| /** |
| * @fileoverview gl-matrix - High performance matrix and vector operations |
| * @author Brandon Jones |
| * @author Colin MacKenzie IV |
| * @version 2.1.0 |
| */ |
| |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| |
| (function() { |
| "use strict"; |
| |
| var shim = {}; |
| if (typeof(exports) === 'undefined') { |
| if(typeof define == 'function' && typeof define.amd == 'object' && define.amd) { |
| shim.exports = {}; |
| define(function() { |
| return shim.exports; |
| }); |
| } else { |
| // gl-matrix lives in a browser, define its namespaces in global |
| shim.exports = window; |
| } |
| } |
| else { |
| // gl-matrix lives in commonjs, define its namespaces in exports |
| shim.exports = exports; |
| } |
| |
| (function(exports) { |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| |
| if(!GLMAT_EPSILON) { |
| var GLMAT_EPSILON = 0.000001; |
| } |
| |
| if(!GLMAT_ARRAY_TYPE) { |
| var GLMAT_ARRAY_TYPE = (typeof Float32Array !== 'undefined') ? Float32Array : Array; |
| } |
| |
| /** |
| * @class Common utilities |
| * @name glMatrix |
| */ |
| var glMatrix = {}; |
| |
| /** |
| * Sets the type of array used when creating new vectors and matricies |
| * |
| * @param {Type} type Array type, such as Float32Array or Array |
| */ |
| glMatrix.setMatrixArrayType = function(type) { |
| GLMAT_ARRAY_TYPE = type; |
| } |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.glMatrix = glMatrix; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 2 Dimensional Vector |
| * @name vec2 |
| */ |
| |
| var vec2 = {}; |
| |
| /** |
| * Creates a new, empty vec2 |
| * |
| * @returns {vec2} a new 2D vector |
| */ |
| vec2.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(2); |
| out[0] = 0; |
| out[1] = 0; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec2 initialized with values from an existing vector |
| * |
| * @param {vec2} a vector to clone |
| * @returns {vec2} a new 2D vector |
| */ |
| vec2.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(2); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec2 initialized with the given values |
| * |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @returns {vec2} a new 2D vector |
| */ |
| vec2.fromValues = function(x, y) { |
| var out = new GLMAT_ARRAY_TYPE(2); |
| out[0] = x; |
| out[1] = y; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one vec2 to another |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the source vector |
| * @returns {vec2} out |
| */ |
| vec2.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| return out; |
| }; |
| |
| /** |
| * Set the components of a vec2 to the given values |
| * |
| * @param {vec2} out the receiving vector |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @returns {vec2} out |
| */ |
| vec2.set = function(out, x, y) { |
| out[0] = x; |
| out[1] = y; |
| return out; |
| }; |
| |
| /** |
| * Adds two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.add = function(out, a, b) { |
| out[0] = a[0] + b[0]; |
| out[1] = a[1] + b[1]; |
| return out; |
| }; |
| |
| /** |
| * Subtracts two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.subtract = function(out, a, b) { |
| out[0] = a[0] - b[0]; |
| out[1] = a[1] - b[1]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec2.subtract} |
| * @function |
| */ |
| vec2.sub = vec2.subtract; |
| |
| /** |
| * Multiplies two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.multiply = function(out, a, b) { |
| out[0] = a[0] * b[0]; |
| out[1] = a[1] * b[1]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec2.multiply} |
| * @function |
| */ |
| vec2.mul = vec2.multiply; |
| |
| /** |
| * Divides two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.divide = function(out, a, b) { |
| out[0] = a[0] / b[0]; |
| out[1] = a[1] / b[1]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec2.divide} |
| * @function |
| */ |
| vec2.div = vec2.divide; |
| |
| /** |
| * Returns the minimum of two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.min = function(out, a, b) { |
| out[0] = Math.min(a[0], b[0]); |
| out[1] = Math.min(a[1], b[1]); |
| return out; |
| }; |
| |
| /** |
| * Returns the maximum of two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec2} out |
| */ |
| vec2.max = function(out, a, b) { |
| out[0] = Math.max(a[0], b[0]); |
| out[1] = Math.max(a[1], b[1]); |
| return out; |
| }; |
| |
| /** |
| * Scales a vec2 by a scalar number |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the vector to scale |
| * @param {Number} b amount to scale the vector by |
| * @returns {vec2} out |
| */ |
| vec2.scale = function(out, a, b) { |
| out[0] = a[0] * b; |
| out[1] = a[1] * b; |
| return out; |
| }; |
| |
| /** |
| * Calculates the euclidian distance between two vec2's |
| * |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {Number} distance between a and b |
| */ |
| vec2.distance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1]; |
| return Math.sqrt(x*x + y*y); |
| }; |
| |
| /** |
| * Alias for {@link vec2.distance} |
| * @function |
| */ |
| vec2.dist = vec2.distance; |
| |
| /** |
| * Calculates the squared euclidian distance between two vec2's |
| * |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {Number} squared distance between a and b |
| */ |
| vec2.squaredDistance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1]; |
| return x*x + y*y; |
| }; |
| |
| /** |
| * Alias for {@link vec2.squaredDistance} |
| * @function |
| */ |
| vec2.sqrDist = vec2.squaredDistance; |
| |
| /** |
| * Calculates the length of a vec2 |
| * |
| * @param {vec2} a vector to calculate length of |
| * @returns {Number} length of a |
| */ |
| vec2.length = function (a) { |
| var x = a[0], |
| y = a[1]; |
| return Math.sqrt(x*x + y*y); |
| }; |
| |
| /** |
| * Alias for {@link vec2.length} |
| * @function |
| */ |
| vec2.len = vec2.length; |
| |
| /** |
| * Calculates the squared length of a vec2 |
| * |
| * @param {vec2} a vector to calculate squared length of |
| * @returns {Number} squared length of a |
| */ |
| vec2.squaredLength = function (a) { |
| var x = a[0], |
| y = a[1]; |
| return x*x + y*y; |
| }; |
| |
| /** |
| * Alias for {@link vec2.squaredLength} |
| * @function |
| */ |
| vec2.sqrLen = vec2.squaredLength; |
| |
| /** |
| * Negates the components of a vec2 |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a vector to negate |
| * @returns {vec2} out |
| */ |
| vec2.negate = function(out, a) { |
| out[0] = -a[0]; |
| out[1] = -a[1]; |
| return out; |
| }; |
| |
| /** |
| * Normalize a vec2 |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a vector to normalize |
| * @returns {vec2} out |
| */ |
| vec2.normalize = function(out, a) { |
| var x = a[0], |
| y = a[1]; |
| var len = x*x + y*y; |
| if (len > 0) { |
| //TODO: evaluate use of glm_invsqrt here? |
| len = 1 / Math.sqrt(len); |
| out[0] = a[0] * len; |
| out[1] = a[1] * len; |
| } |
| return out; |
| }; |
| |
| /** |
| * Calculates the dot product of two vec2's |
| * |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {Number} dot product of a and b |
| */ |
| vec2.dot = function (a, b) { |
| return a[0] * b[0] + a[1] * b[1]; |
| }; |
| |
| /** |
| * Computes the cross product of two vec2's |
| * Note that the cross product must by definition produce a 3D vector |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @returns {vec3} out |
| */ |
| vec2.cross = function(out, a, b) { |
| var z = a[0] * b[1] - a[1] * b[0]; |
| out[0] = out[1] = 0; |
| out[2] = z; |
| return out; |
| }; |
| |
| /** |
| * Performs a linear interpolation between two vec2's |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the first operand |
| * @param {vec2} b the second operand |
| * @param {Number} t interpolation amount between the two inputs |
| * @returns {vec2} out |
| */ |
| vec2.lerp = function (out, a, b, t) { |
| var ax = a[0], |
| ay = a[1]; |
| out[0] = ax + t * (b[0] - ax); |
| out[1] = ay + t * (b[1] - ay); |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec2 with a mat2 |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the vector to transform |
| * @param {mat2} m matrix to transform with |
| * @returns {vec2} out |
| */ |
| vec2.transformMat2 = function(out, a, m) { |
| var x = a[0], |
| y = a[1]; |
| out[0] = m[0] * x + m[2] * y; |
| out[1] = m[1] * x + m[3] * y; |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec2 with a mat2d |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the vector to transform |
| * @param {mat2d} m matrix to transform with |
| * @returns {vec2} out |
| */ |
| vec2.transformMat2d = function(out, a, m) { |
| var x = a[0], |
| y = a[1]; |
| out[0] = m[0] * x + m[2] * y + m[4]; |
| out[1] = m[1] * x + m[3] * y + m[5]; |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec2 with a mat3 |
| * 3rd vector component is implicitly '1' |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the vector to transform |
| * @param {mat3} m matrix to transform with |
| * @returns {vec2} out |
| */ |
| vec2.transformMat3 = function(out, a, m) { |
| var x = a[0], |
| y = a[1]; |
| out[0] = m[0] * x + m[3] * y + m[6]; |
| out[1] = m[1] * x + m[4] * y + m[7]; |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec2 with a mat4 |
| * 3rd vector component is implicitly '0' |
| * 4th vector component is implicitly '1' |
| * |
| * @param {vec2} out the receiving vector |
| * @param {vec2} a the vector to transform |
| * @param {mat4} m matrix to transform with |
| * @returns {vec2} out |
| */ |
| vec2.transformMat4 = function(out, a, m) { |
| var x = a[0], |
| y = a[1]; |
| out[0] = m[0] * x + m[4] * y + m[12]; |
| out[1] = m[1] * x + m[5] * y + m[13]; |
| return out; |
| }; |
| |
| /** |
| * Perform some operation over an array of vec2s. |
| * |
| * @param {Array} a the array of vectors to iterate over |
| * @param {Number} stride Number of elements between the start of each vec2. If 0 assumes tightly packed |
| * @param {Number} offset Number of elements to skip at the beginning of the array |
| * @param {Number} count Number of vec2s to iterate over. If 0 iterates over entire array |
| * @param {Function} fn Function to call for each vector in the array |
| * @param {Object} [arg] additional argument to pass to fn |
| * @returns {Array} a |
| * @function |
| */ |
| vec2.forEach = (function() { |
| var vec = vec2.create(); |
| |
| return function(a, stride, offset, count, fn, arg) { |
| var i, l; |
| if(!stride) { |
| stride = 2; |
| } |
| |
| if(!offset) { |
| offset = 0; |
| } |
| |
| if(count) { |
| l = Math.min((count * stride) + offset, a.length); |
| } else { |
| l = a.length; |
| } |
| |
| for(i = offset; i < l; i += stride) { |
| vec[0] = a[i]; vec[1] = a[i+1]; |
| fn(vec, vec, arg); |
| a[i] = vec[0]; a[i+1] = vec[1]; |
| } |
| |
| return a; |
| }; |
| })(); |
| |
| /** |
| * Returns a string representation of a vector |
| * |
| * @param {vec2} vec vector to represent as a string |
| * @returns {String} string representation of the vector |
| */ |
| vec2.str = function (a) { |
| return 'vec2(' + a[0] + ', ' + a[1] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.vec2 = vec2; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 3 Dimensional Vector |
| * @name vec3 |
| */ |
| |
| var vec3 = {}; |
| |
| /** |
| * Creates a new, empty vec3 |
| * |
| * @returns {vec3} a new 3D vector |
| */ |
| vec3.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(3); |
| out[0] = 0; |
| out[1] = 0; |
| out[2] = 0; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec3 initialized with values from an existing vector |
| * |
| * @param {vec3} a vector to clone |
| * @returns {vec3} a new 3D vector |
| */ |
| vec3.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(3); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec3 initialized with the given values |
| * |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @returns {vec3} a new 3D vector |
| */ |
| vec3.fromValues = function(x, y, z) { |
| var out = new GLMAT_ARRAY_TYPE(3); |
| out[0] = x; |
| out[1] = y; |
| out[2] = z; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one vec3 to another |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the source vector |
| * @returns {vec3} out |
| */ |
| vec3.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| return out; |
| }; |
| |
| /** |
| * Set the components of a vec3 to the given values |
| * |
| * @param {vec3} out the receiving vector |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @returns {vec3} out |
| */ |
| vec3.set = function(out, x, y, z) { |
| out[0] = x; |
| out[1] = y; |
| out[2] = z; |
| return out; |
| }; |
| |
| /** |
| * Adds two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.add = function(out, a, b) { |
| out[0] = a[0] + b[0]; |
| out[1] = a[1] + b[1]; |
| out[2] = a[2] + b[2]; |
| return out; |
| }; |
| |
| /** |
| * Subtracts two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.subtract = function(out, a, b) { |
| out[0] = a[0] - b[0]; |
| out[1] = a[1] - b[1]; |
| out[2] = a[2] - b[2]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec3.subtract} |
| * @function |
| */ |
| vec3.sub = vec3.subtract; |
| |
| /** |
| * Multiplies two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.multiply = function(out, a, b) { |
| out[0] = a[0] * b[0]; |
| out[1] = a[1] * b[1]; |
| out[2] = a[2] * b[2]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec3.multiply} |
| * @function |
| */ |
| vec3.mul = vec3.multiply; |
| |
| /** |
| * Divides two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.divide = function(out, a, b) { |
| out[0] = a[0] / b[0]; |
| out[1] = a[1] / b[1]; |
| out[2] = a[2] / b[2]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec3.divide} |
| * @function |
| */ |
| vec3.div = vec3.divide; |
| |
| /** |
| * Returns the minimum of two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.min = function(out, a, b) { |
| out[0] = Math.min(a[0], b[0]); |
| out[1] = Math.min(a[1], b[1]); |
| out[2] = Math.min(a[2], b[2]); |
| return out; |
| }; |
| |
| /** |
| * Returns the maximum of two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.max = function(out, a, b) { |
| out[0] = Math.max(a[0], b[0]); |
| out[1] = Math.max(a[1], b[1]); |
| out[2] = Math.max(a[2], b[2]); |
| return out; |
| }; |
| |
| /** |
| * Scales a vec3 by a scalar number |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the vector to scale |
| * @param {Number} b amount to scale the vector by |
| * @returns {vec3} out |
| */ |
| vec3.scale = function(out, a, b) { |
| out[0] = a[0] * b; |
| out[1] = a[1] * b; |
| out[2] = a[2] * b; |
| return out; |
| }; |
| |
| /** |
| * Calculates the euclidian distance between two vec3's |
| * |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {Number} distance between a and b |
| */ |
| vec3.distance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1], |
| z = b[2] - a[2]; |
| return Math.sqrt(x*x + y*y + z*z); |
| }; |
| |
| /** |
| * Alias for {@link vec3.distance} |
| * @function |
| */ |
| vec3.dist = vec3.distance; |
| |
| /** |
| * Calculates the squared euclidian distance between two vec3's |
| * |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {Number} squared distance between a and b |
| */ |
| vec3.squaredDistance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1], |
| z = b[2] - a[2]; |
| return x*x + y*y + z*z; |
| }; |
| |
| /** |
| * Alias for {@link vec3.squaredDistance} |
| * @function |
| */ |
| vec3.sqrDist = vec3.squaredDistance; |
| |
| /** |
| * Calculates the length of a vec3 |
| * |
| * @param {vec3} a vector to calculate length of |
| * @returns {Number} length of a |
| */ |
| vec3.length = function (a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2]; |
| return Math.sqrt(x*x + y*y + z*z); |
| }; |
| |
| /** |
| * Alias for {@link vec3.length} |
| * @function |
| */ |
| vec3.len = vec3.length; |
| |
| /** |
| * Calculates the squared length of a vec3 |
| * |
| * @param {vec3} a vector to calculate squared length of |
| * @returns {Number} squared length of a |
| */ |
| vec3.squaredLength = function (a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2]; |
| return x*x + y*y + z*z; |
| }; |
| |
| /** |
| * Alias for {@link vec3.squaredLength} |
| * @function |
| */ |
| vec3.sqrLen = vec3.squaredLength; |
| |
| /** |
| * Negates the components of a vec3 |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a vector to negate |
| * @returns {vec3} out |
| */ |
| vec3.negate = function(out, a) { |
| out[0] = -a[0]; |
| out[1] = -a[1]; |
| out[2] = -a[2]; |
| return out; |
| }; |
| |
| /** |
| * Normalize a vec3 |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a vector to normalize |
| * @returns {vec3} out |
| */ |
| vec3.normalize = function(out, a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2]; |
| var len = x*x + y*y + z*z; |
| if (len > 0) { |
| //TODO: evaluate use of glm_invsqrt here? |
| len = 1 / Math.sqrt(len); |
| out[0] = a[0] * len; |
| out[1] = a[1] * len; |
| out[2] = a[2] * len; |
| } |
| return out; |
| }; |
| |
| /** |
| * Calculates the dot product of two vec3's |
| * |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {Number} dot product of a and b |
| */ |
| vec3.dot = function (a, b) { |
| return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; |
| }; |
| |
| /** |
| * Computes the cross product of two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @returns {vec3} out |
| */ |
| vec3.cross = function(out, a, b) { |
| var ax = a[0], ay = a[1], az = a[2], |
| bx = b[0], by = b[1], bz = b[2]; |
| |
| out[0] = ay * bz - az * by; |
| out[1] = az * bx - ax * bz; |
| out[2] = ax * by - ay * bx; |
| return out; |
| }; |
| |
| /** |
| * Performs a linear interpolation between two vec3's |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the first operand |
| * @param {vec3} b the second operand |
| * @param {Number} t interpolation amount between the two inputs |
| * @returns {vec3} out |
| */ |
| vec3.lerp = function (out, a, b, t) { |
| var ax = a[0], |
| ay = a[1], |
| az = a[2]; |
| out[0] = ax + t * (b[0] - ax); |
| out[1] = ay + t * (b[1] - ay); |
| out[2] = az + t * (b[2] - az); |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec3 with a mat4. |
| * 4th vector component is implicitly '1' |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the vector to transform |
| * @param {mat4} m matrix to transform with |
| * @returns {vec3} out |
| */ |
| vec3.transformMat4 = function(out, a, m) { |
| var x = a[0], y = a[1], z = a[2]; |
| out[0] = m[0] * x + m[4] * y + m[8] * z + m[12]; |
| out[1] = m[1] * x + m[5] * y + m[9] * z + m[13]; |
| out[2] = m[2] * x + m[6] * y + m[10] * z + m[14]; |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec3 with a quat |
| * |
| * @param {vec3} out the receiving vector |
| * @param {vec3} a the vector to transform |
| * @param {quat} q quaternion to transform with |
| * @returns {vec3} out |
| */ |
| vec3.transformQuat = function(out, a, q) { |
| var x = a[0], y = a[1], z = a[2], |
| qx = q[0], qy = q[1], qz = q[2], qw = q[3], |
| |
| // calculate quat * vec |
| ix = qw * x + qy * z - qz * y, |
| iy = qw * y + qz * x - qx * z, |
| iz = qw * z + qx * y - qy * x, |
| iw = -qx * x - qy * y - qz * z; |
| |
| // calculate result * inverse quat |
| out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; |
| out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; |
| out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; |
| return out; |
| }; |
| |
| /** |
| * Perform some operation over an array of vec3s. |
| * |
| * @param {Array} a the array of vectors to iterate over |
| * @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed |
| * @param {Number} offset Number of elements to skip at the beginning of the array |
| * @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array |
| * @param {Function} fn Function to call for each vector in the array |
| * @param {Object} [arg] additional argument to pass to fn |
| * @returns {Array} a |
| * @function |
| */ |
| vec3.forEach = (function() { |
| var vec = vec3.create(); |
| |
| return function(a, stride, offset, count, fn, arg) { |
| var i, l; |
| if(!stride) { |
| stride = 3; |
| } |
| |
| if(!offset) { |
| offset = 0; |
| } |
| |
| if(count) { |
| l = Math.min((count * stride) + offset, a.length); |
| } else { |
| l = a.length; |
| } |
| |
| for(i = offset; i < l; i += stride) { |
| vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2]; |
| fn(vec, vec, arg); |
| a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2]; |
| } |
| |
| return a; |
| }; |
| })(); |
| |
| /** |
| * Returns a string representation of a vector |
| * |
| * @param {vec3} vec vector to represent as a string |
| * @returns {String} string representation of the vector |
| */ |
| vec3.str = function (a) { |
| return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.vec3 = vec3; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 4 Dimensional Vector |
| * @name vec4 |
| */ |
| |
| var vec4 = {}; |
| |
| /** |
| * Creates a new, empty vec4 |
| * |
| * @returns {vec4} a new 4D vector |
| */ |
| vec4.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = 0; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec4 initialized with values from an existing vector |
| * |
| * @param {vec4} a vector to clone |
| * @returns {vec4} a new 4D vector |
| */ |
| vec4.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| return out; |
| }; |
| |
| /** |
| * Creates a new vec4 initialized with the given values |
| * |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @param {Number} w W component |
| * @returns {vec4} a new 4D vector |
| */ |
| vec4.fromValues = function(x, y, z, w) { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = x; |
| out[1] = y; |
| out[2] = z; |
| out[3] = w; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one vec4 to another |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the source vector |
| * @returns {vec4} out |
| */ |
| vec4.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| return out; |
| }; |
| |
| /** |
| * Set the components of a vec4 to the given values |
| * |
| * @param {vec4} out the receiving vector |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @param {Number} w W component |
| * @returns {vec4} out |
| */ |
| vec4.set = function(out, x, y, z, w) { |
| out[0] = x; |
| out[1] = y; |
| out[2] = z; |
| out[3] = w; |
| return out; |
| }; |
| |
| /** |
| * Adds two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.add = function(out, a, b) { |
| out[0] = a[0] + b[0]; |
| out[1] = a[1] + b[1]; |
| out[2] = a[2] + b[2]; |
| out[3] = a[3] + b[3]; |
| return out; |
| }; |
| |
| /** |
| * Subtracts two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.subtract = function(out, a, b) { |
| out[0] = a[0] - b[0]; |
| out[1] = a[1] - b[1]; |
| out[2] = a[2] - b[2]; |
| out[3] = a[3] - b[3]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec4.subtract} |
| * @function |
| */ |
| vec4.sub = vec4.subtract; |
| |
| /** |
| * Multiplies two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.multiply = function(out, a, b) { |
| out[0] = a[0] * b[0]; |
| out[1] = a[1] * b[1]; |
| out[2] = a[2] * b[2]; |
| out[3] = a[3] * b[3]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec4.multiply} |
| * @function |
| */ |
| vec4.mul = vec4.multiply; |
| |
| /** |
| * Divides two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.divide = function(out, a, b) { |
| out[0] = a[0] / b[0]; |
| out[1] = a[1] / b[1]; |
| out[2] = a[2] / b[2]; |
| out[3] = a[3] / b[3]; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link vec4.divide} |
| * @function |
| */ |
| vec4.div = vec4.divide; |
| |
| /** |
| * Returns the minimum of two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.min = function(out, a, b) { |
| out[0] = Math.min(a[0], b[0]); |
| out[1] = Math.min(a[1], b[1]); |
| out[2] = Math.min(a[2], b[2]); |
| out[3] = Math.min(a[3], b[3]); |
| return out; |
| }; |
| |
| /** |
| * Returns the maximum of two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {vec4} out |
| */ |
| vec4.max = function(out, a, b) { |
| out[0] = Math.max(a[0], b[0]); |
| out[1] = Math.max(a[1], b[1]); |
| out[2] = Math.max(a[2], b[2]); |
| out[3] = Math.max(a[3], b[3]); |
| return out; |
| }; |
| |
| /** |
| * Scales a vec4 by a scalar number |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the vector to scale |
| * @param {Number} b amount to scale the vector by |
| * @returns {vec4} out |
| */ |
| vec4.scale = function(out, a, b) { |
| out[0] = a[0] * b; |
| out[1] = a[1] * b; |
| out[2] = a[2] * b; |
| out[3] = a[3] * b; |
| return out; |
| }; |
| |
| /** |
| * Calculates the euclidian distance between two vec4's |
| * |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {Number} distance between a and b |
| */ |
| vec4.distance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1], |
| z = b[2] - a[2], |
| w = b[3] - a[3]; |
| return Math.sqrt(x*x + y*y + z*z + w*w); |
| }; |
| |
| /** |
| * Alias for {@link vec4.distance} |
| * @function |
| */ |
| vec4.dist = vec4.distance; |
| |
| /** |
| * Calculates the squared euclidian distance between two vec4's |
| * |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {Number} squared distance between a and b |
| */ |
| vec4.squaredDistance = function(a, b) { |
| var x = b[0] - a[0], |
| y = b[1] - a[1], |
| z = b[2] - a[2], |
| w = b[3] - a[3]; |
| return x*x + y*y + z*z + w*w; |
| }; |
| |
| /** |
| * Alias for {@link vec4.squaredDistance} |
| * @function |
| */ |
| vec4.sqrDist = vec4.squaredDistance; |
| |
| /** |
| * Calculates the length of a vec4 |
| * |
| * @param {vec4} a vector to calculate length of |
| * @returns {Number} length of a |
| */ |
| vec4.length = function (a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2], |
| w = a[3]; |
| return Math.sqrt(x*x + y*y + z*z + w*w); |
| }; |
| |
| /** |
| * Alias for {@link vec4.length} |
| * @function |
| */ |
| vec4.len = vec4.length; |
| |
| /** |
| * Calculates the squared length of a vec4 |
| * |
| * @param {vec4} a vector to calculate squared length of |
| * @returns {Number} squared length of a |
| */ |
| vec4.squaredLength = function (a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2], |
| w = a[3]; |
| return x*x + y*y + z*z + w*w; |
| }; |
| |
| /** |
| * Alias for {@link vec4.squaredLength} |
| * @function |
| */ |
| vec4.sqrLen = vec4.squaredLength; |
| |
| /** |
| * Negates the components of a vec4 |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a vector to negate |
| * @returns {vec4} out |
| */ |
| vec4.negate = function(out, a) { |
| out[0] = -a[0]; |
| out[1] = -a[1]; |
| out[2] = -a[2]; |
| out[3] = -a[3]; |
| return out; |
| }; |
| |
| /** |
| * Normalize a vec4 |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a vector to normalize |
| * @returns {vec4} out |
| */ |
| vec4.normalize = function(out, a) { |
| var x = a[0], |
| y = a[1], |
| z = a[2], |
| w = a[3]; |
| var len = x*x + y*y + z*z + w*w; |
| if (len > 0) { |
| len = 1 / Math.sqrt(len); |
| out[0] = a[0] * len; |
| out[1] = a[1] * len; |
| out[2] = a[2] * len; |
| out[3] = a[3] * len; |
| } |
| return out; |
| }; |
| |
| /** |
| * Calculates the dot product of two vec4's |
| * |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @returns {Number} dot product of a and b |
| */ |
| vec4.dot = function (a, b) { |
| return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3]; |
| }; |
| |
| /** |
| * Performs a linear interpolation between two vec4's |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the first operand |
| * @param {vec4} b the second operand |
| * @param {Number} t interpolation amount between the two inputs |
| * @returns {vec4} out |
| */ |
| vec4.lerp = function (out, a, b, t) { |
| var ax = a[0], |
| ay = a[1], |
| az = a[2], |
| aw = a[3]; |
| out[0] = ax + t * (b[0] - ax); |
| out[1] = ay + t * (b[1] - ay); |
| out[2] = az + t * (b[2] - az); |
| out[3] = aw + t * (b[3] - aw); |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec4 with a mat4. |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the vector to transform |
| * @param {mat4} m matrix to transform with |
| * @returns {vec4} out |
| */ |
| vec4.transformMat4 = function(out, a, m) { |
| var x = a[0], y = a[1], z = a[2], w = a[3]; |
| out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w; |
| out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w; |
| out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w; |
| out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w; |
| return out; |
| }; |
| |
| /** |
| * Transforms the vec4 with a quat |
| * |
| * @param {vec4} out the receiving vector |
| * @param {vec4} a the vector to transform |
| * @param {quat} q quaternion to transform with |
| * @returns {vec4} out |
| */ |
| vec4.transformQuat = function(out, a, q) { |
| var x = a[0], y = a[1], z = a[2], |
| qx = q[0], qy = q[1], qz = q[2], qw = q[3], |
| |
| // calculate quat * vec |
| ix = qw * x + qy * z - qz * y, |
| iy = qw * y + qz * x - qx * z, |
| iz = qw * z + qx * y - qy * x, |
| iw = -qx * x - qy * y - qz * z; |
| |
| // calculate result * inverse quat |
| out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; |
| out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; |
| out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; |
| return out; |
| }; |
| |
| /** |
| * Perform some operation over an array of vec4s. |
| * |
| * @param {Array} a the array of vectors to iterate over |
| * @param {Number} stride Number of elements between the start of each vec4. If 0 assumes tightly packed |
| * @param {Number} offset Number of elements to skip at the beginning of the array |
| * @param {Number} count Number of vec2s to iterate over. If 0 iterates over entire array |
| * @param {Function} fn Function to call for each vector in the array |
| * @param {Object} [arg] additional argument to pass to fn |
| * @returns {Array} a |
| * @function |
| */ |
| vec4.forEach = (function() { |
| var vec = vec4.create(); |
| |
| return function(a, stride, offset, count, fn, arg) { |
| var i, l; |
| if(!stride) { |
| stride = 4; |
| } |
| |
| if(!offset) { |
| offset = 0; |
| } |
| |
| if(count) { |
| l = Math.min((count * stride) + offset, a.length); |
| } else { |
| l = a.length; |
| } |
| |
| for(i = offset; i < l; i += stride) { |
| vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2]; vec[3] = a[i+3]; |
| fn(vec, vec, arg); |
| a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2]; a[i+3] = vec[3]; |
| } |
| |
| return a; |
| }; |
| })(); |
| |
| /** |
| * Returns a string representation of a vector |
| * |
| * @param {vec4} vec vector to represent as a string |
| * @returns {String} string representation of the vector |
| */ |
| vec4.str = function (a) { |
| return 'vec4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.vec4 = vec4; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 2x2 Matrix |
| * @name mat2 |
| */ |
| |
| var mat2 = {}; |
| |
| /** |
| * Creates a new identity mat2 |
| * |
| * @returns {mat2} a new 2x2 matrix |
| */ |
| mat2.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| return out; |
| }; |
| |
| /** |
| * Creates a new mat2 initialized with values from an existing matrix |
| * |
| * @param {mat2} a matrix to clone |
| * @returns {mat2} a new 2x2 matrix |
| */ |
| mat2.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one mat2 to another |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the source matrix |
| * @returns {mat2} out |
| */ |
| mat2.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| return out; |
| }; |
| |
| /** |
| * Set a mat2 to the identity matrix |
| * |
| * @param {mat2} out the receiving matrix |
| * @returns {mat2} out |
| */ |
| mat2.identity = function(out) { |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| return out; |
| }; |
| |
| /** |
| * Transpose the values of a mat2 |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the source matrix |
| * @returns {mat2} out |
| */ |
| mat2.transpose = function(out, a) { |
| // If we are transposing ourselves we can skip a few steps but have to cache some values |
| if (out === a) { |
| var a1 = a[1]; |
| out[1] = a[2]; |
| out[2] = a1; |
| } else { |
| out[0] = a[0]; |
| out[1] = a[2]; |
| out[2] = a[1]; |
| out[3] = a[3]; |
| } |
| |
| return out; |
| }; |
| |
| /** |
| * Inverts a mat2 |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the source matrix |
| * @returns {mat2} out |
| */ |
| mat2.invert = function(out, a) { |
| var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], |
| |
| // Calculate the determinant |
| det = a0 * a3 - a2 * a1; |
| |
| if (!det) { |
| return null; |
| } |
| det = 1.0 / det; |
| |
| out[0] = a3 * det; |
| out[1] = -a1 * det; |
| out[2] = -a2 * det; |
| out[3] = a0 * det; |
| |
| return out; |
| }; |
| |
| /** |
| * Calculates the adjugate of a mat2 |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the source matrix |
| * @returns {mat2} out |
| */ |
| mat2.adjoint = function(out, a) { |
| // Caching this value is nessecary if out == a |
| var a0 = a[0]; |
| out[0] = a[3]; |
| out[1] = -a[1]; |
| out[2] = -a[2]; |
| out[3] = a0; |
| |
| return out; |
| }; |
| |
| /** |
| * Calculates the determinant of a mat2 |
| * |
| * @param {mat2} a the source matrix |
| * @returns {Number} determinant of a |
| */ |
| mat2.determinant = function (a) { |
| return a[0] * a[3] - a[2] * a[1]; |
| }; |
| |
| /** |
| * Multiplies two mat2's |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the first operand |
| * @param {mat2} b the second operand |
| * @returns {mat2} out |
| */ |
| mat2.multiply = function (out, a, b) { |
| var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3]; |
| var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3]; |
| out[0] = a0 * b0 + a1 * b2; |
| out[1] = a0 * b1 + a1 * b3; |
| out[2] = a2 * b0 + a3 * b2; |
| out[3] = a2 * b1 + a3 * b3; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link mat2.multiply} |
| * @function |
| */ |
| mat2.mul = mat2.multiply; |
| |
| /** |
| * Rotates a mat2 by the given angle |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat2} out |
| */ |
| mat2.rotate = function (out, a, rad) { |
| var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], |
| s = Math.sin(rad), |
| c = Math.cos(rad); |
| out[0] = a0 * c + a1 * s; |
| out[1] = a0 * -s + a1 * c; |
| out[2] = a2 * c + a3 * s; |
| out[3] = a2 * -s + a3 * c; |
| return out; |
| }; |
| |
| /** |
| * Scales the mat2 by the dimensions in the given vec2 |
| * |
| * @param {mat2} out the receiving matrix |
| * @param {mat2} a the matrix to rotate |
| * @param {vec2} v the vec2 to scale the matrix by |
| * @returns {mat2} out |
| **/ |
| mat2.scale = function(out, a, v) { |
| var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], |
| v0 = v[0], v1 = v[1]; |
| out[0] = a0 * v0; |
| out[1] = a1 * v1; |
| out[2] = a2 * v0; |
| out[3] = a3 * v1; |
| return out; |
| }; |
| |
| /** |
| * Returns a string representation of a mat2 |
| * |
| * @param {mat2} mat matrix to represent as a string |
| * @returns {String} string representation of the matrix |
| */ |
| mat2.str = function (a) { |
| return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.mat2 = mat2; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 2x3 Matrix |
| * @name mat2d |
| * |
| * @description |
| * A mat2d contains six elements defined as: |
| * <pre> |
| * [a, b, |
| * c, d, |
| * tx,ty] |
| * </pre> |
| * This is a short form for the 3x3 matrix: |
| * <pre> |
| * [a, b, 0 |
| * c, d, 0 |
| * tx,ty,1] |
| * </pre> |
| * The last column is ignored so the array is shorter and operations are faster. |
| */ |
| |
| var mat2d = {}; |
| |
| /** |
| * Creates a new identity mat2d |
| * |
| * @returns {mat2d} a new 2x3 matrix |
| */ |
| mat2d.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(6); |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| out[4] = 0; |
| out[5] = 0; |
| return out; |
| }; |
| |
| /** |
| * Creates a new mat2d initialized with values from an existing matrix |
| * |
| * @param {mat2d} a matrix to clone |
| * @returns {mat2d} a new 2x3 matrix |
| */ |
| mat2d.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(6); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one mat2d to another |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the source matrix |
| * @returns {mat2d} out |
| */ |
| mat2d.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| return out; |
| }; |
| |
| /** |
| * Set a mat2d to the identity matrix |
| * |
| * @param {mat2d} out the receiving matrix |
| * @returns {mat2d} out |
| */ |
| mat2d.identity = function(out) { |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| out[4] = 0; |
| out[5] = 0; |
| return out; |
| }; |
| |
| /** |
| * Inverts a mat2d |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the source matrix |
| * @returns {mat2d} out |
| */ |
| mat2d.invert = function(out, a) { |
| var aa = a[0], ab = a[1], ac = a[2], ad = a[3], |
| atx = a[4], aty = a[5]; |
| |
| var det = aa * ad - ab * ac; |
| if(!det){ |
| return null; |
| } |
| det = 1.0 / det; |
| |
| out[0] = ad * det; |
| out[1] = -ab * det; |
| out[2] = -ac * det; |
| out[3] = aa * det; |
| out[4] = (ac * aty - ad * atx) * det; |
| out[5] = (ab * atx - aa * aty) * det; |
| return out; |
| }; |
| |
| /** |
| * Calculates the determinant of a mat2d |
| * |
| * @param {mat2d} a the source matrix |
| * @returns {Number} determinant of a |
| */ |
| mat2d.determinant = function (a) { |
| return a[0] * a[3] - a[1] * a[2]; |
| }; |
| |
| /** |
| * Multiplies two mat2d's |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the first operand |
| * @param {mat2d} b the second operand |
| * @returns {mat2d} out |
| */ |
| mat2d.multiply = function (out, a, b) { |
| var aa = a[0], ab = a[1], ac = a[2], ad = a[3], |
| atx = a[4], aty = a[5], |
| ba = b[0], bb = b[1], bc = b[2], bd = b[3], |
| btx = b[4], bty = b[5]; |
| |
| out[0] = aa*ba + ab*bc; |
| out[1] = aa*bb + ab*bd; |
| out[2] = ac*ba + ad*bc; |
| out[3] = ac*bb + ad*bd; |
| out[4] = ba*atx + bc*aty + btx; |
| out[5] = bb*atx + bd*aty + bty; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link mat2d.multiply} |
| * @function |
| */ |
| mat2d.mul = mat2d.multiply; |
| |
| |
| /** |
| * Rotates a mat2d by the given angle |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat2d} out |
| */ |
| mat2d.rotate = function (out, a, rad) { |
| var aa = a[0], |
| ab = a[1], |
| ac = a[2], |
| ad = a[3], |
| atx = a[4], |
| aty = a[5], |
| st = Math.sin(rad), |
| ct = Math.cos(rad); |
| |
| out[0] = aa*ct + ab*st; |
| out[1] = -aa*st + ab*ct; |
| out[2] = ac*ct + ad*st; |
| out[3] = -ac*st + ct*ad; |
| out[4] = ct*atx + st*aty; |
| out[5] = ct*aty - st*atx; |
| return out; |
| }; |
| |
| /** |
| * Scales the mat2d by the dimensions in the given vec2 |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the matrix to translate |
| * @param {mat2d} v the vec2 to scale the matrix by |
| * @returns {mat2d} out |
| **/ |
| mat2d.scale = function(out, a, v) { |
| var vx = v[0], vy = v[1]; |
| out[0] = a[0] * vx; |
| out[1] = a[1] * vy; |
| out[2] = a[2] * vx; |
| out[3] = a[3] * vy; |
| out[4] = a[4] * vx; |
| out[5] = a[5] * vy; |
| return out; |
| }; |
| |
| /** |
| * Translates the mat2d by the dimensions in the given vec2 |
| * |
| * @param {mat2d} out the receiving matrix |
| * @param {mat2d} a the matrix to translate |
| * @param {mat2d} v the vec2 to translate the matrix by |
| * @returns {mat2d} out |
| **/ |
| mat2d.translate = function(out, a, v) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4] + v[0]; |
| out[5] = a[5] + v[1]; |
| return out; |
| }; |
| |
| /** |
| * Returns a string representation of a mat2d |
| * |
| * @param {mat2d} a matrix to represent as a string |
| * @returns {String} string representation of the matrix |
| */ |
| mat2d.str = function (a) { |
| return 'mat2d(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + |
| a[3] + ', ' + a[4] + ', ' + a[5] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.mat2d = mat2d; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 3x3 Matrix |
| * @name mat3 |
| */ |
| |
| var mat3 = {}; |
| |
| /** |
| * Creates a new identity mat3 |
| * |
| * @returns {mat3} a new 3x3 matrix |
| */ |
| mat3.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(9); |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 1; |
| out[5] = 0; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 1; |
| return out; |
| }; |
| |
| /** |
| * Copies the upper-left 3x3 values into the given mat3. |
| * |
| * @param {mat3} out the receiving 3x3 matrix |
| * @param {mat4} a the source 4x4 matrix |
| * @returns {mat3} out |
| */ |
| mat3.fromMat4 = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[4]; |
| out[4] = a[5]; |
| out[5] = a[6]; |
| out[6] = a[8]; |
| out[7] = a[9]; |
| out[8] = a[10]; |
| return out; |
| }; |
| |
| /** |
| * Creates a new mat3 initialized with values from an existing matrix |
| * |
| * @param {mat3} a matrix to clone |
| * @returns {mat3} a new 3x3 matrix |
| */ |
| mat3.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(9); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[8] = a[8]; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one mat3 to another |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the source matrix |
| * @returns {mat3} out |
| */ |
| mat3.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[8] = a[8]; |
| return out; |
| }; |
| |
| /** |
| * Set a mat3 to the identity matrix |
| * |
| * @param {mat3} out the receiving matrix |
| * @returns {mat3} out |
| */ |
| mat3.identity = function(out) { |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 1; |
| out[5] = 0; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 1; |
| return out; |
| }; |
| |
| /** |
| * Transpose the values of a mat3 |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the source matrix |
| * @returns {mat3} out |
| */ |
| mat3.transpose = function(out, a) { |
| // If we are transposing ourselves we can skip a few steps but have to cache some values |
| if (out === a) { |
| var a01 = a[1], a02 = a[2], a12 = a[5]; |
| out[1] = a[3]; |
| out[2] = a[6]; |
| out[3] = a01; |
| out[5] = a[7]; |
| out[6] = a02; |
| out[7] = a12; |
| } else { |
| out[0] = a[0]; |
| out[1] = a[3]; |
| out[2] = a[6]; |
| out[3] = a[1]; |
| out[4] = a[4]; |
| out[5] = a[7]; |
| out[6] = a[2]; |
| out[7] = a[5]; |
| out[8] = a[8]; |
| } |
| |
| return out; |
| }; |
| |
| /** |
| * Inverts a mat3 |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the source matrix |
| * @returns {mat3} out |
| */ |
| mat3.invert = function(out, a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8], |
| |
| b01 = a22 * a11 - a12 * a21, |
| b11 = -a22 * a10 + a12 * a20, |
| b21 = a21 * a10 - a11 * a20, |
| |
| // Calculate the determinant |
| det = a00 * b01 + a01 * b11 + a02 * b21; |
| |
| if (!det) { |
| return null; |
| } |
| det = 1.0 / det; |
| |
| out[0] = b01 * det; |
| out[1] = (-a22 * a01 + a02 * a21) * det; |
| out[2] = (a12 * a01 - a02 * a11) * det; |
| out[3] = b11 * det; |
| out[4] = (a22 * a00 - a02 * a20) * det; |
| out[5] = (-a12 * a00 + a02 * a10) * det; |
| out[6] = b21 * det; |
| out[7] = (-a21 * a00 + a01 * a20) * det; |
| out[8] = (a11 * a00 - a01 * a10) * det; |
| return out; |
| }; |
| |
| /** |
| * Calculates the adjugate of a mat3 |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the source matrix |
| * @returns {mat3} out |
| */ |
| mat3.adjoint = function(out, a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8]; |
| |
| out[0] = (a11 * a22 - a12 * a21); |
| out[1] = (a02 * a21 - a01 * a22); |
| out[2] = (a01 * a12 - a02 * a11); |
| out[3] = (a12 * a20 - a10 * a22); |
| out[4] = (a00 * a22 - a02 * a20); |
| out[5] = (a02 * a10 - a00 * a12); |
| out[6] = (a10 * a21 - a11 * a20); |
| out[7] = (a01 * a20 - a00 * a21); |
| out[8] = (a00 * a11 - a01 * a10); |
| return out; |
| }; |
| |
| /** |
| * Calculates the determinant of a mat3 |
| * |
| * @param {mat3} a the source matrix |
| * @returns {Number} determinant of a |
| */ |
| mat3.determinant = function (a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8]; |
| |
| return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); |
| }; |
| |
| /** |
| * Multiplies two mat3's |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the first operand |
| * @param {mat3} b the second operand |
| * @returns {mat3} out |
| */ |
| mat3.multiply = function (out, a, b) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8], |
| |
| b00 = b[0], b01 = b[1], b02 = b[2], |
| b10 = b[3], b11 = b[4], b12 = b[5], |
| b20 = b[6], b21 = b[7], b22 = b[8]; |
| |
| out[0] = b00 * a00 + b01 * a10 + b02 * a20; |
| out[1] = b00 * a01 + b01 * a11 + b02 * a21; |
| out[2] = b00 * a02 + b01 * a12 + b02 * a22; |
| |
| out[3] = b10 * a00 + b11 * a10 + b12 * a20; |
| out[4] = b10 * a01 + b11 * a11 + b12 * a21; |
| out[5] = b10 * a02 + b11 * a12 + b12 * a22; |
| |
| out[6] = b20 * a00 + b21 * a10 + b22 * a20; |
| out[7] = b20 * a01 + b21 * a11 + b22 * a21; |
| out[8] = b20 * a02 + b21 * a12 + b22 * a22; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link mat3.multiply} |
| * @function |
| */ |
| mat3.mul = mat3.multiply; |
| |
| /** |
| * Translate a mat3 by the given vector |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the matrix to translate |
| * @param {vec2} v vector to translate by |
| * @returns {mat3} out |
| */ |
| mat3.translate = function(out, a, v) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8], |
| x = v[0], y = v[1]; |
| |
| out[0] = a00; |
| out[1] = a01; |
| out[2] = a02; |
| |
| out[3] = a10; |
| out[4] = a11; |
| out[5] = a12; |
| |
| out[6] = x * a00 + y * a10 + a20; |
| out[7] = x * a01 + y * a11 + a21; |
| out[8] = x * a02 + y * a12 + a22; |
| return out; |
| }; |
| |
| /** |
| * Rotates a mat3 by the given angle |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat3} out |
| */ |
| mat3.rotate = function (out, a, rad) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], |
| a10 = a[3], a11 = a[4], a12 = a[5], |
| a20 = a[6], a21 = a[7], a22 = a[8], |
| |
| s = Math.sin(rad), |
| c = Math.cos(rad); |
| |
| out[0] = c * a00 + s * a10; |
| out[1] = c * a01 + s * a11; |
| out[2] = c * a02 + s * a12; |
| |
| out[3] = c * a10 - s * a00; |
| out[4] = c * a11 - s * a01; |
| out[5] = c * a12 - s * a02; |
| |
| out[6] = a20; |
| out[7] = a21; |
| out[8] = a22; |
| return out; |
| }; |
| |
| /** |
| * Scales the mat3 by the dimensions in the given vec2 |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the matrix to rotate |
| * @param {vec2} v the vec2 to scale the matrix by |
| * @returns {mat3} out |
| **/ |
| mat3.scale = function(out, a, v) { |
| var x = v[0], y = v[2]; |
| |
| out[0] = x * a[0]; |
| out[1] = x * a[1]; |
| out[2] = x * a[2]; |
| |
| out[3] = y * a[3]; |
| out[4] = y * a[4]; |
| out[5] = y * a[5]; |
| |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[8] = a[8]; |
| return out; |
| }; |
| |
| /** |
| * Copies the values from a mat2d into a mat3 |
| * |
| * @param {mat3} out the receiving matrix |
| * @param {mat3} a the matrix to rotate |
| * @param {vec2} v the vec2 to scale the matrix by |
| * @returns {mat3} out |
| **/ |
| mat3.fromMat2d = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = 0; |
| |
| out[3] = a[2]; |
| out[4] = a[3]; |
| out[5] = 0; |
| |
| out[6] = a[4]; |
| out[7] = a[5]; |
| out[8] = 1; |
| return out; |
| }; |
| |
| /** |
| * Calculates a 3x3 matrix from the given quaternion |
| * |
| * @param {mat3} out mat3 receiving operation result |
| * @param {quat} q Quaternion to create matrix from |
| * |
| * @returns {mat3} out |
| */ |
| mat3.fromQuat = function (out, q) { |
| var x = q[0], y = q[1], z = q[2], w = q[3], |
| x2 = x + x, |
| y2 = y + y, |
| z2 = z + z, |
| |
| xx = x * x2, |
| xy = x * y2, |
| xz = x * z2, |
| yy = y * y2, |
| yz = y * z2, |
| zz = z * z2, |
| wx = w * x2, |
| wy = w * y2, |
| wz = w * z2; |
| |
| out[0] = 1 - (yy + zz); |
| out[1] = xy + wz; |
| out[2] = xz - wy; |
| |
| out[3] = xy - wz; |
| out[4] = 1 - (xx + zz); |
| out[5] = yz + wx; |
| |
| out[6] = xz + wy; |
| out[7] = yz - wx; |
| out[8] = 1 - (xx + yy); |
| |
| return out; |
| }; |
| |
| /** |
| * Returns a string representation of a mat3 |
| * |
| * @param {mat3} mat matrix to represent as a string |
| * @returns {String} string representation of the matrix |
| */ |
| mat3.str = function (a) { |
| return 'mat3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + |
| a[3] + ', ' + a[4] + ', ' + a[5] + ', ' + |
| a[6] + ', ' + a[7] + ', ' + a[8] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.mat3 = mat3; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class 4x4 Matrix |
| * @name mat4 |
| */ |
| |
| var mat4 = {}; |
| |
| /** |
| * Creates a new identity mat4 |
| * |
| * @returns {mat4} a new 4x4 matrix |
| */ |
| mat4.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(16); |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 0; |
| out[5] = 1; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 0; |
| out[9] = 0; |
| out[10] = 1; |
| out[11] = 0; |
| out[12] = 0; |
| out[13] = 0; |
| out[14] = 0; |
| out[15] = 1; |
| return out; |
| }; |
| |
| /** |
| * Creates a new mat4 initialized with values from an existing matrix |
| * |
| * @param {mat4} a matrix to clone |
| * @returns {mat4} a new 4x4 matrix |
| */ |
| mat4.clone = function(a) { |
| var out = new GLMAT_ARRAY_TYPE(16); |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[8] = a[8]; |
| out[9] = a[9]; |
| out[10] = a[10]; |
| out[11] = a[11]; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| return out; |
| }; |
| |
| /** |
| * Copy the values from one mat4 to another |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the source matrix |
| * @returns {mat4} out |
| */ |
| mat4.copy = function(out, a) { |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[4] = a[4]; |
| out[5] = a[5]; |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[8] = a[8]; |
| out[9] = a[9]; |
| out[10] = a[10]; |
| out[11] = a[11]; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| return out; |
| }; |
| |
| /** |
| * Set a mat4 to the identity matrix |
| * |
| * @param {mat4} out the receiving matrix |
| * @returns {mat4} out |
| */ |
| mat4.identity = function(out) { |
| out[0] = 1; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 0; |
| out[5] = 1; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 0; |
| out[9] = 0; |
| out[10] = 1; |
| out[11] = 0; |
| out[12] = 0; |
| out[13] = 0; |
| out[14] = 0; |
| out[15] = 1; |
| return out; |
| }; |
| |
| /** |
| * Transpose the values of a mat4 |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the source matrix |
| * @returns {mat4} out |
| */ |
| mat4.transpose = function(out, a) { |
| // If we are transposing ourselves we can skip a few steps but have to cache some values |
| if (out === a) { |
| var a01 = a[1], a02 = a[2], a03 = a[3], |
| a12 = a[6], a13 = a[7], |
| a23 = a[11]; |
| |
| out[1] = a[4]; |
| out[2] = a[8]; |
| out[3] = a[12]; |
| out[4] = a01; |
| out[6] = a[9]; |
| out[7] = a[13]; |
| out[8] = a02; |
| out[9] = a12; |
| out[11] = a[14]; |
| out[12] = a03; |
| out[13] = a13; |
| out[14] = a23; |
| } else { |
| out[0] = a[0]; |
| out[1] = a[4]; |
| out[2] = a[8]; |
| out[3] = a[12]; |
| out[4] = a[1]; |
| out[5] = a[5]; |
| out[6] = a[9]; |
| out[7] = a[13]; |
| out[8] = a[2]; |
| out[9] = a[6]; |
| out[10] = a[10]; |
| out[11] = a[14]; |
| out[12] = a[3]; |
| out[13] = a[7]; |
| out[14] = a[11]; |
| out[15] = a[15]; |
| } |
| |
| return out; |
| }; |
| |
| /** |
| * Inverts a mat4 |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the source matrix |
| * @returns {mat4} out |
| */ |
| mat4.invert = function(out, a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], |
| a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], |
| a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], |
| a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], |
| |
| b00 = a00 * a11 - a01 * a10, |
| b01 = a00 * a12 - a02 * a10, |
| b02 = a00 * a13 - a03 * a10, |
| b03 = a01 * a12 - a02 * a11, |
| b04 = a01 * a13 - a03 * a11, |
| b05 = a02 * a13 - a03 * a12, |
| b06 = a20 * a31 - a21 * a30, |
| b07 = a20 * a32 - a22 * a30, |
| b08 = a20 * a33 - a23 * a30, |
| b09 = a21 * a32 - a22 * a31, |
| b10 = a21 * a33 - a23 * a31, |
| b11 = a22 * a33 - a23 * a32, |
| |
| // Calculate the determinant |
| det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| |
| if (!det) { |
| return null; |
| } |
| det = 1.0 / det; |
| |
| out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det; |
| out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det; |
| out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det; |
| out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det; |
| out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det; |
| out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det; |
| out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det; |
| out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det; |
| out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det; |
| out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det; |
| out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det; |
| out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det; |
| out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det; |
| out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det; |
| out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det; |
| out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det; |
| |
| return out; |
| }; |
| |
| /** |
| * Calculates the adjugate of a mat4 |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the source matrix |
| * @returns {mat4} out |
| */ |
| mat4.adjoint = function(out, a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], |
| a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], |
| a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], |
| a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15]; |
| |
| out[0] = (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22)); |
| out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22)); |
| out[2] = (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12)); |
| out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12)); |
| out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22)); |
| out[5] = (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22)); |
| out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12)); |
| out[7] = (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12)); |
| out[8] = (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21)); |
| out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21)); |
| out[10] = (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11)); |
| out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11)); |
| out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21)); |
| out[13] = (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21)); |
| out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11)); |
| out[15] = (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11)); |
| return out; |
| }; |
| |
| /** |
| * Calculates the determinant of a mat4 |
| * |
| * @param {mat4} a the source matrix |
| * @returns {Number} determinant of a |
| */ |
| mat4.determinant = function (a) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], |
| a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], |
| a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], |
| a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15], |
| |
| b00 = a00 * a11 - a01 * a10, |
| b01 = a00 * a12 - a02 * a10, |
| b02 = a00 * a13 - a03 * a10, |
| b03 = a01 * a12 - a02 * a11, |
| b04 = a01 * a13 - a03 * a11, |
| b05 = a02 * a13 - a03 * a12, |
| b06 = a20 * a31 - a21 * a30, |
| b07 = a20 * a32 - a22 * a30, |
| b08 = a20 * a33 - a23 * a30, |
| b09 = a21 * a32 - a22 * a31, |
| b10 = a21 * a33 - a23 * a31, |
| b11 = a22 * a33 - a23 * a32; |
| |
| // Calculate the determinant |
| return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| }; |
| |
| /** |
| * Multiplies two mat4's |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the first operand |
| * @param {mat4} b the second operand |
| * @returns {mat4} out |
| */ |
| mat4.multiply = function (out, a, b) { |
| var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3], |
| a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7], |
| a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11], |
| a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15]; |
| |
| // Cache only the current line of the second matrix |
| var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3]; |
| out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30; |
| out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31; |
| out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32; |
| out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33; |
| |
| b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7]; |
| out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30; |
| out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31; |
| out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32; |
| out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33; |
| |
| b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11]; |
| out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30; |
| out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31; |
| out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32; |
| out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33; |
| |
| b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15]; |
| out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30; |
| out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31; |
| out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32; |
| out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link mat4.multiply} |
| * @function |
| */ |
| mat4.mul = mat4.multiply; |
| |
| /** |
| * Translate a mat4 by the given vector |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to translate |
| * @param {vec3} v vector to translate by |
| * @returns {mat4} out |
| */ |
| mat4.translate = function (out, a, v) { |
| var x = v[0], y = v[1], z = v[2], |
| a00, a01, a02, a03, |
| a10, a11, a12, a13, |
| a20, a21, a22, a23; |
| |
| if (a === out) { |
| out[12] = a[0] * x + a[4] * y + a[8] * z + a[12]; |
| out[13] = a[1] * x + a[5] * y + a[9] * z + a[13]; |
| out[14] = a[2] * x + a[6] * y + a[10] * z + a[14]; |
| out[15] = a[3] * x + a[7] * y + a[11] * z + a[15]; |
| } else { |
| a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3]; |
| a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7]; |
| a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11]; |
| |
| out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03; |
| out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13; |
| out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23; |
| |
| out[12] = a00 * x + a10 * y + a20 * z + a[12]; |
| out[13] = a01 * x + a11 * y + a21 * z + a[13]; |
| out[14] = a02 * x + a12 * y + a22 * z + a[14]; |
| out[15] = a03 * x + a13 * y + a23 * z + a[15]; |
| } |
| |
| return out; |
| }; |
| |
| /** |
| * Scales the mat4 by the dimensions in the given vec3 |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to scale |
| * @param {vec3} v the vec3 to scale the matrix by |
| * @returns {mat4} out |
| **/ |
| mat4.scale = function(out, a, v) { |
| var x = v[0], y = v[1], z = v[2]; |
| |
| out[0] = a[0] * x; |
| out[1] = a[1] * x; |
| out[2] = a[2] * x; |
| out[3] = a[3] * x; |
| out[4] = a[4] * y; |
| out[5] = a[5] * y; |
| out[6] = a[6] * y; |
| out[7] = a[7] * y; |
| out[8] = a[8] * z; |
| out[9] = a[9] * z; |
| out[10] = a[10] * z; |
| out[11] = a[11] * z; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| return out; |
| }; |
| |
| /** |
| * Rotates a mat4 by the given angle |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @param {vec3} axis the axis to rotate around |
| * @returns {mat4} out |
| */ |
| mat4.rotate = function (out, a, rad, axis) { |
| var x = axis[0], y = axis[1], z = axis[2], |
| len = Math.sqrt(x * x + y * y + z * z), |
| s, c, t, |
| a00, a01, a02, a03, |
| a10, a11, a12, a13, |
| a20, a21, a22, a23, |
| b00, b01, b02, |
| b10, b11, b12, |
| b20, b21, b22; |
| |
| if (Math.abs(len) < GLMAT_EPSILON) { return null; } |
| |
| len = 1 / len; |
| x *= len; |
| y *= len; |
| z *= len; |
| |
| s = Math.sin(rad); |
| c = Math.cos(rad); |
| t = 1 - c; |
| |
| a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3]; |
| a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7]; |
| a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11]; |
| |
| // Construct the elements of the rotation matrix |
| b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s; |
| b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s; |
| b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c; |
| |
| // Perform rotation-specific matrix multiplication |
| out[0] = a00 * b00 + a10 * b01 + a20 * b02; |
| out[1] = a01 * b00 + a11 * b01 + a21 * b02; |
| out[2] = a02 * b00 + a12 * b01 + a22 * b02; |
| out[3] = a03 * b00 + a13 * b01 + a23 * b02; |
| out[4] = a00 * b10 + a10 * b11 + a20 * b12; |
| out[5] = a01 * b10 + a11 * b11 + a21 * b12; |
| out[6] = a02 * b10 + a12 * b11 + a22 * b12; |
| out[7] = a03 * b10 + a13 * b11 + a23 * b12; |
| out[8] = a00 * b20 + a10 * b21 + a20 * b22; |
| out[9] = a01 * b20 + a11 * b21 + a21 * b22; |
| out[10] = a02 * b20 + a12 * b21 + a22 * b22; |
| out[11] = a03 * b20 + a13 * b21 + a23 * b22; |
| |
| if (a !== out) { // If the source and destination differ, copy the unchanged last row |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| } |
| return out; |
| }; |
| |
| /** |
| * Rotates a matrix by the given angle around the X axis |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat4} out |
| */ |
| mat4.rotateX = function (out, a, rad) { |
| var s = Math.sin(rad), |
| c = Math.cos(rad), |
| a10 = a[4], |
| a11 = a[5], |
| a12 = a[6], |
| a13 = a[7], |
| a20 = a[8], |
| a21 = a[9], |
| a22 = a[10], |
| a23 = a[11]; |
| |
| if (a !== out) { // If the source and destination differ, copy the unchanged rows |
| out[0] = a[0]; |
| out[1] = a[1]; |
| out[2] = a[2]; |
| out[3] = a[3]; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| } |
| |
| // Perform axis-specific matrix multiplication |
| out[4] = a10 * c + a20 * s; |
| out[5] = a11 * c + a21 * s; |
| out[6] = a12 * c + a22 * s; |
| out[7] = a13 * c + a23 * s; |
| out[8] = a20 * c - a10 * s; |
| out[9] = a21 * c - a11 * s; |
| out[10] = a22 * c - a12 * s; |
| out[11] = a23 * c - a13 * s; |
| return out; |
| }; |
| |
| /** |
| * Rotates a matrix by the given angle around the Y axis |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat4} out |
| */ |
| mat4.rotateY = function (out, a, rad) { |
| var s = Math.sin(rad), |
| c = Math.cos(rad), |
| a00 = a[0], |
| a01 = a[1], |
| a02 = a[2], |
| a03 = a[3], |
| a20 = a[8], |
| a21 = a[9], |
| a22 = a[10], |
| a23 = a[11]; |
| |
| if (a !== out) { // If the source and destination differ, copy the unchanged rows |
| out[4] = a[4]; |
| out[5] = a[5]; |
| out[6] = a[6]; |
| out[7] = a[7]; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| } |
| |
| // Perform axis-specific matrix multiplication |
| out[0] = a00 * c - a20 * s; |
| out[1] = a01 * c - a21 * s; |
| out[2] = a02 * c - a22 * s; |
| out[3] = a03 * c - a23 * s; |
| out[8] = a00 * s + a20 * c; |
| out[9] = a01 * s + a21 * c; |
| out[10] = a02 * s + a22 * c; |
| out[11] = a03 * s + a23 * c; |
| return out; |
| }; |
| |
| /** |
| * Rotates a matrix by the given angle around the Z axis |
| * |
| * @param {mat4} out the receiving matrix |
| * @param {mat4} a the matrix to rotate |
| * @param {Number} rad the angle to rotate the matrix by |
| * @returns {mat4} out |
| */ |
| mat4.rotateZ = function (out, a, rad) { |
| var s = Math.sin(rad), |
| c = Math.cos(rad), |
| a00 = a[0], |
| a01 = a[1], |
| a02 = a[2], |
| a03 = a[3], |
| a10 = a[4], |
| a11 = a[5], |
| a12 = a[6], |
| a13 = a[7]; |
| |
| if (a !== out) { // If the source and destination differ, copy the unchanged last row |
| out[8] = a[8]; |
| out[9] = a[9]; |
| out[10] = a[10]; |
| out[11] = a[11]; |
| out[12] = a[12]; |
| out[13] = a[13]; |
| out[14] = a[14]; |
| out[15] = a[15]; |
| } |
| |
| // Perform axis-specific matrix multiplication |
| out[0] = a00 * c + a10 * s; |
| out[1] = a01 * c + a11 * s; |
| out[2] = a02 * c + a12 * s; |
| out[3] = a03 * c + a13 * s; |
| out[4] = a10 * c - a00 * s; |
| out[5] = a11 * c - a01 * s; |
| out[6] = a12 * c - a02 * s; |
| out[7] = a13 * c - a03 * s; |
| return out; |
| }; |
| |
| /** |
| * Creates a matrix from a quaternion rotation and vector translation |
| * This is equivalent to (but much faster than): |
| * |
| * mat4.identity(dest); |
| * mat4.translate(dest, vec); |
| * var quatMat = mat4.create(); |
| * quat4.toMat4(quat, quatMat); |
| * mat4.multiply(dest, quatMat); |
| * |
| * @param {mat4} out mat4 receiving operation result |
| * @param {quat4} q Rotation quaternion |
| * @param {vec3} v Translation vector |
| * @returns {mat4} out |
| */ |
| mat4.fromRotationTranslation = function (out, q, v) { |
| // Quaternion math |
| var x = q[0], y = q[1], z = q[2], w = q[3], |
| x2 = x + x, |
| y2 = y + y, |
| z2 = z + z, |
| |
| xx = x * x2, |
| xy = x * y2, |
| xz = x * z2, |
| yy = y * y2, |
| yz = y * z2, |
| zz = z * z2, |
| wx = w * x2, |
| wy = w * y2, |
| wz = w * z2; |
| |
| out[0] = 1 - (yy + zz); |
| out[1] = xy + wz; |
| out[2] = xz - wy; |
| out[3] = 0; |
| out[4] = xy - wz; |
| out[5] = 1 - (xx + zz); |
| out[6] = yz + wx; |
| out[7] = 0; |
| out[8] = xz + wy; |
| out[9] = yz - wx; |
| out[10] = 1 - (xx + yy); |
| out[11] = 0; |
| out[12] = v[0]; |
| out[13] = v[1]; |
| out[14] = v[2]; |
| out[15] = 1; |
| |
| return out; |
| }; |
| |
| /** |
| * Calculates a 4x4 matrix from the given quaternion |
| * |
| * @param {mat4} out mat4 receiving operation result |
| * @param {quat} q Quaternion to create matrix from |
| * |
| * @returns {mat4} out |
| */ |
| mat4.fromQuat = function (out, q) { |
| var x = q[0], y = q[1], z = q[2], w = q[3], |
| x2 = x + x, |
| y2 = y + y, |
| z2 = z + z, |
| |
| xx = x * x2, |
| xy = x * y2, |
| xz = x * z2, |
| yy = y * y2, |
| yz = y * z2, |
| zz = z * z2, |
| wx = w * x2, |
| wy = w * y2, |
| wz = w * z2; |
| |
| out[0] = 1 - (yy + zz); |
| out[1] = xy + wz; |
| out[2] = xz - wy; |
| out[3] = 0; |
| |
| out[4] = xy - wz; |
| out[5] = 1 - (xx + zz); |
| out[6] = yz + wx; |
| out[7] = 0; |
| |
| out[8] = xz + wy; |
| out[9] = yz - wx; |
| out[10] = 1 - (xx + yy); |
| out[11] = 0; |
| |
| out[12] = 0; |
| out[13] = 0; |
| out[14] = 0; |
| out[15] = 1; |
| |
| return out; |
| }; |
| |
| /** |
| * Generates a frustum matrix with the given bounds |
| * |
| * @param {mat4} out mat4 frustum matrix will be written into |
| * @param {Number} left Left bound of the frustum |
| * @param {Number} right Right bound of the frustum |
| * @param {Number} bottom Bottom bound of the frustum |
| * @param {Number} top Top bound of the frustum |
| * @param {Number} near Near bound of the frustum |
| * @param {Number} far Far bound of the frustum |
| * @returns {mat4} out |
| */ |
| mat4.frustum = function (out, left, right, bottom, top, near, far) { |
| var rl = 1 / (right - left), |
| tb = 1 / (top - bottom), |
| nf = 1 / (near - far); |
| out[0] = (near * 2) * rl; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 0; |
| out[5] = (near * 2) * tb; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = (right + left) * rl; |
| out[9] = (top + bottom) * tb; |
| out[10] = (far + near) * nf; |
| out[11] = -1; |
| out[12] = 0; |
| out[13] = 0; |
| out[14] = (far * near * 2) * nf; |
| out[15] = 0; |
| return out; |
| }; |
| |
| /** |
| * Generates a perspective projection matrix with the given bounds |
| * |
| * @param {mat4} out mat4 frustum matrix will be written into |
| * @param {number} fovy Vertical field of view in radians |
| * @param {number} aspect Aspect ratio. typically viewport width/height |
| * @param {number} near Near bound of the frustum |
| * @param {number} far Far bound of the frustum |
| * @returns {mat4} out |
| */ |
| mat4.perspective = function (out, fovy, aspect, near, far) { |
| var f = 1.0 / Math.tan(fovy / 2), |
| nf = 1 / (near - far); |
| out[0] = f / aspect; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 0; |
| out[5] = f; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 0; |
| out[9] = 0; |
| out[10] = (far + near) * nf; |
| out[11] = -1; |
| out[12] = 0; |
| out[13] = 0; |
| out[14] = (2 * far * near) * nf; |
| out[15] = 0; |
| return out; |
| }; |
| |
| /** |
| * Generates a orthogonal projection matrix with the given bounds |
| * |
| * @param {mat4} out mat4 frustum matrix will be written into |
| * @param {number} left Left bound of the frustum |
| * @param {number} right Right bound of the frustum |
| * @param {number} bottom Bottom bound of the frustum |
| * @param {number} top Top bound of the frustum |
| * @param {number} near Near bound of the frustum |
| * @param {number} far Far bound of the frustum |
| * @returns {mat4} out |
| */ |
| mat4.ortho = function (out, left, right, bottom, top, near, far) { |
| var lr = 1 / (left - right), |
| bt = 1 / (bottom - top), |
| nf = 1 / (near - far); |
| out[0] = -2 * lr; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 0; |
| out[4] = 0; |
| out[5] = -2 * bt; |
| out[6] = 0; |
| out[7] = 0; |
| out[8] = 0; |
| out[9] = 0; |
| out[10] = 2 * nf; |
| out[11] = 0; |
| out[12] = (left + right) * lr; |
| out[13] = (top + bottom) * bt; |
| out[14] = (far + near) * nf; |
| out[15] = 1; |
| return out; |
| }; |
| |
| /** |
| * Generates a look-at matrix with the given eye position, focal point, and up axis |
| * |
| * @param {mat4} out mat4 frustum matrix will be written into |
| * @param {vec3} eye Position of the viewer |
| * @param {vec3} center Point the viewer is looking at |
| * @param {vec3} up vec3 pointing up |
| * @returns {mat4} out |
| */ |
| mat4.lookAt = function (out, eye, center, up) { |
| var x0, x1, x2, y0, y1, y2, z0, z1, z2, len, |
| eyex = eye[0], |
| eyey = eye[1], |
| eyez = eye[2], |
| upx = up[0], |
| upy = up[1], |
| upz = up[2], |
| centerx = center[0], |
| centery = center[1], |
| centerz = center[2]; |
| |
| if (Math.abs(eyex - centerx) < GLMAT_EPSILON && |
| Math.abs(eyey - centery) < GLMAT_EPSILON && |
| Math.abs(eyez - centerz) < GLMAT_EPSILON) { |
| return mat4.identity(out); |
| } |
| |
| z0 = eyex - centerx; |
| z1 = eyey - centery; |
| z2 = eyez - centerz; |
| |
| len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2); |
| z0 *= len; |
| z1 *= len; |
| z2 *= len; |
| |
| x0 = upy * z2 - upz * z1; |
| x1 = upz * z0 - upx * z2; |
| x2 = upx * z1 - upy * z0; |
| len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2); |
| if (!len) { |
| x0 = 0; |
| x1 = 0; |
| x2 = 0; |
| } else { |
| len = 1 / len; |
| x0 *= len; |
| x1 *= len; |
| x2 *= len; |
| } |
| |
| y0 = z1 * x2 - z2 * x1; |
| y1 = z2 * x0 - z0 * x2; |
| y2 = z0 * x1 - z1 * x0; |
| |
| len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2); |
| if (!len) { |
| y0 = 0; |
| y1 = 0; |
| y2 = 0; |
| } else { |
| len = 1 / len; |
| y0 *= len; |
| y1 *= len; |
| y2 *= len; |
| } |
| |
| out[0] = x0; |
| out[1] = y0; |
| out[2] = z0; |
| out[3] = 0; |
| out[4] = x1; |
| out[5] = y1; |
| out[6] = z1; |
| out[7] = 0; |
| out[8] = x2; |
| out[9] = y2; |
| out[10] = z2; |
| out[11] = 0; |
| out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez); |
| out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez); |
| out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez); |
| out[15] = 1; |
| |
| return out; |
| }; |
| |
| /** |
| * Returns a string representation of a mat4 |
| * |
| * @param {mat4} mat matrix to represent as a string |
| * @returns {String} string representation of the matrix |
| */ |
| mat4.str = function (a) { |
| return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' + |
| a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' + |
| a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' + |
| a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.mat4 = mat4; |
| } |
| ; |
| /* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without modification, |
| are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON |
| ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /** |
| * @class Quaternion |
| * @name quat |
| */ |
| |
| var quat = {}; |
| |
| /** |
| * Creates a new identity quat |
| * |
| * @returns {quat} a new quaternion |
| */ |
| quat.create = function() { |
| var out = new GLMAT_ARRAY_TYPE(4); |
| out[0] = 0; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| return out; |
| }; |
| |
| /** |
| * Creates a new quat initialized with values from an existing quaternion |
| * |
| * @param {quat} a quaternion to clone |
| * @returns {quat} a new quaternion |
| * @function |
| */ |
| quat.clone = vec4.clone; |
| |
| /** |
| * Creates a new quat initialized with the given values |
| * |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @param {Number} w W component |
| * @returns {quat} a new quaternion |
| * @function |
| */ |
| quat.fromValues = vec4.fromValues; |
| |
| /** |
| * Copy the values from one quat to another |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a the source quaternion |
| * @returns {quat} out |
| * @function |
| */ |
| quat.copy = vec4.copy; |
| |
| /** |
| * Set the components of a quat to the given values |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {Number} x X component |
| * @param {Number} y Y component |
| * @param {Number} z Z component |
| * @param {Number} w W component |
| * @returns {quat} out |
| * @function |
| */ |
| quat.set = vec4.set; |
| |
| /** |
| * Set a quat to the identity quaternion |
| * |
| * @param {quat} out the receiving quaternion |
| * @returns {quat} out |
| */ |
| quat.identity = function(out) { |
| out[0] = 0; |
| out[1] = 0; |
| out[2] = 0; |
| out[3] = 1; |
| return out; |
| }; |
| |
| /** |
| * Sets a quat from the given angle and rotation axis, |
| * then returns it. |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {vec3} axis the axis around which to rotate |
| * @param {Number} rad the angle in radians |
| * @returns {quat} out |
| **/ |
| quat.setAxisAngle = function(out, axis, rad) { |
| rad = rad * 0.5; |
| var s = Math.sin(rad); |
| out[0] = s * axis[0]; |
| out[1] = s * axis[1]; |
| out[2] = s * axis[2]; |
| out[3] = Math.cos(rad); |
| return out; |
| }; |
| |
| /** |
| * Adds two quat's |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a the first operand |
| * @param {quat} b the second operand |
| * @returns {quat} out |
| * @function |
| */ |
| quat.add = vec4.add; |
| |
| /** |
| * Multiplies two quat's |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a the first operand |
| * @param {quat} b the second operand |
| * @returns {quat} out |
| */ |
| quat.multiply = function(out, a, b) { |
| var ax = a[0], ay = a[1], az = a[2], aw = a[3], |
| bx = b[0], by = b[1], bz = b[2], bw = b[3]; |
| |
| out[0] = ax * bw + aw * bx + ay * bz - az * by; |
| out[1] = ay * bw + aw * by + az * bx - ax * bz; |
| out[2] = az * bw + aw * bz + ax * by - ay * bx; |
| out[3] = aw * bw - ax * bx - ay * by - az * bz; |
| return out; |
| }; |
| |
| /** |
| * Alias for {@link quat.multiply} |
| * @function |
| */ |
| quat.mul = quat.multiply; |
| |
| /** |
| * Scales a quat by a scalar number |
| * |
| * @param {quat} out the receiving vector |
| * @param {quat} a the vector to scale |
| * @param {Number} b amount to scale the vector by |
| * @returns {quat} out |
| * @function |
| */ |
| quat.scale = vec4.scale; |
| |
| /** |
| * Rotates a quaternion by the given angle around the X axis |
| * |
| * @param {quat} out quat receiving operation result |
| * @param {quat} a quat to rotate |
| * @param {number} rad angle (in radians) to rotate |
| * @returns {quat} out |
| */ |
| quat.rotateX = function (out, a, rad) { |
| rad *= 0.5; |
| |
| var ax = a[0], ay = a[1], az = a[2], aw = a[3], |
| bx = Math.sin(rad), bw = Math.cos(rad); |
| |
| out[0] = ax * bw + aw * bx; |
| out[1] = ay * bw + az * bx; |
| out[2] = az * bw - ay * bx; |
| out[3] = aw * bw - ax * bx; |
| return out; |
| }; |
| |
| /** |
| * Rotates a quaternion by the given angle around the Y axis |
| * |
| * @param {quat} out quat receiving operation result |
| * @param {quat} a quat to rotate |
| * @param {number} rad angle (in radians) to rotate |
| * @returns {quat} out |
| */ |
| quat.rotateY = function (out, a, rad) { |
| rad *= 0.5; |
| |
| var ax = a[0], ay = a[1], az = a[2], aw = a[3], |
| by = Math.sin(rad), bw = Math.cos(rad); |
| |
| out[0] = ax * bw - az * by; |
| out[1] = ay * bw + aw * by; |
| out[2] = az * bw + ax * by; |
| out[3] = aw * bw - ay * by; |
| return out; |
| }; |
| |
| /** |
| * Rotates a quaternion by the given angle around the Z axis |
| * |
| * @param {quat} out quat receiving operation result |
| * @param {quat} a quat to rotate |
| * @param {number} rad angle (in radians) to rotate |
| * @returns {quat} out |
| */ |
| quat.rotateZ = function (out, a, rad) { |
| rad *= 0.5; |
| |
| var ax = a[0], ay = a[1], az = a[2], aw = a[3], |
| bz = Math.sin(rad), bw = Math.cos(rad); |
| |
| out[0] = ax * bw + ay * bz; |
| out[1] = ay * bw - ax * bz; |
| out[2] = az * bw + aw * bz; |
| out[3] = aw * bw - az * bz; |
| return out; |
| }; |
| |
| /** |
| * Calculates the W component of a quat from the X, Y, and Z components. |
| * Assumes that quaternion is 1 unit in length. |
| * Any existing W component will be ignored. |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a quat to calculate W component of |
| * @returns {quat} out |
| */ |
| quat.calculateW = function (out, a) { |
| var x = a[0], y = a[1], z = a[2]; |
| |
| out[0] = x; |
| out[1] = y; |
| out[2] = z; |
| out[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); |
| return out; |
| }; |
| |
| /** |
| * Calculates the dot product of two quat's |
| * |
| * @param {quat} a the first operand |
| * @param {quat} b the second operand |
| * @returns {Number} dot product of a and b |
| * @function |
| */ |
| quat.dot = vec4.dot; |
| |
| /** |
| * Performs a linear interpolation between two quat's |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a the first operand |
| * @param {quat} b the second operand |
| * @param {Number} t interpolation amount between the two inputs |
| * @returns {quat} out |
| * @function |
| */ |
| quat.lerp = vec4.lerp; |
| |
| /** |
| * Performs a spherical linear interpolation between two quat |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a the first operand |
| * @param {quat} b the second operand |
| * @param {Number} t interpolation amount between the two inputs |
| * @returns {quat} out |
| */ |
| quat.slerp = function (out, a, b, t) { |
| var ax = a[0], ay = a[1], az = a[2], aw = a[3], |
| bx = b[0], by = b[1], bz = b[2], bw = b[3]; |
| |
| var cosHalfTheta = ax * bx + ay * by + az * bz + aw * bw, |
| halfTheta, |
| sinHalfTheta, |
| ratioA, |
| ratioB; |
| |
| if (Math.abs(cosHalfTheta) >= 1.0) { |
| if (out !== a) { |
| out[0] = ax; |
| out[1] = ay; |
| out[2] = az; |
| out[3] = aw; |
| } |
| return out; |
| } |
| |
| halfTheta = Math.acos(cosHalfTheta); |
| sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta * cosHalfTheta); |
| |
| if (Math.abs(sinHalfTheta) < 0.001) { |
| out[0] = (ax * 0.5 + bx * 0.5); |
| out[1] = (ay * 0.5 + by * 0.5); |
| out[2] = (az * 0.5 + bz * 0.5); |
| out[3] = (aw * 0.5 + bw * 0.5); |
| return out; |
| } |
| |
| ratioA = Math.sin((1 - t) * halfTheta) / sinHalfTheta; |
| ratioB = Math.sin(t * halfTheta) / sinHalfTheta; |
| |
| out[0] = (ax * ratioA + bx * ratioB); |
| out[1] = (ay * ratioA + by * ratioB); |
| out[2] = (az * ratioA + bz * ratioB); |
| out[3] = (aw * ratioA + bw * ratioB); |
| |
| return out; |
| }; |
| |
| /** |
| * Calculates the inverse of a quat |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a quat to calculate inverse of |
| * @returns {quat} out |
| */ |
| quat.invert = function(out, a) { |
| var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], |
| dot = a0*a0 + a1*a1 + a2*a2 + a3*a3, |
| invDot = dot ? 1.0/dot : 0; |
| |
| // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0 |
| |
| out[0] = -a0*invDot; |
| out[1] = -a1*invDot; |
| out[2] = -a2*invDot; |
| out[3] = a3*invDot; |
| return out; |
| }; |
| |
| /** |
| * Calculates the conjugate of a quat |
| * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result. |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a quat to calculate conjugate of |
| * @returns {quat} out |
| */ |
| quat.conjugate = function (out, a) { |
| out[0] = -a[0]; |
| out[1] = -a[1]; |
| out[2] = -a[2]; |
| out[3] = a[3]; |
| return out; |
| }; |
| |
| /** |
| * Calculates the length of a quat |
| * |
| * @param {quat} a vector to calculate length of |
| * @returns {Number} length of a |
| * @function |
| */ |
| quat.length = vec4.length; |
| |
| /** |
| * Alias for {@link quat.length} |
| * @function |
| */ |
| quat.len = quat.length; |
| |
| /** |
| * Calculates the squared length of a quat |
| * |
| * @param {quat} a vector to calculate squared length of |
| * @returns {Number} squared length of a |
| * @function |
| */ |
| quat.squaredLength = vec4.squaredLength; |
| |
| /** |
| * Alias for {@link quat.squaredLength} |
| * @function |
| */ |
| quat.sqrLen = quat.squaredLength; |
| |
| /** |
| * Normalize a quat |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {quat} a quaternion to normalize |
| * @returns {quat} out |
| * @function |
| */ |
| quat.normalize = vec4.normalize; |
| |
| /** |
| * Creates a quaternion from the given 3x3 rotation matrix. |
| * |
| * @param {quat} out the receiving quaternion |
| * @param {mat3} m rotation matrix |
| * @returns {quat} out |
| * @function |
| */ |
| quat.fromMat3 = (function() { |
| var s_iNext = [1,2,0]; |
| return function(out, m) { |
| // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes |
| // article "Quaternion Calculus and Fast Animation". |
| var fTrace = m[0] + m[4] + m[8]; |
| var fRoot; |
| |
| if ( fTrace > 0.0 ) { |
| // |w| > 1/2, may as well choose w > 1/2 |
| fRoot = Math.sqrt(fTrace + 1.0); // 2w |
| out[3] = 0.5 * fRoot; |
| fRoot = 0.5/fRoot; // 1/(4w) |
| out[0] = (m[7]-m[5])*fRoot; |
| out[1] = (m[2]-m[6])*fRoot; |
| out[2] = (m[3]-m[1])*fRoot; |
| } else { |
| // |w| <= 1/2 |
| var i = 0; |
| if ( m[4] > m[0] ) |
| i = 1; |
| if ( m[8] > m[i*3+i] ) |
| i = 2; |
| var j = s_iNext[i]; |
| var k = s_iNext[j]; |
| |
| fRoot = Math.sqrt(m[i*3+i]-m[j*3+j]-m[k*3+k] + 1.0); |
| out[i] = 0.5 * fRoot; |
| fRoot = 0.5 / fRoot; |
| out[3] = (m[k*3+j] - m[j*3+k]) * fRoot; |
| out[j] = (m[j*3+i] + m[i*3+j]) * fRoot; |
| out[k] = (m[k*3+i] + m[i*3+k]) * fRoot; |
| } |
| |
| return out; |
| }; |
| })(); |
| |
| /** |
| * Returns a string representation of a quatenion |
| * |
| * @param {quat} vec vector to represent as a string |
| * @returns {String} string representation of the vector |
| */ |
| quat.str = function (a) { |
| return 'quat(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')'; |
| }; |
| |
| if(typeof(exports) !== 'undefined') { |
| exports.quat = quat; |
| } |
| ; |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| })(shim.exports); |
| })(); |