dz == 0 || sinAngle == 0 || aspect == 0) { |
| return mat; |
| } |
| |
| var cot = Math.cos(angle) / sinAngle; |
| |
| mat[0] = cot / aspect; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = cot; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = -(far + near) / dz; |
| mat[11] = -1; |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = -(2 * near * far) / dz; |
| mat[15] = 0; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix an orthographic projection matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} left The coordinate of the left clipping plane. |
| * @param {number} right The coordinate of the right clipping plane. |
| * @param {number} bottom The coordinate of the bottom clipping plane. |
| * @param {number} top The coordinate of the top clipping plane. |
| * @param {number} near The distance to the near clipping plane. |
| * @param {number} far The distance to the far clipping plane. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeOrtho = function(mat, left, right, bottom, top, near, far) { |
| var x = 2 / (right - left); |
| var y = 2 / (top - bottom); |
| var z = -2 / (far - near); |
| var a = -(right + left) / (right - left); |
| var b = -(top + bottom) / (top - bottom); |
| var c = -(far + near) / (far - near); |
| |
| mat[0] = x; |
| mat[1] = 0; |
| mat[2] = 0; |
| mat[3] = 0; |
| mat[4] = 0; |
| mat[5] = y; |
| mat[6] = 0; |
| mat[7] = 0; |
| mat[8] = 0; |
| mat[9] = 0; |
| mat[10] = z; |
| mat[11] = 0; |
| mat[12] = a; |
| mat[13] = b; |
| mat[14] = c; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a modelview matrix of a camera so that |
| * the camera is 'looking at' the given center point. |
| * |
| * Note that unlike most other goog.vec functions where we inline |
| * everything, this function does not inline various goog.vec |
| * functions. This makes the code more readable, but somewhat |
| * less efficient. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {goog.vec.vec3d.Type} eyePt The position of the eye point |
| * (camera origin). |
| * @param {goog.vec.vec3d.Type} centerPt The point to aim the camera at. |
| * @param {goog.vec.vec3d.Type} worldUpVec The vector that identifies |
| * the up direction for the camera. |
| * @return {goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeLookAt = function(mat, eyePt, centerPt, worldUpVec) { |
| // Compute the direction vector from the eye point to the center point and |
| // normalize. |
| var fwdVec = goog.vec.mat4d.tmpvec4d_[0]; |
| goog.vec.vec3d.subtract(centerPt, eyePt, fwdVec); |
| goog.vec.vec3d.normalize(fwdVec, fwdVec); |
| fwdVec[3] = 0; |
| |
| // Compute the side vector from the forward vector and the input up vector. |
| var sideVec = goog.vec.mat4d.tmpvec4d_[1]; |
| goog.vec.vec3d.cross(fwdVec, worldUpVec, sideVec); |
| goog.vec.vec3d.normalize(sideVec, sideVec); |
| sideVec[3] = 0; |
| |
| // Now the up vector to form the orthonormal basis. |
| var upVec = goog.vec.mat4d.tmpvec4d_[2]; |
| goog.vec.vec3d.cross(sideVec, fwdVec, upVec); |
| goog.vec.vec3d.normalize(upVec, upVec); |
| upVec[3] = 0; |
| |
| // Update the view matrix with the new orthonormal basis and position the |
| // camera at the given eye point. |
| goog.vec.vec3d.negate(fwdVec, fwdVec); |
| goog.vec.mat4d.setRow(mat, 0, sideVec); |
| goog.vec.mat4d.setRow(mat, 1, upVec); |
| goog.vec.mat4d.setRow(mat, 2, fwdVec); |
| goog.vec.mat4d.setRowValues(mat, 3, 0, 0, 0, 1); |
| goog.vec.mat4d.translate( |
| mat, -eyePt[0], -eyePt[1], -eyePt[2]); |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Decomposes a matrix into the lookAt vectors eyePt, fwdVec and worldUpVec. |
| * The matrix represents the modelview matrix of a camera. It is the inverse |
| * of lookAt except for the output of the fwdVec instead of centerPt. |
| * The centerPt itself cannot be recovered from a modelview matrix. |
| * |
| * Note that unlike most other goog.vec functions where we inline |
| * everything, this function does not inline various goog.vec |
| * functions. This makes the code more readable, but somewhat |
| * less efficient. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {goog.vec.vec3d.Type} eyePt The position of the eye point |
| * (camera origin). |
| * @param {goog.vec.vec3d.Type} fwdVec The vector describing where |
| * the camera points to. |
| * @param {goog.vec.vec3d.Type} worldUpVec The vector that |
| * identifies the up direction for the camera. |
| * @return {boolean} True if the method succeeds, false otherwise. |
| * The method can only fail if the inverse of viewMatrix is not defined. |
| */ |
| goog.vec.mat4d.toLookAt = function(mat, eyePt, fwdVec, worldUpVec) { |
| // Get eye of the camera. |
| var matInverse = goog.vec.mat4d.tmpmat4d_[0]; |
| if (!goog.vec.mat4d.invert(mat, matInverse)) { |
| // The input matrix does not have a valid inverse. |
| return false; |
| } |
| |
| if (eyePt) { |
| eyePt[0] = matInverse[12]; |
| eyePt[1] = matInverse[13]; |
| eyePt[2] = matInverse[14]; |
| } |
| |
| // Get forward vector from the definition of lookAt. |
| if (fwdVec || worldUpVec) { |
| if (!fwdVec) { |
| fwdVec = goog.vec.mat4d.tmpvec3d_[0]; |
| } |
| fwdVec[0] = -mat[2]; |
| fwdVec[1] = -mat[6]; |
| fwdVec[2] = -mat[10]; |
| // Normalize forward vector. |
| goog.vec.vec3d.normalize(fwdVec, fwdVec); |
| } |
| |
| if (worldUpVec) { |
| // Get side vector from the definition of gluLookAt. |
| var side = goog.vec.mat4d.tmpvec3d_[1]; |
| side[0] = mat[0]; |
| side[1] = mat[4]; |
| side[2] = mat[8]; |
| // Compute up vector as a up = side x forward. |
| goog.vec.vec3d.cross(side, fwdVec, worldUpVec); |
| // Normalize up vector. |
| goog.vec.vec3d.normalize(worldUpVec, worldUpVec); |
| } |
| return true; |
| }; |
| |
| |
| /** |
| * Makes the given 4x4 matrix a rotation matrix given Euler angles using |
| * the ZXZ convention. |
| * Given the euler angles [theta1, theta2, theta3], the rotation is defined as |
| * rotation = rotation_z(theta1) * rotation_x(theta2) * rotation_z(theta3), |
| * with theta1 in [0, 2 * pi], theta2 in [0, pi] and theta3 in [0, 2 * pi]. |
| * rotation_x(theta) means rotation around the X axis of theta radians, |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} theta1 The angle of rotation around the Z axis in radians. |
| * @param {number} theta2 The angle of rotation around the X axis in radians. |
| * @param {number} theta3 The angle of rotation around the Z axis in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.makeEulerZXZ = function(mat, theta1, theta2, theta3) { |
| var c1 = Math.cos(theta1); |
| var s1 = Math.sin(theta1); |
| |
| var c2 = Math.cos(theta2); |
| var s2 = Math.sin(theta2); |
| |
| var c3 = Math.cos(theta3); |
| var s3 = Math.sin(theta3); |
| |
| mat[0] = c1 * c3 - c2 * s1 * s3; |
| mat[1] = c2 * c1 * s3 + c3 * s1; |
| mat[2] = s3 * s2; |
| mat[3] = 0; |
| |
| mat[4] = -c1 * s3 - c3 * c2 * s1; |
| mat[5] = c1 * c2 * c3 - s1 * s3; |
| mat[6] = c3 * s2; |
| mat[7] = 0; |
| |
| mat[8] = s2 * s1; |
| mat[9] = -c1 * s2; |
| mat[10] = c2; |
| mat[11] = 0; |
| |
| mat[12] = 0; |
| mat[13] = 0; |
| mat[14] = 0; |
| mat[15] = 1; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Decomposes a rotation matrix into Euler angles using the ZXZ convention so |
| * that rotation = rotation_z(theta1) * rotation_x(theta2) * rotation_z(theta3), |
| * with theta1 in [0, 2 * pi], theta2 in [0, pi] and theta3 in [0, 2 * pi]. |
| * rotation_x(theta) means rotation around the X axis of theta radians. |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {goog.vec.vec3d.Type} euler The ZXZ Euler angles in |
| * radians as [theta1, theta2, theta3]. |
| * @param {boolean=} opt_theta2IsNegative Whether theta2 is in [-pi, 0] instead |
| * of the default [0, pi]. |
| * @return {!goog.vec.vec4d.Type} return euler so that operations can be |
| * chained together. |
| */ |
| goog.vec.mat4d.toEulerZXZ = function(mat, euler, opt_theta2IsNegative) { |
| // There is an ambiguity in the sign of sinTheta2 because of the sqrt. |
| var sinTheta2 = Math.sqrt(mat[2] * mat[2] + mat[6] * mat[6]); |
| |
| // By default we explicitely constrain theta2 to be in [0, pi], |
| // so sinTheta2 is always positive. We can change the behavior and specify |
| // theta2 to be negative in [-pi, 0] with opt_Theta2IsNegative. |
| var signTheta2 = opt_theta2IsNegative ? -1 : 1; |
| |
| if (sinTheta2 > goog.vec.EPSILON) { |
| euler[2] = Math.atan2(mat[2] * signTheta2, mat[6] * signTheta2); |
| euler[1] = Math.atan2(sinTheta2 * signTheta2, mat[10]); |
| euler[0] = Math.atan2(mat[8] * signTheta2, -mat[9] * signTheta2); |
| } else { |
| // There is also an arbitrary choice for theta1 = 0 or theta2 = 0 here. |
| // We assume theta1 = 0 as some applications do not allow the camera to roll |
| // (i.e. have theta1 != 0). |
| euler[0] = 0; |
| euler[1] = Math.atan2(sinTheta2 * signTheta2, mat[10]); |
| euler[2] = Math.atan2(mat[1], mat[0]); |
| } |
| |
| // Atan2 outputs angles in [-pi, pi] so we bring them back to [0, 2 * pi]. |
| euler[0] = (euler[0] + Math.PI * 2) % (Math.PI * 2); |
| euler[2] = (euler[2] + Math.PI * 2) % (Math.PI * 2); |
| // For theta2 we want the angle to be in [0, pi] or [-pi, 0] depending on |
| // signTheta2. |
| euler[1] = ((euler[1] * signTheta2 + Math.PI * 2) % (Math.PI * 2)) * |
| signTheta2; |
| |
| return euler; |
| }; |
| |
| |
| /** |
| * Translates the given matrix by x,y,z. Equvialent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeTranslate(goog.vec.mat4d.create(), x, y, z), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} x The translation along the x axis. |
| * @param {number} y The translation along the y axis. |
| * @param {number} z The translation along the z axis. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.translate = function(mat, x, y, z) { |
| mat[12] += mat[0] * x + mat[4] * y + mat[8] * z; |
| mat[13] += mat[1] * x + mat[5] * y + mat[9] * z; |
| mat[14] += mat[2] * x + mat[6] * y + mat[10] * z; |
| mat[15] += mat[3] * x + mat[7] * y + mat[11] * z; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Scales the given matrix by x,y,z. Equivalent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeScale(goog.vec.mat4d.create(), x, y, z), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} x The x scale factor. |
| * @param {number} y The y scale factor. |
| * @param {number} z The z scale factor. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.scale = function(mat, x, y, z) { |
| mat[0] = mat[0] * x; |
| mat[1] = mat[1] * x; |
| mat[2] = mat[2] * x; |
| mat[3] = mat[3] * x; |
| mat[4] = mat[4] * y; |
| mat[5] = mat[5] * y; |
| mat[6] = mat[6] * y; |
| mat[7] = mat[7] * y; |
| mat[8] = mat[8] * z; |
| mat[9] = mat[9] * z; |
| mat[10] = mat[10] * z; |
| mat[11] = mat[11] * z; |
| mat[12] = mat[12]; |
| mat[13] = mat[13]; |
| mat[14] = mat[14]; |
| mat[15] = mat[15]; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Rotate the given matrix by angle about the x,y,z axis. Equivalent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeRotate(goog.vec.mat4d.create(), angle, x, y, z), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The angle in radians. |
| * @param {number} x The x component of the rotation axis. |
| * @param {number} y The y component of the rotation axis. |
| * @param {number} z The z component of the rotation axis. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.rotate = function(mat, angle, x, y, z) { |
| var m00 = mat[0], m10 = mat[1], m20 = mat[2], m30 = mat[3]; |
| var m01 = mat[4], m11 = mat[5], m21 = mat[6], m31 = mat[7]; |
| var m02 = mat[8], m12 = mat[9], m22 = mat[10], m32 = mat[11]; |
| |
| var cosAngle = Math.cos(angle); |
| var sinAngle = Math.sin(angle); |
| var diffCosAngle = 1 - cosAngle; |
| var r00 = x * x * diffCosAngle + cosAngle; |
| var r10 = x * y * diffCosAngle + z * sinAngle; |
| var r20 = x * z * diffCosAngle - y * sinAngle; |
| |
| var r01 = x * y * diffCosAngle - z * sinAngle; |
| var r11 = y * y * diffCosAngle + cosAngle; |
| var r21 = y * z * diffCosAngle + x * sinAngle; |
| |
| var r02 = x * z * diffCosAngle + y * sinAngle; |
| var r12 = y * z * diffCosAngle - x * sinAngle; |
| var r22 = z * z * diffCosAngle + cosAngle; |
| |
| mat[0] = m00 * r00 + m01 * r10 + m02 * r20; |
| mat[1] = m10 * r00 + m11 * r10 + m12 * r20; |
| mat[2] = m20 * r00 + m21 * r10 + m22 * r20; |
| mat[3] = m30 * r00 + m31 * r10 + m32 * r20; |
| mat[4] = m00 * r01 + m01 * r11 + m02 * r21; |
| mat[5] = m10 * r01 + m11 * r11 + m12 * r21; |
| mat[6] = m20 * r01 + m21 * r11 + m22 * r21; |
| mat[7] = m30 * r01 + m31 * r11 + m32 * r21; |
| mat[8] = m00 * r02 + m01 * r12 + m02 * r22; |
| mat[9] = m10 * r02 + m11 * r12 + m12 * r22; |
| mat[10] = m20 * r02 + m21 * r12 + m22 * r22; |
| mat[11] = m30 * r02 + m31 * r12 + m32 * r22; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Rotate the given matrix by angle about the x axis. Equivalent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeRotateX(goog.vec.mat4d.create(), angle), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.rotateX = function(mat, angle) { |
| var m01 = mat[4], m11 = mat[5], m21 = mat[6], m31 = mat[7]; |
| var m02 = mat[8], m12 = mat[9], m22 = mat[10], m32 = mat[11]; |
| |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[4] = m01 * c + m02 * s; |
| mat[5] = m11 * c + m12 * s; |
| mat[6] = m21 * c + m22 * s; |
| mat[7] = m31 * c + m32 * s; |
| mat[8] = m01 * -s + m02 * c; |
| mat[9] = m11 * -s + m12 * c; |
| mat[10] = m21 * -s + m22 * c; |
| mat[11] = m31 * -s + m32 * c; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Rotate the given matrix by angle about the y axis. Equivalent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeRotateY(goog.vec.mat4d.create(), angle), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.rotateY = function(mat, angle) { |
| var m00 = mat[0], m10 = mat[1], m20 = mat[2], m30 = mat[3]; |
| var m02 = mat[8], m12 = mat[9], m22 = mat[10], m32 = mat[11]; |
| |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[0] = m00 * c + m02 * -s; |
| mat[1] = m10 * c + m12 * -s; |
| mat[2] = m20 * c + m22 * -s; |
| mat[3] = m30 * c + m32 * -s; |
| mat[8] = m00 * s + m02 * c; |
| mat[9] = m10 * s + m12 * c; |
| mat[10] = m20 * s + m22 * c; |
| mat[11] = m30 * s + m32 * c; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Rotate the given matrix by angle about the z axis. Equivalent to: |
| * goog.vec.mat4d.multMat( |
| * mat, |
| * goog.vec.mat4d.makeRotateZ(goog.vec.mat4d.create(), angle), |
| * mat); |
| * |
| * @param {goog.vec.mat4d.Type} mat The matrix. |
| * @param {number} angle The angle in radians. |
| * @return {!goog.vec.mat4d.Type} return mat so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.rotateZ = function(mat, angle) { |
| var m00 = mat[0], m10 = mat[1], m20 = mat[2], m30 = mat[3]; |
| var m01 = mat[4], m11 = mat[5], m21 = mat[6], m31 = mat[7]; |
| |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| |
| mat[0] = m00 * c + m01 * s; |
| mat[1] = m10 * c + m11 * s; |
| mat[2] = m20 * c + m21 * s; |
| mat[3] = m30 * c + m31 * s; |
| mat[4] = m00 * -s + m01 * c; |
| mat[5] = m10 * -s + m11 * c; |
| mat[6] = m20 * -s + m21 * c; |
| mat[7] = m30 * -s + m31 * c; |
| |
| return mat; |
| }; |
| |
| |
| /** |
| * Retrieves the translation component of the transformation matrix. |
| * |
| * @param {goog.vec.mat4d.Type} mat The transformation matrix. |
| * @param {goog.vec.vec3d.Type} translation The vector for storing the |
| * result. |
| * @return {!goog.vec.vec3d.Type} return translation so that operations can be |
| * chained. |
| */ |
| goog.vec.mat4d.getTranslation = function(mat, translation) { |
| translation[0] = mat[12]; |
| translation[1] = mat[13]; |
| translation[2] = mat[14]; |
| return translation; |
| }; |
| |
| |
| /** |
| * @type {Array<goog.vec.vec3d.Type>} |
| * @private |
| */ |
| goog.vec.mat4d.tmpvec3d_ = [ |
| goog.vec.vec3d.create(), |
| goog.vec.vec3d.create() |
| ]; |
| |
| |
| /** |
| * @type {Array<goog.vec.vec4d.Type>} |
| * @private |
| */ |
| goog.vec.mat4d.tmpvec4d_ = [ |
| goog.vec.vec4d.create(), |
| goog.vec.vec4d.create(), |
| goog.vec.vec4d.create() |
| ]; |
| |
| |
| /** |
| * @type {Array<goog.vec.mat4d.Type>} |
| * @private |
| */ |
| goog.vec.mat4d.tmpmat4d_ = [ |
| goog.vec.mat4d.create() |
| ]; |