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Diffstat (limited to 'contexts/data/lib/closure-library/closure/goog/vec/matrix3.js')
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diff --git a/contexts/data/lib/closure-library/closure/goog/vec/matrix3.js b/contexts/data/lib/closure-library/closure/goog/vec/matrix3.js deleted file mode 100644 index fc47af4..0000000 --- a/contexts/data/lib/closure-library/closure/goog/vec/matrix3.js +++ /dev/null @@ -1,722 +0,0 @@ -// Copyright 2011 The Closure Library Authors. All Rights Reserved. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS-IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -/** - * @fileoverview WARNING: DEPRECATED. Use Mat3 instead. - * 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. - * - */ -goog.provide('goog.vec.Matrix3'); - -goog.require('goog.vec'); - - -/** - * @typedef {goog.vec.ArrayType} - */ -goog.vec.Matrix3.Type; - - -/** - * Creates the array representation of a 3x3 matrix. The use of the array - * directly eliminates any overhead associated with the class representation - * defined above. The returned matrix is cleared to all zeros. - * - * @return {goog.vec.Matrix3.Type} The new, nine element array. - */ -goog.vec.Matrix3.create = function() { - return new Float32Array(9); -}; - - -/** - * Creates the array representation of a 3x3 matrix. The use of the array - * directly eliminates any overhead associated with the class representation - * defined above. The returned matrix is initialized with the identity. - * - * @return {goog.vec.Matrix3.Type} The new, nine element array. - */ -goog.vec.Matrix3.createIdentity = function() { - var mat = goog.vec.Matrix3.create(); - mat[0] = mat[4] = mat[8] = 1; - return mat; -}; - - -/** - * Creates a 3x3 matrix initialized from the given array. - * - * @param {goog.vec.ArrayType} matrix The array containing the - * matrix values in column major order. - * @return {goog.vec.Matrix3.Type} The new, nine element array. - */ -goog.vec.Matrix3.createFromArray = function(matrix) { - var newMatrix = goog.vec.Matrix3.create(); - goog.vec.Matrix3.setFromArray(newMatrix, matrix); - return newMatrix; -}; - - -/** - * Creates a 3x3 matrix initialized from the given values. - * - * @param {number} v00 The values at (0, 0). - * @param {number} v10 The values at (1, 0). - * @param {number} v20 The values at (2, 0). - * @param {number} 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.Matrix3.Type} The new, nine element array. - */ -goog.vec.Matrix3.createFromValues = function( - v00, v10, v20, v01, v11, v21, v02, v12, v22) { - var newMatrix = goog.vec.Matrix3.create(); - goog.vec.Matrix3.setFromValues( - newMatrix, v00, v10, v20, v01, v11, v21, v02, v12, v22); - return newMatrix; -}; - - -/** - * Creates a clone of a 3x3 matrix. - * - * @param {goog.vec.Matrix3.Type} matrix The source 3x3 matrix. - * @return {goog.vec.Matrix3.Type} The new 3x3 element matrix. - */ -goog.vec.Matrix3.clone = - goog.vec.Matrix3.createFromArray; - - -/** - * Retrieves the element at the requested row and column. - * - * @param {goog.vec.ArrayType} mat The matrix containing the - * value to retrieve. - * @param {number} row The row index. - * @param {number} column The column index. - * @return {number} The element value at the requested row, column indices. - */ -goog.vec.Matrix3.getElement = function(mat, row, column) { - return mat[row + column * 3]; -}; - - -/** - * Sets the element at the requested row and column. - * - * @param {goog.vec.ArrayType} mat The matrix containing the - * value to retrieve. - * @param {number} row The row index. - * @param {number} column The column index. - * @param {number} value The value to set at the requested row, column. - */ -goog.vec.Matrix3.setElement = function(mat, row, column, value) { - mat[row + column * 3] = value; -}; - - -/** - * Initializes the matrix from the set of values. Note the values supplied are - * in column major order. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {number} v00 The values at (0, 0). - * @param {number} v10 The values at (1, 0). - * @param {number} v20 The values at (2, 0). - * @param {number} 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). - */ -goog.vec.Matrix3.setFromValues = function( - mat, v00, v10, v20, v01, v11, v21, v02, v12, v22) { - 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; -}; - - -/** - * Sets the matrix from the array of values stored in column major order. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {goog.vec.ArrayType} values The column major ordered - * array of values to store in the matrix. - */ -goog.vec.Matrix3.setFromArray = function(mat, values) { - mat[0] = values[0]; - mat[1] = values[1]; - mat[2] = values[2]; - mat[3] = values[3]; - mat[4] = values[4]; - mat[5] = values[5]; - mat[6] = values[6]; - mat[7] = values[7]; - mat[8] = values[8]; -}; - - -/** - * Sets the matrix from the array of values stored in row major order. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {goog.vec.ArrayType} values The row major ordered array - * of values to store in the matrix. - */ -goog.vec.Matrix3.setFromRowMajorArray = function(mat, values) { - 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]; -}; - - -/** - * Sets the diagonal values of the matrix from the given values. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {number} v00 The values for (0, 0). - * @param {number} v11 The values for (1, 1). - * @param {number} v22 The values for (2, 2). - */ -goog.vec.Matrix3.setDiagonalValues = function(mat, v00, v11, v22) { - mat[0] = v00; - mat[4] = v11; - mat[8] = v22; -}; - - -/** - * Sets the diagonal values of the matrix from the given vector. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {goog.vec.ArrayType} vec The vector containing the - * values. - */ -goog.vec.Matrix3.setDiagonal = function(mat, vec) { - mat[0] = vec[0]; - mat[4] = vec[1]; - mat[8] = vec[2]; -}; - - -/** - * Sets the specified column with the supplied values. - * - * @param {goog.vec.ArrayType} mat The matrix to recieve the - * values. - * @param {number} column The column index to set the values on. - * @param {number} v0 The value for row 0. - * @param {number} v1 The value for row 1. - * @param {number} v2 The value for row 2. - */ -goog.vec.Matrix3.setColumnValues = function( - mat, column, v0, v1, v2) { - var i = column * 3; - mat[i] = v0; - mat[i + 1] = v1; - mat[i + 2] = v2; -}; - - -/** - * Sets the specified column with the value from the supplied array. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {number} column The column index to set the values on. - * @param {goog.vec.ArrayType} vec The vector elements for the - * column. - */ -goog.vec.Matrix3.setColumn = function(mat, column, vec) { - var i = column * 3; - mat[i] = vec[0]; - mat[i + 1] = vec[1]; - mat[i + 2] = vec[2]; -}; - - -/** - * Retrieves the specified column from the matrix into the given vector - * array. - * - * @param {goog.vec.ArrayType} mat The matrix supplying the - * values. - * @param {number} column The column to get the values from. - * @param {goog.vec.ArrayType} vec The vector elements to receive - * the column. - */ -goog.vec.Matrix3.getColumn = function(mat, column, vec) { - var i = column * 3; - vec[0] = mat[i]; - vec[1] = mat[i + 1]; - vec[2] = mat[i + 2]; -}; - - -/** - * Sets the columns of the matrix from the set of vector elements. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {goog.vec.ArrayType} vec0 The values for column 0. - * @param {goog.vec.ArrayType} vec1 The values for column 1. - * @param {goog.vec.ArrayType} vec2 The values for column 2. - */ -goog.vec.Matrix3.setColumns = function( - mat, vec0, vec1, vec2) { - goog.vec.Matrix3.setColumn(mat, 0, vec0); - goog.vec.Matrix3.setColumn(mat, 1, vec1); - goog.vec.Matrix3.setColumn(mat, 2, vec2); -}; - - -/** - * Retrieves the column values from the given matrix into the given vector - * elements. - * - * @param {goog.vec.ArrayType} mat The matrix containing the - * columns to retrieve. - * @param {goog.vec.ArrayType} vec0 The vector elements to receive - * column 0. - * @param {goog.vec.ArrayType} vec1 The vector elements to receive - * column 1. - * @param {goog.vec.ArrayType} vec2 The vector elements to receive - * column 2. - */ -goog.vec.Matrix3.getColumns = function( - mat, vec0, vec1, vec2) { - goog.vec.Matrix3.getColumn(mat, 0, vec0); - goog.vec.Matrix3.getColumn(mat, 1, vec1); - goog.vec.Matrix3.getColumn(mat, 2, vec2); -}; - - -/** - * Sets the row values from the supplied values. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {number} row The index of the row to receive the values. - * @param {number} v0 The value for column 0. - * @param {number} v1 The value for column 1. - * @param {number} v2 The value for column 2. - */ -goog.vec.Matrix3.setRowValues = function(mat, row, v0, v1, v2) { - mat[row] = v0; - mat[row + 3] = v1; - mat[row + 6] = v2; -}; - - -/** - * Sets the row values from the supplied vector. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * row values. - * @param {number} row The index of the row. - * @param {goog.vec.ArrayType} vec The vector containing the values. - */ -goog.vec.Matrix3.setRow = function(mat, row, vec) { - mat[row] = vec[0]; - mat[row + 3] = vec[1]; - mat[row + 6] = vec[2]; -}; - - -/** - * Retrieves the row values into the given vector. - * - * @param {goog.vec.ArrayType} mat The matrix supplying the - * values. - * @param {number} row The index of the row supplying the values. - * @param {goog.vec.ArrayType} vec The vector to receive the row. - */ -goog.vec.Matrix3.getRow = function(mat, row, vec) { - vec[0] = mat[row]; - vec[1] = mat[row + 3]; - vec[2] = mat[row + 6]; -}; - - -/** - * Sets the rows of the matrix from the supplied vectors. - * - * @param {goog.vec.ArrayType} mat The matrix to receive the - * values. - * @param {goog.vec.ArrayType} vec0 The values for row 0. - * @param {goog.vec.ArrayType} vec1 The values for row 1. - * @param {goog.vec.ArrayType} vec2 The values for row 2. - */ -goog.vec.Matrix3.setRows = function( - mat, vec0, vec1, vec2) { - goog.vec.Matrix3.setRow(mat, 0, vec0); - goog.vec.Matrix3.setRow(mat, 1, vec1); - goog.vec.Matrix3.setRow(mat, 2, vec2); -}; - - -/** - * Retrieves the rows of the matrix into the supplied vectors. - * - * @param {goog.vec.ArrayType} mat The matrix to supplying - * the values. - * @param {goog.vec.ArrayType} vec0 The vector to receive row 0. - * @param {goog.vec.ArrayType} vec1 The vector to receive row 1. - * @param {goog.vec.ArrayType} vec2 The vector to receive row 2. - */ -goog.vec.Matrix3.getRows = function( - mat, vec0, vec1, vec2) { - goog.vec.Matrix3.getRow(mat, 0, vec0); - goog.vec.Matrix3.getRow(mat, 1, vec1); - goog.vec.Matrix3.getRow(mat, 2, vec2); -}; - - -/** - * Clears the given matrix to zero. - * - * @param {goog.vec.ArrayType} mat The matrix to clear. - */ -goog.vec.Matrix3.setZero = function(mat) { - mat[0] = 0; - mat[1] = 0; - mat[2] = 0; - mat[3] = 0; - mat[4] = 0; - mat[5] = 0; - mat[6] = 0; - mat[7] = 0; - mat[8] = 0; -}; - - -/** - * Sets the given matrix to the identity matrix. - * - * @param {goog.vec.ArrayType} mat The matrix to set. - */ -goog.vec.Matrix3.setIdentity = function(mat) { - 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; -}; - - -/** - * Performs a per-component addition of the matrices mat0 and mat1, storing - * the result into resultMat. - * - * @param {goog.vec.ArrayType} mat0 The first addend. - * @param {goog.vec.ArrayType} mat1 The second addend. - * @param {goog.vec.ArrayType} resultMat The matrix to - * receive the results (may be either mat0 or mat1). - * @return {goog.vec.ArrayType} return resultMat so that operations can be - * chained together. - */ -goog.vec.Matrix3.add = function(mat0, mat1, resultMat) { - resultMat[0] = mat0[0] + mat1[0]; - resultMat[1] = mat0[1] + mat1[1]; - resultMat[2] = mat0[2] + mat1[2]; - resultMat[3] = mat0[3] + mat1[3]; - resultMat[4] = mat0[4] + mat1[4]; - resultMat[5] = mat0[5] + mat1[5]; - resultMat[6] = mat0[6] + mat1[6]; - resultMat[7] = mat0[7] + mat1[7]; - resultMat[8] = mat0[8] + mat1[8]; - return resultMat; -}; - - -/** - * Performs a per-component subtraction of the matrices mat0 and mat1, - * storing the result into resultMat. - * - * @param {goog.vec.ArrayType} mat0 The minuend. - * @param {goog.vec.ArrayType} mat1 The subtrahend. - * @param {goog.vec.ArrayType} resultMat The matrix to receive - * the results (may be either mat0 or mat1). - * @return {goog.vec.ArrayType} return resultMat so that operations can be - * chained together. - */ -goog.vec.Matrix3.subtract = function(mat0, mat1, resultMat) { - resultMat[0] = mat0[0] - mat1[0]; - resultMat[1] = mat0[1] - mat1[1]; - resultMat[2] = mat0[2] - mat1[2]; - resultMat[3] = mat0[3] - mat1[3]; - resultMat[4] = mat0[4] - mat1[4]; - resultMat[5] = mat0[5] - mat1[5]; - resultMat[6] = mat0[6] - mat1[6]; - resultMat[7] = mat0[7] - mat1[7]; - resultMat[8] = mat0[8] - mat1[8]; - return resultMat; -}; - - -/** - * Performs a component-wise multiplication of mat0 with the given scalar - * storing the result into resultMat. - * - * @param {goog.vec.ArrayType} mat0 The matrix to scale. - * @param {number} scalar The scalar value to multiple to each element of mat0. - * @param {goog.vec.ArrayType} resultMat The matrix to receive - * the results (may be mat0). - * @return {goog.vec.ArrayType} return resultMat so that operations can be - * chained together. - */ -goog.vec.Matrix3.scale = function(mat0, scalar, resultMat) { - resultMat[0] = mat0[0] * scalar; - resultMat[1] = mat0[1] * scalar; - resultMat[2] = mat0[2] * scalar; - resultMat[3] = mat0[3] * scalar; - resultMat[4] = mat0[4] * scalar; - resultMat[5] = mat0[5] * scalar; - resultMat[6] = mat0[6] * scalar; - resultMat[7] = mat0[7] * scalar; - resultMat[8] = mat0[8] * scalar; - return resultMat; -}; - - -/** - * Multiplies the two matrices mat0 and mat1 using matrix multiplication, - * storing the result into resultMat. - * - * @param {goog.vec.ArrayType} mat0 The first (left hand) matrix. - * @param {goog.vec.ArrayType} mat1 The second (right hand) - * matrix. - * @param {goog.vec.ArrayType} resultMat The matrix to receive - * the results (may be either mat0 or mat1). - * @return {goog.vec.ArrayType} return resultMat so that operations can be - * chained together. - */ -goog.vec.Matrix3.multMat = function(mat0, mat1, resultMat) { - var a00 = mat0[0], a10 = mat0[1], a20 = mat0[2]; - var a01 = mat0[3], a11 = mat0[4], a21 = mat0[5]; - var a02 = mat0[6], a12 = mat0[7], a22 = mat0[8]; - - var b00 = mat1[0], b10 = mat1[1], b20 = mat1[2]; - var b01 = mat1[3], b11 = mat1[4], b21 = mat1[5]; - var b02 = mat1[6], b12 = mat1[7], 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.ArrayType} mat The matrix to transpose. - * @param {goog.vec.ArrayType} resultMat The matrix to receive - * the results (may be mat). - * @return {goog.vec.ArrayType} return resultMat so that operations can be - * chained together. - */ -goog.vec.Matrix3.transpose = function(mat, resultMat) { - if (resultMat == mat) { - var a10 = mat[1], a20 = mat[2], 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.ArrayType} mat0 The matrix to invert. - * @param {goog.vec.ArrayType} 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.Matrix3.invert = function(mat0, resultMat) { - var a00 = mat0[0], a10 = mat0[1], a20 = mat0[2]; - var a01 = mat0[3], a11 = mat0[4], a21 = mat0[5]; - var a02 = mat0[6], a12 = mat0[7], a22 = mat0[8]; - - var t00 = a11 * a22 - a12 * a21; - var t10 = a12 * a20 - a10 * a22; - var t20 = a10 * a21 - a11 * a20; - var det = a00 * t00 + a01 * t10 + a02 * t20; - if (det == 0) { - return false; - } - - var 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.ArrayType} mat0 The first matrix. - * @param {goog.vec.ArrayType} mat1 The second matrix. - * @return {boolean} True if the the two matrices are equivalent. - */ -goog.vec.Matrix3.equals = function(mat0, mat1) { - return mat0.length == mat1.length && - mat0[0] == mat1[0] && mat0[1] == mat1[1] && mat0[2] == mat1[2] && - mat0[3] == mat1[3] && mat0[4] == mat1[4] && mat0[5] == mat1[5] && - mat0[6] == mat1[6] && mat0[7] == mat1[7] && mat0[8] == mat1[8]; -}; - - -/** - * Transforms the given vector with the given matrix storing the resulting, - * transformed matrix into resultVec. - * - * @param {goog.vec.ArrayType} mat The matrix supplying the - * transformation. - * @param {goog.vec.ArrayType} vec The vector to transform. - * @param {goog.vec.ArrayType} resultVec The vector to - * receive the results (may be vec). - * @return {goog.vec.ArrayType} return resultVec so that operations can be - * chained together. - */ -goog.vec.Matrix3.multVec3 = function(mat, vec, resultVec) { - var x = vec[0], y = vec[1], 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; -}; - - -/** - * Initializes the given 3x3 matrix as a translation matrix with x and y - * translation values. - * - * @param {goog.vec.ArrayType} mat The 3x3 (9-element) matrix - * array to receive the new translation matrix. - * @param {number} x The translation along the x axis. - * @param {number} y The translation along the y axis. - */ -goog.vec.Matrix3.makeTranslate = function(mat, x, y) { - goog.vec.Matrix3.setIdentity(mat); - goog.vec.Matrix3.setColumnValues(mat, 2, x, y, 1); -}; - - -/** - * Initializes the given 3x3 matrix as a scale matrix with x, y and z scale - * factors. - * @param {goog.vec.ArrayType} 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. - */ -goog.vec.Matrix3.makeScale = function(mat, x, y, z) { - goog.vec.Matrix3.setIdentity(mat); - goog.vec.Matrix3.setDiagonalValues(mat, x, y, z); -}; - - -/** - * Initializes the given 3x3 matrix as a rotation matrix with the given rotation - * angle about the axis defined by the vector (ax, ay, az). - * @param {goog.vec.ArrayType} mat The 3x3 (9-element) matrix - * array to receive the new scale matrix. - * @param {number} angle The rotation angle in radians. - * @param {number} ax The x component of the rotation axis. - * @param {number} ay The y component of the rotation axis. - * @param {number} az The z component of the rotation axis. - */ -goog.vec.Matrix3.makeAxisAngleRotate = function( - mat, angle, ax, ay, az) { - var c = Math.cos(angle); - var d = 1 - c; - var s = Math.sin(angle); - - goog.vec.Matrix3.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); -}; |