/**
* @license
* Copyright The Closure Library Authors.
* SPDX-License-Identifier: Apache-2.0
*/
////////////////////////// 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');
/** @suppress {extraRequire} */
goog.require('goog.vec.Quaternion');
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() {
'use strict';
return new Float64Array(16);
};
/**
* Creates a mat4d identity matrix.
*
* @return {!goog.vec.mat4d.Type} The new mat4d.
*/
goog.vec.mat4d.createIdentity = function() {
'use strict';
const mat = goog.vec.mat4d.create();
mat[0] = mat[5] = mat[10] = mat[15] = 1;
return mat;
};
/**
* 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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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 {
const offset = opt_diagonal > 0 ? 4 * opt_diagonal : -opt_diagonal;
for (let 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 receive 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) {
'use strict';
const 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) {
'use strict';
const 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) {
'use strict';
const 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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
const a00 = mat0[0];
const a10 = mat0[1];
const a20 = mat0[2];
const a30 = mat0[3];
const a01 = mat0[4];
const a11 = mat0[5];
const a21 = mat0[6];
const a31 = mat0[7];
const a02 = mat0[8];
const a12 = mat0[9];
const a22 = mat0[10];
const a32 = mat0[11];
const a03 = mat0[12];
const a13 = mat0[13];
const a23 = mat0[14];
const a33 = mat0[15];
const b00 = mat1[0];
const b10 = mat1[1];
const b20 = mat1[2];
const b30 = mat1[3];
const b01 = mat1[4];
const b11 = mat1[5];
const b21 = mat1[6];
const b31 = mat1[7];
const b02 = mat1[8];
const b12 = mat1[9];
const b22 = mat1[10];
const b32 = mat1[11];
const b03 = mat1[12];
const b13 = mat1[13];
const b23 = mat1[14];
const 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) {
'use strict';
if (resultMat == mat) {
const a10 = mat[1];
const a20 = mat[2];
const a30 = mat[3];
const a21 = mat[6];
const a31 = mat[7];
const 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) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m30 = mat[3];
const m01 = mat[4];
const m11 = mat[5];
const m21 = mat[6];
const m31 = mat[7];
const m02 = mat[8];
const m12 = mat[9];
const m22 = mat[10];
const m32 = mat[11];
const m03 = mat[12];
const m13 = mat[13];
const m23 = mat[14];
const m33 = mat[15];
const a0 = m00 * m11 - m10 * m01;
const a1 = m00 * m21 - m20 * m01;
const a2 = m00 * m31 - m30 * m01;
const a3 = m10 * m21 - m20 * m11;
const a4 = m10 * m31 - m30 * m11;
const a5 = m20 * m31 - m30 * m21;
const b0 = m02 * m13 - m12 * m03;
const b1 = m02 * m23 - m22 * m03;
const b2 = m02 * m33 - m32 * m03;
const b3 = m12 * m23 - m22 * m13;
const b4 = m12 * m33 - m32 * m13;
const 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) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m30 = mat[3];
const m01 = mat[4];
const m11 = mat[5];
const m21 = mat[6];
const m31 = mat[7];
const m02 = mat[8];
const m12 = mat[9];
const m22 = mat[10];
const m32 = mat[11];
const m03 = mat[12];
const m13 = mat[13];
const m23 = mat[14];
const m33 = mat[15];
const a0 = m00 * m11 - m10 * m01;
const a1 = m00 * m21 - m20 * m01;
const a2 = m00 * m31 - m30 * m01;
const a3 = m10 * m21 - m20 * m11;
const a4 = m10 * m31 - m30 * m11;
const a5 = m20 * m31 - m30 * m21;
const b0 = m02 * m13 - m12 * m03;
const b1 = m02 * m23 - m22 * m03;
const b2 = m02 * m33 - m32 * m03;
const b3 = m12 * m23 - m22 * m13;
const b4 = m12 * m33 - m32 * m13;
const b5 = m22 * m33 - m32 * m23;
const det = a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0;
if (det == 0) {
return false;
}
const 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 two matrices are equivalent.
*/
goog.vec.mat4d.equals = function(mat0, mat1) {
'use strict';
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) {
'use strict';
const x = vec[0];
const y = vec[1];
const 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) {
'use strict';
const x = vec[0];
const y = vec[1];
const 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) {
'use strict';
const x = vec[0];
const y = vec[1];
const z = vec[2];
const 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) {
'use strict';
const w = vec[3];
const x = vec[0];
const y = vec[1];
const z = vec[2];
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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
const c = Math.cos(angle);
const d = 1 - c;
const 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) {
'use strict';
const c = Math.cos(angle);
const 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) {
'use strict';
const c = Math.cos(angle);
const 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) {
'use strict';
const c = Math.cos(angle);
const 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;
};
/**
* Creates a matrix from a quaternion rotation and vector translation.
*
* This is a specialization of makeRotationTranslationScaleOrigin.
*
* This is equivalent to, but faster than:
* goog.vec.mat4d.makeIdentity(m);
* goog.vec.mat4d.translate(m, tx, ty, tz);
* goog.vec.mat4d.rotate(m, theta, rx, ry, rz);
* and:
* goog.vec.Quaternion.toRotationMatrix4(rotation, mat);
* mat[12] = translation[0];
* mat[13] = translation[1];
* mat[14] = translation[2];
* See http://jsperf.com/goog-vec-makerotationtranslation2 .
*
* @param {!goog.vec.mat4d.Type} mat The matrix.
* @param {!goog.vec.Quaternion.AnyType} rotation The quaternion rotation.
* Note: this quaternion is assumed to already be normalized.
* @param {!goog.vec.vec3d.Type} translation The vector translation.
* @return {!goog.vec.mat4d.Type} return mat so that operations can be
* chained.
*/
goog.vec.mat4d.makeRotationTranslation = function(mat, rotation, translation) {
'use strict';
// Quaternion math
const w = rotation[3];
const x = rotation[0];
const y = rotation[1];
const z = rotation[2];
const x2 = 2 * x;
const y2 = 2 * y;
const z2 = 2 * z;
const xx = x * x2;
const xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
mat[0] = 1 - (yy + zz);
mat[1] = xy + wz;
mat[2] = xz - wy;
mat[3] = 0;
mat[4] = xy - wz;
mat[5] = 1 - (xx + zz);
mat[6] = yz + wx;
mat[7] = 0;
mat[8] = xz + wy;
mat[9] = yz - wx;
mat[10] = 1 - (xx + yy);
mat[11] = 0;
mat[12] = translation[0];
mat[13] = translation[1];
mat[14] = translation[2];
mat[15] = 1;
return mat;
};
/**
* Creates a matrix from a quaternion rotation, vector translation, and
* vector scale.
*
* This is a specialization of makeRotationTranslationScaleOrigin.
*
* This is equivalent to, but faster than:
* goog.vec.mat4d.makeIdentity(m);
* goog.vec.mat4d.translate(m, tx, ty, tz);
* goog.vec.mat4d.rotate(m, theta, rx, ry, rz);
* goog.vec.mat4d.scale(m, sx, sy, sz);
*
* @param {!goog.vec.mat4d.Type} mat The matrix.
* @param {!goog.vec.Quaternion.AnyType} rotation The quaternion rotation.
* Note: this quaternion is assumed to already be normalized.
* @param {!goog.vec.vec3d.Type} translation The vector translation.
* @param {!goog.vec.vec3d.Type} scale The vector scale.
* @return {!goog.vec.mat4d.Type} return mat so that operations can be
* chained.
*/
goog.vec.mat4d.makeRotationTranslationScale = function(
mat, rotation, translation, scale) {
'use strict';
// Quaternion math
const w = rotation[3];
const x = rotation[0];
const y = rotation[1];
const z = rotation[2];
const x2 = 2 * x;
const y2 = 2 * y;
const z2 = 2 * z;
const xx = x * x2;
const xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
const sx = scale[0];
const sy = scale[1];
const sz = scale[2];
mat[0] = (1 - (yy + zz)) * sx;
mat[1] = (xy + wz) * sx;
mat[2] = (xz - wy) * sx;
mat[3] = 0;
mat[4] = (xy - wz) * sy;
mat[5] = (1 - (xx + zz)) * sy;
mat[6] = (yz + wx) * sy;
mat[7] = 0;
mat[8] = (xz + wy) * sz;
mat[9] = (yz - wx) * sz;
mat[10] = (1 - (xx + yy)) * sz;
mat[11] = 0;
mat[12] = translation[0];
mat[13] = translation[1];
mat[14] = translation[2];
mat[15] = 1;
return mat;
};
/**
* Creates a matrix from a quaternion rotation, vector translation, and
* vector scale, rotating and scaling about the given origin.
*
* This is equivalent to, but faster than:
* goog.vec.mat4d.makeIdentity(m);
* goog.vec.mat4d.translate(m, tx, ty, tz);
* goog.vec.mat4d.translate(m, ox, oy, oz);
* goog.vec.mat4d.rotate(m, theta, rx, ry, rz);
* goog.vec.mat4d.scale(m, sx, sy, sz);
* goog.vec.mat4d.translate(m, -ox, -oy, -oz);
* See http://jsperf.com/glmatrix-matrix-variant-test/3 for performance
* results of a similar function in the glmatrix library.
*
* @param {!goog.vec.mat4d.Type} mat The matrix.
* @param {!goog.vec.Quaternion.AnyType} rotation The quaternion rotation.
* Note: this quaternion is assumed to already be normalized.
* @param {!goog.vec.vec3d.Type} translation The vector translation.
* @param {!goog.vec.vec3d.Type} scale The vector scale.
* @param {!goog.vec.vec3d.Type} origin The origin about which to scale and
* rotate.
* @return {!goog.vec.mat4d.Type} return mat so that operations can be
* chained.
*/
goog.vec.mat4d.makeRotationTranslationScaleOrigin = function(
mat, rotation, translation, scale, origin) {
'use strict';
// Quaternion math
const w = rotation[3];
const x = rotation[0];
const y = rotation[1];
const z = rotation[2];
const x2 = 2 * x;
const y2 = 2 * y;
const z2 = 2 * z;
const xx = x * x2;
const xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
const sx = scale[0];
const sy = scale[1];
const sz = scale[2];
const ox = origin[0];
const oy = origin[1];
const oz = origin[2];
mat[0] = (1 - (yy + zz)) * sx;
mat[1] = (xy + wz) * sx;
mat[2] = (xz - wy) * sx;
mat[3] = 0;
mat[4] = (xy - wz) * sy;
mat[5] = (1 - (xx + zz)) * sy;
mat[6] = (yz + wx) * sy;
mat[7] = 0;
mat[8] = (xz + wy) * sz;
mat[9] = (yz - wx) * sz;
mat[10] = (1 - (xx + yy)) * sz;
mat[11] = 0;
mat[12] = translation[0] + ox - (mat[0] * ox + mat[4] * oy + mat[8] * oz);
mat[13] = translation[1] + oy - (mat[1] * ox + mat[5] * oy + mat[9] * oz);
mat[14] = translation[2] + oz - (mat[2] * ox + mat[6] * oy + mat[10] * oz);
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) {
'use strict';
const x = (2 * near) / (right - left);
const y = (2 * near) / (top - bottom);
const a = (right + left) / (right - left);
const b = (top + bottom) / (top - bottom);
const c = -(far + near) / (far - near);
const 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;
};
/**
* Makes 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) {
'use strict';
const angle = fovy / 2;
const dz = far - near;
const sinAngle = Math.sin(angle);
if (dz == 0 || sinAngle == 0 || aspect == 0) {
return mat;
}
const 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) {
'use strict';
const x = 2 / (right - left);
const y = 2 / (top - bottom);
const z = -2 / (far - near);
const a = -(right + left) / (right - left);
const b = -(top + bottom) / (top - bottom);
const 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) {
'use strict';
// Compute the direction vector from the eye point to the center point and
// normalize.
const 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.
const 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.
const 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) {
'use strict';
// Get eye of the camera.
const 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.
const 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) {
'use strict';
const c1 = Math.cos(theta1);
const s1 = Math.sin(theta1);
const c2 = Math.cos(theta2);
const s2 = Math.sin(theta2);
const c3 = Math.cos(theta3);
const 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) {
'use strict';
// There is an ambiguity in the sign of sinTheta2 because of the sqrt.
const 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.
const 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) {
'use strict';
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) {
'use strict';
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) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m30 = mat[3];
const m01 = mat[4];
const m11 = mat[5];
const m21 = mat[6];
const m31 = mat[7];
const m02 = mat[8];
const m12 = mat[9];
const m22 = mat[10];
const m32 = mat[11];
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
const diffCosAngle = 1 - cosAngle;
const r00 = x * x * diffCosAngle + cosAngle;
const r10 = x * y * diffCosAngle + z * sinAngle;
const r20 = x * z * diffCosAngle - y * sinAngle;
const r01 = x * y * diffCosAngle - z * sinAngle;
const r11 = y * y * diffCosAngle + cosAngle;
const r21 = y * z * diffCosAngle + x * sinAngle;
const r02 = x * z * diffCosAngle + y * sinAngle;
const r12 = y * z * diffCosAngle - x * sinAngle;
const 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) {
'use strict';
const m01 = mat[4];
const m11 = mat[5];
const m21 = mat[6];
const m31 = mat[7];
const m02 = mat[8];
const m12 = mat[9];
const m22 = mat[10];
const m32 = mat[11];
const c = Math.cos(angle);
const 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) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m30 = mat[3];
const m02 = mat[8];
const m12 = mat[9];
const m22 = mat[10];
const m32 = mat[11];
const c = Math.cos(angle);
const 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) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m30 = mat[3];
const m01 = mat[4];
const m11 = mat[5];
const m21 = mat[6];
const m31 = mat[7];
const c = Math.cos(angle);
const 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) {
'use strict';
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()];
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