| // Copyright 2011 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. |
| |
| /** |
| * @fileoverview WARNING: DEPRECATED. Use Mat4 instead. |
| * Implements 4x4 matrices and their related functions which are |
| * compatible with WebGL. The API is structured to avoid unnecessary memory |
| * allocations. The last parameter will typically be the output vector and |
| * an object can be both an input and output parameter to all methods except |
| * where noted. Matrix operations follow the mathematical form when multiplying |
| * vectors as follows: resultVec = matrix * vec. |
| * |
| */ |
| goog.provide('goog.vec.Matrix4'); |
| |
| goog.require('goog.vec'); |
| goog.require('goog.vec.Vec3'); |
| goog.require('goog.vec.Vec4'); |
| |
| |
| /** |
| * @typedef {goog.vec.ArrayType} |
| */ |
| goog.vec.Matrix4.Type; |
| |
| |
| /** |
| * Creates the array representation of a 4x4 matrix. The use of the array |
| * directly eliminates any overhead associated with the class representation |
| * defined above. The returned matrix is cleared to all zeros. |
| * |
| * @return {goog.vec.Matrix4.Type} The new, sixteen element array. |
| */ |
| goog.vec.Matrix4.create = function() { |
| return new Float32Array(16); |
| }; |
| |
| |
| /** |
| * Creates the array representation of a 4x4 matrix. The use of the array |
| * directly eliminates any overhead associated with the class representation |
| * defined above. The returned matrix is initialized with the identity |
| * |
| * @return {goog.vec.Matrix4.Type} The new, sixteen element array. |
| */ |
| goog.vec.Matrix4.createIdentity = function() { |
| var mat = goog.vec.Matrix4.create(); |
| mat[0] = mat[5] = mat[10] = mat[15] = 1; |
| return mat; |
| }; |
| |
| |
| /** |
| * Creates a 4x4 matrix initialized from the given array. |
| * |
| * @param {goog.vec.ArrayType} matrix The array containing the |
| * matrix values in column major order. |
| * @return {goog.vec.Matrix4.Type} The new, 16 element array. |
| */ |
| goog.vec.Matrix4.createFromArray = function(matrix) { |
| var newMatrix = goog.vec.Matrix4.create(); |
| goog.vec.Matrix4.setFromArray(newMatrix, matrix); |
| return newMatrix; |
| }; |
| |
| |
| /** |
| * Creates a 4x4 matrix initialized from the given 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.Matrix4.Type} The new, 16 element array. |
| */ |
| goog.vec.Matrix4.createFromValues = function( |
| v00, v10, v20, v30, v01, v11, v21, v31, v02, v12, v22, v32, |
| v03, v13, v23, v33) { |
| var newMatrix = goog.vec.Matrix4.create(); |
| goog.vec.Matrix4.setFromValues( |
| newMatrix, v00, v10, v20, v30, v01, v11, v21, v31, v02, v12, v22, v32, |
| v03, v13, v23, v33); |
| return newMatrix; |
| }; |
| |
| |
| /** |
| * Creates a clone of a 4x4 matrix. |
| * |
| * @param {goog.vec.Matrix4.Type} matrix The source 4x4 matrix. |
| * @return {goog.vec.Matrix4.Type} The new, 16 element matrix. |
| */ |
| goog.vec.Matrix4.clone = |
| goog.vec.Matrix4.createFromArray; |
| |
| |
| /** |
| * Retrieves the element at the requested row and column. |
| * |
| * @param {goog.vec.ArrayType} 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.Matrix4.getElement = function(mat, row, column) { |
| return mat[row + column * 4]; |
| }; |
| |
| |
| /** |
| * Sets the element at the requested row and column. |
| * |
| * @param {goog.vec.ArrayType} 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. |
| */ |
| goog.vec.Matrix4.setElement = function(mat, row, column, value) { |
| mat[row + column * 4] = value; |
| }; |
| |
| |
| /** |
| * Initializes the matrix from the set of values. Note the values supplied are |
| * in column major order. |
| * |
| * @param {goog.vec.ArrayType} 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). |
| */ |
| goog.vec.Matrix4.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; |
| }; |
| |
| |
| /** |
| * Sets the matrix from the array of values stored in column major order. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {goog.vec.ArrayType} values The column major ordered |
| * array of values to store in the matrix. |
| */ |
| goog.vec.Matrix4.setFromArray = function(mat, values) { |
| mat[0] = values[0]; |
| mat[1] = values[1]; |
| mat[2] = values[2]; |
| mat[3] = values[3]; |
| mat[4] = values[4]; |
| mat[5] = values[5]; |
| mat[6] = values[6]; |
| mat[7] = values[7]; |
| mat[8] = values[8]; |
| mat[9] = values[9]; |
| mat[10] = values[10]; |
| mat[11] = values[11]; |
| mat[12] = values[12]; |
| mat[13] = values[13]; |
| mat[14] = values[14]; |
| mat[15] = values[15]; |
| }; |
| |
| |
| /** |
| * Sets the matrix from the array of values stored in row major order. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {goog.vec.ArrayType} values The row major ordered array of |
| * values to store in the matrix. |
| */ |
| goog.vec.Matrix4.setFromRowMajorArray = function(mat, values) { |
| mat[0] = values[0]; |
| mat[1] = values[4]; |
| mat[2] = values[8]; |
| mat[3] = values[12]; |
| |
| mat[4] = values[1]; |
| mat[5] = values[5]; |
| mat[6] = values[9]; |
| mat[7] = values[13]; |
| |
| mat[8] = values[2]; |
| mat[9] = values[6]; |
| mat[10] = values[10]; |
| mat[11] = values[14]; |
| |
| mat[12] = values[3]; |
| mat[13] = values[7]; |
| mat[14] = values[11]; |
| mat[15] = values[15]; |
| }; |
| |
| |
| /** |
| * Sets the diagonal values of the matrix from the given values. |
| * |
| * @param {goog.vec.ArrayType} 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). |
| */ |
| goog.vec.Matrix4.setDiagonalValues = function( |
| mat, v00, v11, v22, v33) { |
| mat[0] = v00; |
| mat[5] = v11; |
| mat[10] = v22; |
| mat[15] = v33; |
| }; |
| |
| |
| /** |
| * Sets the diagonal values of the matrix from the given vector. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {goog.vec.ArrayType} vec The vector containing the |
| * values. |
| */ |
| goog.vec.Matrix4.setDiagonal = function(mat, vec) { |
| mat[0] = vec[0]; |
| mat[5] = vec[1]; |
| mat[10] = vec[2]; |
| mat[15] = vec[3]; |
| }; |
| |
| |
| /** |
| * Sets the specified column with the supplied values. |
| * |
| * @param {goog.vec.ArrayType} 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. |
| */ |
| goog.vec.Matrix4.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; |
| }; |
| |
| |
| /** |
| * Sets the specified column with the value from the supplied array. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {number} column The column index to set the values on. |
| * @param {goog.vec.ArrayType} vec The vector of elements for the |
| * column. |
| */ |
| goog.vec.Matrix4.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]; |
| }; |
| |
| |
| /** |
| * Retrieves the specified column from the matrix into the given vector |
| * array. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix supplying the |
| * values. |
| * @param {number} column The column to get the values from. |
| * @param {goog.vec.ArrayType} vec The vector of elements to |
| * receive the column. |
| */ |
| goog.vec.Matrix4.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]; |
| }; |
| |
| |
| /** |
| * Sets the columns of the matrix from the set of vector elements. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {goog.vec.ArrayType} vec0 The values for column 0. |
| * @param {goog.vec.ArrayType} vec1 The values for column 1. |
| * @param {goog.vec.ArrayType} vec2 The values for column 2. |
| * @param {goog.vec.ArrayType} vec3 The values for column 3. |
| */ |
| goog.vec.Matrix4.setColumns = function( |
| mat, vec0, vec1, vec2, vec3) { |
| goog.vec.Matrix4.setColumn(mat, 0, vec0); |
| goog.vec.Matrix4.setColumn(mat, 1, vec1); |
| goog.vec.Matrix4.setColumn(mat, 2, vec2); |
| goog.vec.Matrix4.setColumn(mat, 3, vec3); |
| }; |
| |
| |
| /** |
| * Retrieves the column values from the given matrix into the given vector |
| * elements. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix containing the |
| * columns to retrieve. |
| * @param {goog.vec.ArrayType} vec0 The vector elements to receive |
| * column 0. |
| * @param {goog.vec.ArrayType} vec1 The vector elements to receive |
| * column 1. |
| * @param {goog.vec.ArrayType} vec2 The vector elements to receive |
| * column 2. |
| * @param {goog.vec.ArrayType} vec3 The vector elements to receive |
| * column 3. |
| */ |
| goog.vec.Matrix4.getColumns = function( |
| mat, vec0, vec1, vec2, vec3) { |
| goog.vec.Matrix4.getColumn(mat, 0, vec0); |
| goog.vec.Matrix4.getColumn(mat, 1, vec1); |
| goog.vec.Matrix4.getColumn(mat, 2, vec2); |
| goog.vec.Matrix4.getColumn(mat, 3, vec3); |
| }; |
| |
| |
| /** |
| * Sets the row values from the supplied values. |
| * |
| * @param {goog.vec.ArrayType} 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. |
| */ |
| goog.vec.Matrix4.setRowValues = function(mat, row, v0, v1, v2, v3) { |
| mat[row] = v0; |
| mat[row + 4] = v1; |
| mat[row + 8] = v2; |
| mat[row + 12] = v3; |
| }; |
| |
| |
| /** |
| * Sets the row values from the supplied vector. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * row values. |
| * @param {number} row The index of the row. |
| * @param {goog.vec.ArrayType} vec The vector containing the |
| * values. |
| */ |
| goog.vec.Matrix4.setRow = function(mat, row, vec) { |
| mat[row] = vec[0]; |
| mat[row + 4] = vec[1]; |
| mat[row + 8] = vec[2]; |
| mat[row + 12] = vec[3]; |
| }; |
| |
| |
| /** |
| * Retrieves the row values into the given vector. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix supplying the |
| * values. |
| * @param {number} row The index of the row supplying the values. |
| * @param {goog.vec.ArrayType} vec The vector to receive the |
| * row. |
| */ |
| goog.vec.Matrix4.getRow = function(mat, row, vec) { |
| vec[0] = mat[row]; |
| vec[1] = mat[row + 4]; |
| vec[2] = mat[row + 8]; |
| vec[3] = mat[row + 12]; |
| }; |
| |
| |
| /** |
| * Sets the rows of the matrix from the supplied vectors. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to receive the |
| * values. |
| * @param {goog.vec.ArrayType} vec0 The values for row 0. |
| * @param {goog.vec.ArrayType} vec1 The values for row 1. |
| * @param {goog.vec.ArrayType} vec2 The values for row 2. |
| * @param {goog.vec.ArrayType} vec3 The values for row 3. |
| */ |
| goog.vec.Matrix4.setRows = function( |
| mat, vec0, vec1, vec2, vec3) { |
| goog.vec.Matrix4.setRow(mat, 0, vec0); |
| goog.vec.Matrix4.setRow(mat, 1, vec1); |
| goog.vec.Matrix4.setRow(mat, 2, vec2); |
| goog.vec.Matrix4.setRow(mat, 3, vec3); |
| }; |
| |
| |
| /** |
| * Retrieves the rows of the matrix into the supplied vectors. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to supply the |
| * values. |
| * @param {goog.vec.ArrayType} vec0 The vector to receive row 0. |
| * @param {goog.vec.ArrayType} vec1 The vector to receive row 1. |
| * @param {goog.vec.ArrayType} vec2 The vector to receive row 2. |
| * @param {goog.vec.ArrayType} vec3 The vector to receive row 3. |
| */ |
| goog.vec.Matrix4.getRows = function( |
| mat, vec0, vec1, vec2, vec3) { |
| goog.vec.Matrix4.getRow(mat, 0, vec0); |
| goog.vec.Matrix4.getRow(mat, 1, vec1); |
| goog.vec.Matrix4.getRow(mat, 2, vec2); |
| goog.vec.Matrix4.getRow(mat, 3, vec3); |
| }; |
| |
| |
| /** |
| * Clears the given matrix to zero. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to clear. |
| */ |
| goog.vec.Matrix4.setZero = 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; |
| }; |
| |
| |
| /** |
| * Sets the given matrix to the identity matrix. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix to set. |
| */ |
| goog.vec.Matrix4.setIdentity = 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; |
| }; |
| |
| |
| /** |
| * Performs a per-component addition of the matrix mat0 and mat1, storing |
| * the result into resultMat. |
| * |
| * @param {goog.vec.ArrayType} mat0 The first addend. |
| * @param {goog.vec.ArrayType} mat1 The second addend. |
| * @param {goog.vec.ArrayType} resultMat The matrix to |
| * receive the results (may be either mat0 or mat1). |
| * @return {goog.vec.ArrayType} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.add = 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.ArrayType} mat0 The minuend. |
| * @param {goog.vec.ArrayType} mat1 The subtrahend. |
| * @param {goog.vec.ArrayType} resultMat The matrix to receive |
| * the results (may be either mat0 or mat1). |
| * @return {goog.vec.ArrayType} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.subtract = 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 component-wise multiplication of mat0 with the given scalar |
| * storing the result into resultMat. |
| * |
| * @param {goog.vec.ArrayType} mat0 The matrix to scale. |
| * @param {number} scalar The scalar value to multiple to each element of mat0. |
| * @param {goog.vec.ArrayType} resultMat The matrix to receive |
| * the results (may be mat0). |
| * @return {goog.vec.ArrayType} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.scale = function(mat0, scalar, resultMat) { |
| resultMat[0] = mat0[0] * scalar; |
| resultMat[1] = mat0[1] * scalar; |
| resultMat[2] = mat0[2] * scalar; |
| resultMat[3] = mat0[3] * scalar; |
| resultMat[4] = mat0[4] * scalar; |
| resultMat[5] = mat0[5] * scalar; |
| resultMat[6] = mat0[6] * scalar; |
| resultMat[7] = mat0[7] * scalar; |
| resultMat[8] = mat0[8] * scalar; |
| resultMat[9] = mat0[9] * scalar; |
| resultMat[10] = mat0[10] * scalar; |
| resultMat[11] = mat0[11] * scalar; |
| resultMat[12] = mat0[12] * scalar; |
| resultMat[13] = mat0[13] * scalar; |
| resultMat[14] = mat0[14] * scalar; |
| resultMat[15] = mat0[15] * scalar; |
| return resultMat; |
| }; |
| |
| |
| /** |
| * Multiplies the two matrices mat0 and mat1 using matrix multiplication, |
| * storing the result into resultMat. |
| * |
| * @param {goog.vec.ArrayType} mat0 The first (left hand) matrix. |
| * @param {goog.vec.ArrayType} mat1 The second (right hand) |
| * matrix. |
| * @param {goog.vec.ArrayType} resultMat The matrix to receive |
| * the results (may be either mat0 or mat1). |
| * @return {goog.vec.ArrayType} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix to transpose. |
| * @param {goog.vec.ArrayType} resultMat The matrix to receive |
| * the results (may be mat). |
| * @return {goog.vec.ArrayType} return resultMat so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix to compute the |
| * matrix for. |
| * @return {number} The determinant of the matrix. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix to invert. |
| * @param {goog.vec.ArrayType} 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.Matrix4.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.ArrayType} mat0 The first matrix. |
| * @param {goog.vec.ArrayType} mat1 The second matrix. |
| * @return {boolean} True if the the two matrices are equivalent. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The 3 element vector to |
| * transform. |
| * @param {goog.vec.ArrayType} resultVec The 3 element vector to |
| * receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The 3 element vector to |
| * transform. |
| * @param {goog.vec.ArrayType} resultVec The 3 element vector to |
| * receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The 3 element vector to |
| * transform. |
| * @param {goog.vec.ArrayType} resultVec The 3 element vector |
| * to receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The vector to transform. |
| * @param {goog.vec.ArrayType} resultVec The vector to |
| * receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.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; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. The input matrix is multiplied against the |
| * upper 3x4 matrix omitting the projective component. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The 3 element vector to |
| * transform. |
| * @param {goog.vec.ArrayType} resultVec The 3 element vector to |
| * receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.multVec3ToArray = function(mat, vec, resultVec) { |
| goog.vec.Matrix4.multVec3( |
| mat, vec, /** @type {goog.vec.ArrayType} */ (resultVec)); |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Transforms the given vector with the given matrix storing the resulting, |
| * transformed vector into resultVec. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix supplying the |
| * transformation. |
| * @param {goog.vec.ArrayType} vec The vector to transform. |
| * @param {goog.vec.ArrayType} resultVec The vector to |
| * receive the results (may be vec). |
| * @return {goog.vec.ArrayType} return resultVec so that operations can be |
| * chained together. |
| */ |
| goog.vec.Matrix4.multVec4ToArray = function(mat, vec, resultVec) { |
| goog.vec.Matrix4.multVec4( |
| mat, vec, /** @type {goog.vec.ArrayType} */ (resultVec)); |
| return resultVec; |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as a translation matrix with x, y and z |
| * translation factors. |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.makeTranslate = function(mat, x, y, z) { |
| goog.vec.Matrix4.setIdentity(mat); |
| goog.vec.Matrix4.setColumnValues(mat, 3, x, y, z, 1); |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as a scale matrix with x, y and z scale |
| * factors. |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.makeScale = function(mat, x, y, z) { |
| goog.vec.Matrix4.setIdentity(mat); |
| goog.vec.Matrix4.setDiagonalValues(mat, x, y, z, 1); |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as a rotation matrix with the given rotation |
| * angle about the axis defined by the vector (ax, ay, az). |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.makeAxisAngleRotate = function( |
| mat, angle, ax, ay, az) { |
| var c = Math.cos(angle); |
| var d = 1 - c; |
| var s = Math.sin(angle); |
| |
| goog.vec.Matrix4.setFromValues(mat, |
| ax * ax * d + c, |
| ax * ay * d + az * s, |
| ax * az * d - ay * s, |
| 0, |
| |
| ax * ay * d - az * s, |
| ay * ay * d + c, |
| ay * az * d + ax * s, |
| 0, |
| |
| ax * az * d + ay * s, |
| ay * az * d - ax * s, |
| az * az * d + c, |
| 0, |
| |
| 0, 0, 0, 1); |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as a perspective projection matrix. |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.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); |
| |
| goog.vec.Matrix4.setFromValues(mat, |
| x, 0, 0, 0, |
| 0, y, 0, 0, |
| a, b, c, -1, |
| 0, 0, d, 0 |
| ); |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as a perspective projection matrix given a |
| * field of view and aspect ratio. |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.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; |
| |
| var cot = Math.cos(angle) / sinAngle; |
| goog.vec.Matrix4.setFromValues(mat, |
| cot / aspect, 0, 0, 0, |
| 0, cot, 0, 0, |
| 0, 0, -(far + near) / dz, -1, |
| 0, 0, -(2 * near * far) / dz, 0 |
| ); |
| }; |
| |
| |
| /** |
| * Initializes the given 4x4 matrix as an orthographic projection matrix. |
| * @param {goog.vec.ArrayType} mat The 4x4 (16-element) matrix |
| * array to receive the new translation 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. |
| */ |
| goog.vec.Matrix4.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); |
| |
| goog.vec.Matrix4.setFromValues(mat, |
| x, 0, 0, 0, |
| 0, y, 0, 0, |
| 0, 0, z, 0, |
| a, b, c, 1 |
| ); |
| }; |
| |
| |
| /** |
| * Updates a matrix representing the modelview matrix of a camera so that |
| * the camera is 'looking at' the given center point. |
| * @param {goog.vec.ArrayType} viewMatrix The matrix. |
| * @param {goog.vec.ArrayType} eyePt The position of the eye point |
| * (camera origin). |
| * @param {goog.vec.ArrayType} centerPt The point to aim the camera |
| * at. |
| * @param {goog.vec.ArrayType} worldUpVec The vector that |
| * identifies the up direction for the camera. |
| */ |
| goog.vec.Matrix4.lookAt = function( |
| viewMatrix, eyePt, centerPt, worldUpVec) { |
| // Compute the direction vector from the eye point to the center point and |
| // normalize. |
| var fwdVec = goog.vec.Matrix4.tmpVec4_[0]; |
| goog.vec.Vec3.subtract(centerPt, eyePt, fwdVec); |
| goog.vec.Vec3.normalize(fwdVec, fwdVec); |
| fwdVec[3] = 0; |
| |
| // Compute the side vector from the forward vector and the input up vector. |
| var sideVec = goog.vec.Matrix4.tmpVec4_[1]; |
| goog.vec.Vec3.cross(fwdVec, worldUpVec, sideVec); |
| goog.vec.Vec3.normalize(sideVec, sideVec); |
| sideVec[3] = 0; |
| |
| // Now the up vector to form the orthonormal basis. |
| var upVec = goog.vec.Matrix4.tmpVec4_[2]; |
| goog.vec.Vec3.cross(sideVec, fwdVec, upVec); |
| goog.vec.Vec3.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.Vec3.negate(fwdVec, fwdVec); |
| goog.vec.Matrix4.setRow(viewMatrix, 0, sideVec); |
| goog.vec.Matrix4.setRow(viewMatrix, 1, upVec); |
| goog.vec.Matrix4.setRow(viewMatrix, 2, fwdVec); |
| goog.vec.Matrix4.setRowValues(viewMatrix, 3, 0, 0, 0, 1); |
| goog.vec.Matrix4.applyTranslate( |
| viewMatrix, -eyePt[0], -eyePt[1], -eyePt[2]); |
| }; |
| |
| |
| /** |
| * 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. |
| * @param {goog.vec.ArrayType} viewMatrix The matrix. |
| * @param {goog.vec.ArrayType} eyePt The position of the eye point |
| * (camera origin). |
| * @param {goog.vec.ArrayType} fwdVec The vector describing where |
| * the camera points to. |
| * @param {goog.vec.ArrayType} 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.Matrix4.toLookAt = function( |
| viewMatrix, eyePt, fwdVec, worldUpVec) { |
| // Get eye of the camera. |
| var viewMatrixInverse = goog.vec.Matrix4.tmpMatrix4_[0]; |
| if (!goog.vec.Matrix4.invert(viewMatrix, viewMatrixInverse)) { |
| // The input matrix does not have a valid inverse. |
| return false; |
| } |
| |
| if (eyePt) { |
| eyePt[0] = viewMatrixInverse[12]; |
| eyePt[1] = viewMatrixInverse[13]; |
| eyePt[2] = viewMatrixInverse[14]; |
| } |
| |
| // Get forward vector from the definition of lookAt. |
| if (fwdVec || worldUpVec) { |
| if (!fwdVec) { |
| fwdVec = goog.vec.Matrix4.tmpVec3_[0]; |
| } |
| fwdVec[0] = -viewMatrix[2]; |
| fwdVec[1] = -viewMatrix[6]; |
| fwdVec[2] = -viewMatrix[10]; |
| // Normalize forward vector. |
| goog.vec.Vec3.normalize(fwdVec, fwdVec); |
| } |
| |
| if (worldUpVec) { |
| // Get side vector from the definition of gluLookAt. |
| var side = goog.vec.Matrix4.tmpVec3_[1]; |
| side[0] = viewMatrix[0]; |
| side[1] = viewMatrix[4]; |
| side[2] = viewMatrix[8]; |
| // Compute up vector as a up = side x forward. |
| goog.vec.Vec3.cross(side, fwdVec, worldUpVec); |
| // Normalize up vector. |
| goog.vec.Vec3.normalize(worldUpVec, worldUpVec); |
| } |
| return true; |
| }; |
| |
| |
| /** |
| * Constructs a rotation matrix from its 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), |
| * where rotation_x(theta) means rotation around the X axis of theta radians. |
| * @param {goog.vec.ArrayType} matrix The rotation 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. |
| */ |
| goog.vec.Matrix4.fromEulerZXZ = function( |
| matrix, 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); |
| |
| matrix[0] = c1 * c3 - c2 * s1 * s3; |
| matrix[1] = c2 * c1 * s3 + c3 * s1; |
| matrix[2] = s3 * s2; |
| matrix[3] = 0; |
| |
| matrix[4] = -c1 * s3 - c3 * c2 * s1; |
| matrix[5] = c1 * c2 * c3 - s1 * s3; |
| matrix[6] = c3 * s2; |
| matrix[7] = 0; |
| |
| matrix[8] = s2 * s1; |
| matrix[9] = -c1 * s2; |
| matrix[10] = c2; |
| matrix[11] = 0; |
| |
| matrix[12] = 0; |
| matrix[13] = 0; |
| matrix[14] = 0; |
| matrix[15] = 1; |
| }; |
| |
| |
| /** |
| * Decomposes a rotation matrix into Euler angles using the ZXZ convention. |
| * @param {goog.vec.ArrayType} matrix The rotation matrix. |
| * @param {goog.vec.ArrayType} euler The ZXZ Euler angles in |
| * radians. euler = [roll, tilt, pan]. |
| */ |
| goog.vec.Matrix4.toEulerZXZ = function(matrix, euler) { |
| var s2 = Math.sqrt(matrix[2] * matrix[2] + matrix[6] * matrix[6]); |
| |
| // There is an ambiguity in the sign of s2. We assume the tilt value |
| // is between [-pi/2, 0], so s2 is always negative. |
| if (s2 > goog.vec.EPSILON) { |
| euler[2] = Math.atan2(-matrix[2], -matrix[6]); |
| euler[1] = Math.atan2(-s2, matrix[10]); |
| euler[0] = Math.atan2(-matrix[8], matrix[9]); |
| } else { |
| // There is also an arbitrary choice for roll = 0 or pan = 0 in this case. |
| // We assume roll = 0 as some applications do not allow the camera to roll. |
| euler[0] = 0; |
| euler[1] = Math.atan2(-s2, matrix[10]); |
| euler[2] = Math.atan2(matrix[1], matrix[0]); |
| } |
| }; |
| |
| |
| /** |
| * Applies a translation by x,y,z to the given matrix. |
| * |
| * @param {goog.vec.ArrayType} 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. |
| */ |
| goog.vec.Matrix4.applyTranslate = function(mat, x, y, z) { |
| goog.vec.Matrix4.setColumnValues( |
| mat, 3, |
| mat[0] * x + mat[4] * y + mat[8] * z + mat[12], |
| mat[1] * x + mat[5] * y + mat[9] * z + mat[13], |
| mat[2] * x + mat[6] * y + mat[10] * z + mat[14], |
| mat[3] * x + mat[7] * y + mat[11] * z + mat[15]); |
| }; |
| |
| |
| /** |
| * Applies an x,y,z scale to the given matrix. |
| * |
| * @param {goog.vec.ArrayType} mat The matrix. |
| * @param {number} x The x scale factor. |
| * @param {number} y The y scale factor. |
| * @param {number} z The z scale factor. |
| */ |
| goog.vec.Matrix4.applyScale = function(mat, x, y, z) { |
| goog.vec.Matrix4.setFromValues( |
| mat, |
| mat[0] * x, mat[1] * x, mat[2] * x, mat[3] * x, |
| mat[4] * y, mat[5] * y, mat[6] * y, mat[7] * y, |
| mat[8] * z, mat[9] * z, mat[10] * z, mat[11] * z, |
| mat[12], mat[13], mat[14], mat[15]); |
| }; |
| |
| |
| /** |
| * Applies a rotation by angle about the x,y,z axis to the given matrix. |
| * |
| * @param {goog.vec.ArrayType} 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. |
| */ |
| goog.vec.Matrix4.applyRotate = 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 m03 = mat[12], m13 = mat[13], m23 = mat[14], m33 = mat[15]; |
| |
| 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; |
| |
| goog.vec.Matrix4.setFromValues( |
| mat, |
| m00 * r00 + m01 * r10 + m02 * r20, |
| m10 * r00 + m11 * r10 + m12 * r20, |
| m20 * r00 + m21 * r10 + m22 * r20, |
| m30 * r00 + m31 * r10 + m32 * r20, |
| |
| m00 * r01 + m01 * r11 + m02 * r21, |
| m10 * r01 + m11 * r11 + m12 * r21, |
| m20 * r01 + m21 * r11 + m22 * r21, |
| m30 * r01 + m31 * r11 + m32 * r21, |
| |
| m00 * r02 + m01 * r12 + m02 * r22, |
| m10 * r02 + m11 * r12 + m12 * r22, |
| m20 * r02 + m21 * r12 + m22 * r22, |
| m30 * r02 + m31 * r12 + m32 * r22, |
| |
| m03, m13, m23, m33); |
| }; |
| |
| |
| /** |
| * @type {!Array<!goog.vec.Vec3.Type>} |
| * @private |
| */ |
| goog.vec.Matrix4.tmpVec3_ = [ |
| goog.vec.Vec3.createNumber(), |
| goog.vec.Vec3.createNumber() |
| ]; |
| |
| |
| /** |
| * @type {!Array<!goog.vec.Vec4.Type>} |
| * @private |
| */ |
| goog.vec.Matrix4.tmpVec4_ = [ |
| goog.vec.Vec4.createNumber(), |
| goog.vec.Vec4.createNumber(), |
| goog.vec.Vec4.createNumber() |
| ]; |
| |
| |
| /** |
| * @type {Array<goog.vec.Matrix4.Type>} |
| * @private |
| */ |
| goog.vec.Matrix4.tmpMatrix4_ = [ |
| goog.vec.Matrix4.create() |
| ]; |