/**
* @license
* Copyright The Closure Library Authors.
* SPDX-License-Identifier: Apache-2.0
*/
/**
* @fileoverview Implements 3x3 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.
*
* The matrices are stored in column-major order.
*/
goog.provide('goog.vec.Mat3');
goog.require('goog.vec');
/** @typedef {!goog.vec.Float32} */ goog.vec.Mat3.Float32;
/** @typedef {!goog.vec.Float64} */ goog.vec.Mat3.Float64;
/** @typedef {!goog.vec.Number} */ goog.vec.Mat3.Number;
/** @typedef {!goog.vec.AnyType} */ goog.vec.Mat3.AnyType;
// The following two types are deprecated - use the above types instead.
/** @typedef {!Float32Array} */ goog.vec.Mat3.Type;
/** @typedef {!goog.vec.ArrayType} */ goog.vec.Mat3.Mat3Like;
/**
* Creates the array representation of a 3x3 matrix of Float32.
* The use of the array directly instead of a class reduces overhead.
* The returned matrix is cleared to all zeros.
*
* @return {!goog.vec.Mat3.Float32} The new matrix.
*/
goog.vec.Mat3.createFloat32 = function() {
'use strict';
return new Float32Array(9);
};
/**
* Creates the array representation of a 3x3 matrix of Float64.
* The returned matrix is cleared to all zeros.
*
* @return {!goog.vec.Mat3.Float64} The new matrix.
*/
goog.vec.Mat3.createFloat64 = function() {
'use strict';
return new Float64Array(9);
};
/**
* Creates the array representation of a 3x3 matrix of Number.
* The returned matrix is cleared to all zeros.
*
* @return {!goog.vec.Mat3.Number} The new matrix.
*/
goog.vec.Mat3.createNumber = function() {
'use strict';
const a = new Array(9);
goog.vec.Mat3.setFromValues(a, 0, 0, 0, 0, 0, 0, 0, 0, 0);
return a;
};
/**
* Creates the array representation of a 3x3 matrix of Float32.
* The returned matrix is cleared to all zeros.
*
* @deprecated Use createFloat32.
* @return {!goog.vec.Mat3.Type} The new matrix.
*/
goog.vec.Mat3.create = function() {
'use strict';
return goog.vec.Mat3.createFloat32();
};
/**
* Creates a 3x3 identity matrix of Float32.
*
* @return {!goog.vec.Mat3.Float32} The new 9 element array.
*/
goog.vec.Mat3.createFloat32Identity = function() {
'use strict';
const mat = goog.vec.Mat3.createFloat32();
mat[0] = mat[4] = mat[8] = 1;
return mat;
};
/**
* Creates a 3x3 identity matrix of Float64.
*
* @return {!goog.vec.Mat3.Float64} The new 9 element array.
*/
goog.vec.Mat3.createFloat64Identity = function() {
'use strict';
const mat = goog.vec.Mat3.createFloat64();
mat[0] = mat[4] = mat[8] = 1;
return mat;
};
/**
* Creates a 3x3 identity matrix of Number.
* The returned matrix is cleared to all zeros.
*
* @return {!goog.vec.Mat3.Number} The new 9 element array.
*/
goog.vec.Mat3.createNumberIdentity = function() {
'use strict';
const a = new Array(9);
goog.vec.Mat3.setFromValues(a, 1, 0, 0, 0, 1, 0, 0, 0, 1);
return a;
};
/**
* Creates the array representation of a 3x3 matrix of Float32.
* The returned matrix is cleared to all zeros.
*
* @deprecated Use createFloat32Identity.
* @return {!goog.vec.Mat3.Type} The new 9 element array.
*/
goog.vec.Mat3.createIdentity = function() {
'use strict';
return goog.vec.Mat3.createFloat32Identity();
};
/**
* Creates a 3x3 matrix of Float32 initialized from the given array.
*
* @param {goog.vec.Mat3.AnyType} matrix The array containing the
* matrix values in column major order.
* @return {!goog.vec.Mat3.Float32} The new, nine element array.
*/
goog.vec.Mat3.createFloat32FromArray = function(matrix) {
'use strict';
const newMatrix = goog.vec.Mat3.createFloat32();
goog.vec.Mat3.setFromArray(newMatrix, matrix);
return newMatrix;
};
/**
* Creates a 3x3 matrix of Float32 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} v01 The values at (0, 1).
* @param {number} v11 The values at (1, 1).
* @param {number} v21 The values at (2, 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).
* @return {!goog.vec.Mat3.Float32} The new, nine element array.
*/
goog.vec.Mat3.createFloat32FromValues = function(
v00, v10, v20, v01, v11, v21, v02, v12, v22) {
'use strict';
const newMatrix = goog.vec.Mat3.createFloat32();
goog.vec.Mat3.setFromValues(
newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
return newMatrix;
};
/**
* Creates a clone of a 3x3 matrix of Float32.
*
* @param {goog.vec.Mat3.Float32} matrix The source 3x3 matrix.
* @return {!goog.vec.Mat3.Float32} The new 3x3 element matrix.
*/
goog.vec.Mat3.cloneFloat32 = goog.vec.Mat3.createFloat32FromArray;
/**
* Creates a 3x3 matrix of Float64 initialized from the given array.
*
* @param {goog.vec.Mat3.AnyType} matrix The array containing the
* matrix values in column major order.
* @return {!goog.vec.Mat3.Float64} The new, nine element array.
*/
goog.vec.Mat3.createFloat64FromArray = function(matrix) {
'use strict';
const newMatrix = goog.vec.Mat3.createFloat64();
goog.vec.Mat3.setFromArray(newMatrix, matrix);
return newMatrix;
};
/**
* Creates a 3x3 matrix of Float64 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} v01 The values at (0, 1).
* @param {number} v11 The values at (1, 1).
* @param {number} v21 The values at (2, 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).
* @return {!goog.vec.Mat3.Float64} The new, nine element array.
*/
goog.vec.Mat3.createFloat64FromValues = function(
v00, v10, v20, v01, v11, v21, v02, v12, v22) {
'use strict';
const newMatrix = goog.vec.Mat3.createFloat64();
goog.vec.Mat3.setFromValues(
newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
return newMatrix;
};
/**
* Creates a clone of a 3x3 matrix of Float64.
*
* @param {goog.vec.Mat3.Float64} matrix The source 3x3 matrix.
* @return {!goog.vec.Mat3.Float64} The new 3x3 element matrix.
*/
goog.vec.Mat3.cloneFloat64 = goog.vec.Mat3.createFloat64FromArray;
/**
* Creates a 3x3 matrix of Float32 initialized from the given array.
*
* @deprecated Use createFloat32FromArray.
* @param {goog.vec.Mat3.Mat3Like} matrix The array containing the
* matrix values in column major order.
* @return {!goog.vec.Mat3.Type} The new, nine element array.
*/
goog.vec.Mat3.createFromArray = function(matrix) {
'use strict';
const newMatrix = goog.vec.Mat3.createFloat32();
goog.vec.Mat3.setFromArray(newMatrix, matrix);
return newMatrix;
};
/**
* Creates a 3x3 matrix of Float32 initialized from the given values.
*
* @deprecated Use createFloat32FromValues.
* @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} v01 The values at (0, 1).
* @param {number} v11 The values at (1, 1).
* @param {number} v21 The values at (2, 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).
* @return {!goog.vec.Mat3.Type} The new, nine element array.
*/
goog.vec.Mat3.createFromValues = function(
v00, v10, v20, v01, v11, v21, v02, v12, v22) {
'use strict';
const newMatrix = goog.vec.Mat3.create();
goog.vec.Mat3.setFromValues(
newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22);
return newMatrix;
};
/**
* Creates a clone of a 3x3 matrix of Float32.
*
* @deprecated Use cloneFloat32.
* @param {goog.vec.Mat3.Mat3Like} matrix The source 3x3 matrix.
* @return {!goog.vec.Mat3.Type} The new 3x3 element matrix.
*/
goog.vec.Mat3.clone = goog.vec.Mat3.createFromArray;
/**
* Retrieves the element at the requested row and column.
*
* @param {goog.vec.Mat3.AnyType} 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.Mat3.getElement = function(mat, row, column) {
'use strict';
return mat[row + column * 3];
};
/**
* Sets the element at the requested row and column.
*
* @param {goog.vec.Mat3.AnyType} 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.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setElement = function(mat, row, column, value) {
'use strict';
mat[row + column * 3] = value;
return mat;
};
/**
* Initializes the matrix from the set of values. Note the values supplied are
* in column major order.
*
* @param {goog.vec.Mat3.AnyType} 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} v01 The values at (0, 1).
* @param {number} v11 The values at (1, 1).
* @param {number} v21 The values at (2, 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).
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setFromValues = function(
mat, v00, v10, v20, v01, v11, v21, v02, v12, v22) {
'use strict';
mat[0] = v00;
mat[1] = v10;
mat[2] = v20;
mat[3] = v01;
mat[4] = v11;
mat[5] = v21;
mat[6] = v02;
mat[7] = v12;
mat[8] = v22;
return mat;
};
/**
* Sets the matrix from the array of values stored in column major order.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {goog.vec.Mat3.AnyType} values The column major ordered
* array of values to store in the matrix.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setFromArray = function(mat, values) {
'use strict';
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];
return mat;
};
/**
* Sets the matrix from the array of values stored in row major order.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {goog.vec.Mat3.AnyType} values The row major ordered array
* of values to store in the matrix.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setFromRowMajorArray = function(mat, values) {
'use strict';
mat[0] = values[0];
mat[1] = values[3];
mat[2] = values[6];
mat[3] = values[1];
mat[4] = values[4];
mat[5] = values[7];
mat[6] = values[2];
mat[7] = values[5];
mat[8] = values[8];
return mat;
};
/**
* Sets the diagonal values of the matrix from the given values.
*
* @param {goog.vec.Mat3.AnyType} 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).
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setDiagonalValues = function(mat, v00, v11, v22) {
'use strict';
mat[0] = v00;
mat[4] = v11;
mat[8] = v22;
return mat;
};
/**
* Sets the diagonal values of the matrix from the given vector.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {goog.vec.Vec3.AnyType} vec The vector containing the values.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setDiagonal = function(mat, vec) {
'use strict';
mat[0] = vec[0];
mat[4] = vec[1];
mat[8] = vec[2];
return mat;
};
/**
* Sets the specified column with the supplied values.
*
* @param {goog.vec.Mat3.AnyType} 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.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setColumnValues = function(mat, column, v0, v1, v2) {
'use strict';
const i = column * 3;
mat[i] = v0;
mat[i + 1] = v1;
mat[i + 2] = v2;
return mat;
};
/**
* Sets the specified column with the value from the supplied array.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {number} column The column index to set the values on.
* @param {goog.vec.Vec3.AnyType} vec The vector elements for the column.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setColumn = function(mat, column, vec) {
'use strict';
const i = column * 3;
mat[i] = vec[0];
mat[i + 1] = vec[1];
mat[i + 2] = vec[2];
return mat;
};
/**
* Retrieves the specified column from the matrix into the given vector
* array.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the values.
* @param {number} column The column to get the values from.
* @param {goog.vec.Vec3.AnyType} vec The vector elements to receive the
* column.
* @return {goog.vec.Vec3.AnyType} return vec so that operations can be
* chained together.
*/
goog.vec.Mat3.getColumn = function(mat, column, vec) {
'use strict';
const i = column * 3;
vec[0] = mat[i];
vec[1] = mat[i + 1];
vec[2] = mat[i + 2];
return vec;
};
/**
* Sets the columns of the matrix from the set of vector elements.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {goog.vec.Vec3.AnyType} vec0 The values for column 0.
* @param {goog.vec.Vec3.AnyType} vec1 The values for column 1.
* @param {goog.vec.Vec3.AnyType} vec2 The values for column 2.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setColumns = function(mat, vec0, vec1, vec2) {
'use strict';
goog.vec.Mat3.setColumn(mat, 0, vec0);
goog.vec.Mat3.setColumn(mat, 1, vec1);
goog.vec.Mat3.setColumn(mat, 2, vec2);
return mat;
};
/**
* Retrieves the column values from the given matrix into the given vector
* elements.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the columns.
* @param {goog.vec.Vec3.AnyType} vec0 The vector to receive column 0.
* @param {goog.vec.Vec3.AnyType} vec1 The vector to receive column 1.
* @param {goog.vec.Vec3.AnyType} vec2 The vector to receive column 2.
*/
goog.vec.Mat3.getColumns = function(mat, vec0, vec1, vec2) {
'use strict';
goog.vec.Mat3.getColumn(mat, 0, vec0);
goog.vec.Mat3.getColumn(mat, 1, vec1);
goog.vec.Mat3.getColumn(mat, 2, vec2);
};
/**
* Sets the row values from the supplied values.
*
* @param {goog.vec.Mat3.AnyType} 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.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setRowValues = function(mat, row, v0, v1, v2) {
'use strict';
mat[row] = v0;
mat[row + 3] = v1;
mat[row + 6] = v2;
return mat;
};
/**
* Sets the row values from the supplied vector.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the row values.
* @param {number} row The index of the row.
* @param {goog.vec.Vec3.AnyType} vec The vector containing the values.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setRow = function(mat, row, vec) {
'use strict';
mat[row] = vec[0];
mat[row + 3] = vec[1];
mat[row + 6] = vec[2];
return mat;
};
/**
* Retrieves the row values into the given vector.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the values.
* @param {number} row The index of the row supplying the values.
* @param {goog.vec.Vec3.AnyType} vec The vector to receive the row.
* @return {goog.vec.Vec3.AnyType} return vec so that operations can be
* chained together.
*/
goog.vec.Mat3.getRow = function(mat, row, vec) {
'use strict';
vec[0] = mat[row];
vec[1] = mat[row + 3];
vec[2] = mat[row + 6];
return vec;
};
/**
* Sets the rows of the matrix from the supplied vectors.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to receive the values.
* @param {goog.vec.Vec3.AnyType} vec0 The values for row 0.
* @param {goog.vec.Vec3.AnyType} vec1 The values for row 1.
* @param {goog.vec.Vec3.AnyType} vec2 The values for row 2.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained together.
*/
goog.vec.Mat3.setRows = function(mat, vec0, vec1, vec2) {
'use strict';
goog.vec.Mat3.setRow(mat, 0, vec0);
goog.vec.Mat3.setRow(mat, 1, vec1);
goog.vec.Mat3.setRow(mat, 2, vec2);
return mat;
};
/**
* Retrieves the rows of the matrix into the supplied vectors.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to supplying the values.
* @param {goog.vec.Vec3.AnyType} vec0 The vector to receive row 0.
* @param {goog.vec.Vec3.AnyType} vec1 The vector to receive row 1.
* @param {goog.vec.Vec3.AnyType} vec2 The vector to receive row 2.
*/
goog.vec.Mat3.getRows = function(mat, vec0, vec1, vec2) {
'use strict';
goog.vec.Mat3.getRow(mat, 0, vec0);
goog.vec.Mat3.getRow(mat, 1, vec1);
goog.vec.Mat3.getRow(mat, 2, vec2);
};
/**
* Makes the given 3x3 matrix the zero matrix.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @return {goog.vec.Mat3.AnyType} return mat so operations can be chained.
*/
goog.vec.Mat3.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;
return mat;
};
/**
* Makes the given 3x3 matrix the identity matrix.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @return {goog.vec.Mat3.AnyType} return mat so operations can be chained.
*/
goog.vec.Mat3.makeIdentity = function(mat) {
'use strict';
mat[0] = 1;
mat[1] = 0;
mat[2] = 0;
mat[3] = 0;
mat[4] = 1;
mat[5] = 0;
mat[6] = 0;
mat[7] = 0;
mat[8] = 1;
return mat;
};
/**
* Performs a per-component addition of the matrices mat0 and mat1, storing
* the result into resultMat.
*
* @param {goog.vec.Mat3.AnyType} mat0 The first addend.
* @param {goog.vec.Mat3.AnyType} mat1 The second addend.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to
* receive the results (may be either mat0 or mat1).
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
* chained together.
*/
goog.vec.Mat3.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];
return resultMat;
};
/**
* Performs a per-component subtraction of the matrices mat0 and mat1,
* storing the result into resultMat.
*
* @param {goog.vec.Mat3.AnyType} mat0 The minuend.
* @param {goog.vec.Mat3.AnyType} mat1 The subtrahend.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
* the results (may be either mat0 or mat1).
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
* chained together.
*/
goog.vec.Mat3.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];
return resultMat;
};
/**
* Multiplies matrix mat0 with the given scalar, storing the result
* into resultMat.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} scalar The scalar value to multiple to each element of mat.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
* the results (may be mat).
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
* chained together.
*/
goog.vec.Mat3.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;
return resultMat;
};
/**
* Multiplies the two matrices mat0 and mat1 using matrix multiplication,
* storing the result into resultMat.
*
* @param {goog.vec.Mat3.AnyType} mat0 The first (left hand) matrix.
* @param {goog.vec.Mat3.AnyType} mat1 The second (right hand) matrix.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
* the results (may be either mat0 or mat1).
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
* chained together.
*/
goog.vec.Mat3.multMat = function(mat0, mat1, resultMat) {
'use strict';
const a00 = mat0[0];
const a10 = mat0[1];
const a20 = mat0[2];
const a01 = mat0[3];
const a11 = mat0[4];
const a21 = mat0[5];
const a02 = mat0[6];
const a12 = mat0[7];
const a22 = mat0[8];
const b00 = mat1[0];
const b10 = mat1[1];
const b20 = mat1[2];
const b01 = mat1[3];
const b11 = mat1[4];
const b21 = mat1[5];
const b02 = mat1[6];
const b12 = mat1[7];
const b22 = mat1[8];
resultMat[0] = a00 * b00 + a01 * b10 + a02 * b20;
resultMat[1] = a10 * b00 + a11 * b10 + a12 * b20;
resultMat[2] = a20 * b00 + a21 * b10 + a22 * b20;
resultMat[3] = a00 * b01 + a01 * b11 + a02 * b21;
resultMat[4] = a10 * b01 + a11 * b11 + a12 * b21;
resultMat[5] = a20 * b01 + a21 * b11 + a22 * b21;
resultMat[6] = a00 * b02 + a01 * b12 + a02 * b22;
resultMat[7] = a10 * b02 + a11 * b12 + a12 * b22;
resultMat[8] = a20 * b02 + a21 * b12 + a22 * b22;
return resultMat;
};
/**
* Transposes the given matrix mat storing the result into resultMat.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix to transpose.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
* the results (may be mat).
* @return {goog.vec.Mat3.AnyType} return resultMat so that operations can be
* chained together.
*/
goog.vec.Mat3.transpose = function(mat, resultMat) {
'use strict';
if (resultMat == mat) {
const a10 = mat[1];
const a20 = mat[2];
const a21 = mat[5];
resultMat[1] = mat[3];
resultMat[2] = mat[6];
resultMat[3] = a10;
resultMat[5] = mat[7];
resultMat[6] = a20;
resultMat[7] = a21;
} else {
resultMat[0] = mat[0];
resultMat[1] = mat[3];
resultMat[2] = mat[6];
resultMat[3] = mat[1];
resultMat[4] = mat[4];
resultMat[5] = mat[7];
resultMat[6] = mat[2];
resultMat[7] = mat[5];
resultMat[8] = mat[8];
}
return resultMat;
};
/**
* Computes the inverse of mat0 storing the result into resultMat. If the
* inverse is defined, this function returns true, false otherwise.
*
* @param {goog.vec.Mat3.AnyType} mat0 The matrix to invert.
* @param {goog.vec.Mat3.AnyType} resultMat The matrix to receive
* the result (may be mat0).
* @return {boolean} True if the inverse is defined. If false is returned,
* resultMat is not modified.
*/
goog.vec.Mat3.invert = function(mat0, resultMat) {
'use strict';
const a00 = mat0[0];
const a10 = mat0[1];
const a20 = mat0[2];
const a01 = mat0[3];
const a11 = mat0[4];
const a21 = mat0[5];
const a02 = mat0[6];
const a12 = mat0[7];
const a22 = mat0[8];
const t00 = a11 * a22 - a12 * a21;
const t10 = a12 * a20 - a10 * a22;
const t20 = a10 * a21 - a11 * a20;
const det = a00 * t00 + a01 * t10 + a02 * t20;
if (det == 0) {
return false;
}
const idet = 1 / det;
resultMat[0] = t00 * idet;
resultMat[3] = (a02 * a21 - a01 * a22) * idet;
resultMat[6] = (a01 * a12 - a02 * a11) * idet;
resultMat[1] = t10 * idet;
resultMat[4] = (a00 * a22 - a02 * a20) * idet;
resultMat[7] = (a02 * a10 - a00 * a12) * idet;
resultMat[2] = t20 * idet;
resultMat[5] = (a01 * a20 - a00 * a21) * idet;
resultMat[8] = (a00 * a11 - a01 * a10) * idet;
return true;
};
/**
* Returns true if the components of mat0 are equal to the components of mat1.
*
* @param {goog.vec.Mat3.AnyType} mat0 The first matrix.
* @param {goog.vec.Mat3.AnyType} mat1 The second matrix.
* @return {boolean} True if the two matrices are equivalent.
*/
goog.vec.Mat3.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];
};
/**
* Transforms the given vector with the given matrix storing the resulting,
* transformed matrix into resultVec.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix supplying the transformation.
* @param {goog.vec.Vec3.AnyType} vec The vector to transform.
* @param {goog.vec.Vec3.AnyType} resultVec The vector to
* receive the results (may be vec).
* @return {goog.vec.Vec3.AnyType} return resultVec so that operations can be
* chained together.
*/
goog.vec.Mat3.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[3] + z * mat[6];
resultVec[1] = x * mat[1] + y * mat[4] + z * mat[7];
resultVec[2] = x * mat[2] + y * mat[5] + z * mat[8];
return resultVec;
};
/**
* Makes the given 3x3 matrix a translation matrix with x and y
* translation values.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} x The translation along the x axis.
* @param {number} y The translation along the y axis.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeTranslate = function(mat, x, y) {
'use strict';
goog.vec.Mat3.makeIdentity(mat);
return goog.vec.Mat3.setColumnValues(mat, 2, x, y, 1);
};
/**
* Makes the given 3x3 matrix a scale matrix with x, y, and z scale factors.
*
* @param {goog.vec.Mat3.AnyType} mat The 3x3 (9-element) matrix
* array to receive the new scale 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.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeScale = function(mat, x, y, z) {
'use strict';
goog.vec.Mat3.makeIdentity(mat);
return goog.vec.Mat3.setDiagonalValues(mat, x, y, z);
};
/**
* Makes the given 3x3 matrix a rotation matrix with the given rotation
* angle about the axis defined by the vector (ax, ay, az).
*
* @param {goog.vec.Mat3.AnyType} 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.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeRotate = function(mat, angle, ax, ay, az) {
'use strict';
const c = Math.cos(angle);
const d = 1 - c;
const s = Math.sin(angle);
return goog.vec.Mat3.setFromValues(
mat, ax * ax * d + c, ax * ay * d + az * s, ax * az * d - ay * s,
ax * ay * d - az * s, ay * ay * d + c, ay * az * d + ax * s,
ax * az * d + ay * s, ay * az * d - ax * s, az * az * d + c);
};
/**
* Makes the given 3x3 matrix a rotation matrix with the given rotation
* angle about the X axis.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The rotation angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeRotateX = function(mat, angle) {
'use strict';
const c = Math.cos(angle);
const s = Math.sin(angle);
return goog.vec.Mat3.setFromValues(mat, 1, 0, 0, 0, c, s, 0, -s, c);
};
/**
* Makes the given 3x3 matrix a rotation matrix with the given rotation
* angle about the Y axis.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The rotation angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeRotateY = function(mat, angle) {
'use strict';
const c = Math.cos(angle);
const s = Math.sin(angle);
return goog.vec.Mat3.setFromValues(mat, c, 0, -s, 0, 1, 0, s, 0, c);
};
/**
* Makes the given 3x3 matrix a rotation matrix with the given rotation
* angle about the Z axis.
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The rotation angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.makeRotateZ = function(mat, angle) {
'use strict';
const c = Math.cos(angle);
const s = Math.sin(angle);
return goog.vec.Mat3.setFromValues(mat, c, s, 0, -s, c, 0, 0, 0, 1);
};
/**
* Rotate the given matrix by angle about the x,y,z axis. Equivalent to:
* goog.vec.Mat3.multMat(
* mat,
* goog.vec.Mat3.makeRotate(goog.vec.Mat3.create(), angle, x, y, z),
* mat);
*
* @param {goog.vec.Mat3.AnyType} 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.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.rotate = function(mat, angle, x, y, z) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m01 = mat[3];
const m11 = mat[4];
const m21 = mat[5];
const m02 = mat[6];
const m12 = mat[7];
const m22 = mat[8];
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;
return goog.vec.Mat3.setFromValues(
mat, m00 * r00 + m01 * r10 + m02 * r20, m10 * r00 + m11 * r10 + m12 * r20,
m20 * r00 + m21 * r10 + m22 * r20,
m00 * r01 + m01 * r11 + m02 * r21, m10 * r01 + m11 * r11 + m12 * r21,
m20 * r01 + m21 * r11 + m22 * r21,
m00 * r02 + m01 * r12 + m02 * r22, m10 * r02 + m11 * r12 + m12 * r22,
m20 * r02 + m21 * r12 + m22 * r22);
};
/**
* Rotate the given matrix by angle about the x axis. Equivalent to:
* goog.vec.Mat3.multMat(
* mat,
* goog.vec.Mat3.makeRotateX(goog.vec.Mat3.create(), angle),
* mat);
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.rotateX = function(mat, angle) {
'use strict';
const m01 = mat[3];
const m11 = mat[4];
const m21 = mat[5];
const m02 = mat[6];
const m12 = mat[7];
const m22 = mat[8];
const c = Math.cos(angle);
const s = Math.sin(angle);
mat[3] = m01 * c + m02 * s;
mat[4] = m11 * c + m12 * s;
mat[5] = m21 * c + m22 * s;
mat[6] = m01 * -s + m02 * c;
mat[7] = m11 * -s + m12 * c;
mat[8] = m21 * -s + m22 * c;
return mat;
};
/**
* Rotate the given matrix by angle about the y axis. Equivalent to:
* goog.vec.Mat3.multMat(
* mat,
* goog.vec.Mat3.makeRotateY(goog.vec.Mat3.create(), angle),
* mat);
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.rotateY = function(mat, angle) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m02 = mat[6];
const m12 = mat[7];
const m22 = mat[8];
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[6] = m00 * s + m02 * c;
mat[7] = m10 * s + m12 * c;
mat[8] = m20 * s + m22 * c;
return mat;
};
/**
* Rotate the given matrix by angle about the z axis. Equivalent to:
* goog.vec.Mat3.multMat(
* mat,
* goog.vec.Mat3.makeRotateZ(goog.vec.Mat3.create(), angle),
* mat);
*
* @param {goog.vec.Mat3.AnyType} mat The matrix.
* @param {number} angle The angle in radians.
* @return {goog.vec.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.rotateZ = function(mat, angle) {
'use strict';
const m00 = mat[0];
const m10 = mat[1];
const m20 = mat[2];
const m01 = mat[3];
const m11 = mat[4];
const m21 = mat[5];
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] = m00 * -s + m01 * c;
mat[4] = m10 * -s + m11 * c;
mat[5] = m20 * -s + m21 * c;
return mat;
};
/**
* Makes the given 3x3 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.Mat3.AnyType} 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.Mat3.AnyType} return mat so that operations can be
* chained.
*/
goog.vec.Mat3.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] = -c1 * s3 - c3 * c2 * s1;
mat[4] = c1 * c2 * c3 - s1 * s3;
mat[5] = c3 * s2;
mat[6] = s2 * s1;
mat[7] = -c1 * s2;
mat[8] = c2;
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.Mat3.AnyType} mat The matrix.
* @param {goog.vec.Vec3.AnyType} 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.Vec3.AnyType} return euler so that operations can be
* chained together.
*/
goog.vec.Mat3.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[5] * mat[5]);
// 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[5] * signTheta2);
euler[1] = Math.atan2(sinTheta2 * signTheta2, mat[8]);
euler[0] = Math.atan2(mat[6] * signTheta2, -mat[7] * 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[8]);
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;
};
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