/**
* @fileoverview gl-matrix - High performance matrix and vector operations for WebGL
* @author Brandon Jones
* @author Colin MacKenzie IV
* @version 1.3.7
*/
/*
* Copyright (c) 2012 Brandon Jones, Colin MacKenzie IV
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
*
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
*
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
*
* 2. Altered source versions must be plainly marked as such, and must not
* be misrepresented as being the original software.
*
* 3. This notice may not be removed or altered from any source
* distribution.
*/
// Updated to use a modification of the "returnExportsGlobal" pattern from https://github.com/umdjs/umd
(function (root, factory) {
if (typeof exports === 'object') {
// Node. Does not work with strict CommonJS, but
// only CommonJS-like enviroments that support module.exports,
// like Node.
module.exports = factory(global);
} else if (typeof define === 'function' && define.amd) {
// AMD. Register as an anonymous module.
define([], function () {
return factory(root);
});
} else {
// Browser globals
factory(root);
}
}(this, function (root) {
"use strict";
// Tweak to your liking
var FLOAT_EPSILON = 0.000001;
var glMath = {};
(function() {
if (typeof(Float32Array) != 'undefined') {
var y = new Float32Array(1);
var i = new Int32Array(y.buffer);
/**
* Fast way to calculate the inverse square root,
* see http://jsperf.com/inverse-square-root/5
*
* If typed arrays are not available, a slower
* implementation will be used.
*
* @param {Number} number the number
* @returns {Number} Inverse square root
*/
glMath.invsqrt = function(number) {
var x2 = number * 0.5;
y[0] = number;
var threehalfs = 1.5;
i[0] = 0x5f3759df - (i[0] >> 1);
var number2 = y[0];
return number2 * (threehalfs - (x2 * number2 * number2));
};
} else {
glMath.invsqrt = function(number) { return 1.0 / Math.sqrt(number); };
}
})();
/**
* @class System-specific optimal array type
* @name MatrixArray
*/
var MatrixArray = null;
// explicitly sets and returns the type of array to use within glMatrix
function setMatrixArrayType(type) {
MatrixArray = type;
return MatrixArray;
}
// auto-detects and returns the best type of array to use within glMatrix, falling
// back to Array if typed arrays are unsupported
function determineMatrixArrayType() {
MatrixArray = (typeof Float32Array !== 'undefined') ? Float32Array : Array;
return MatrixArray;
}
determineMatrixArrayType();
/**
* @class 3 Dimensional Vector
* @name vec3
*/
var vec3 = {};
/**
* Creates a new instance of a vec3 using the default array type
* Any javascript array-like objects containing at least 3 numeric elements can serve as a vec3
*
* @param {vec3} [vec] vec3 containing values to initialize with
*
* @returns {vec3} New vec3
*/
vec3.create = function (vec) {
var dest = new MatrixArray(3);
if (vec) {
dest[0] = vec[0];
dest[1] = vec[1];
dest[2] = vec[2];
} else {
dest[0] = dest[1] = dest[2] = 0;
}
return dest;
};
/**
* Creates a new instance of a vec3, initializing it with the given arguments
*
* @param {number} x X value
* @param {number} y Y value
* @param {number} z Z value
* @returns {vec3} New vec3
*/
vec3.createFrom = function (x, y, z) {
var dest = new MatrixArray(3);
dest[0] = x;
dest[1] = y;
dest[2] = z;
return dest;
};
/**
* Copies the values of one vec3 to another
*
* @param {vec3} vec vec3 containing values to copy
* @param {vec3} dest vec3 receiving copied values
*
* @returns {vec3} dest
*/
vec3.set = function (vec, dest) {
dest[0] = vec[0];
dest[1] = vec[1];
dest[2] = vec[2];
return dest;
};
/**
* Compares two vectors for equality within a certain margin of error
*
* @param {vec3} a First vector
* @param {vec3} b Second vector
*
* @returns {Boolean} True if a is equivalent to b
*/
vec3.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON
);
};
/**
* Performs a vector addition
*
* @param {vec3} vec First operand
* @param {vec3} vec2 Second operand
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.add = function (vec, vec2, dest) {
if (!dest || vec === dest) {
vec[0] += vec2[0];
vec[1] += vec2[1];
vec[2] += vec2[2];
return vec;
}
dest[0] = vec[0] + vec2[0];
dest[1] = vec[1] + vec2[1];
dest[2] = vec[2] + vec2[2];
return dest;
};
/**
* Performs a vector subtraction
*
* @param {vec3} vec First operand
* @param {vec3} vec2 Second operand
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.subtract = function (vec, vec2, dest) {
if (!dest || vec === dest) {
vec[0] -= vec2[0];
vec[1] -= vec2[1];
vec[2] -= vec2[2];
return vec;
}
dest[0] = vec[0] - vec2[0];
dest[1] = vec[1] - vec2[1];
dest[2] = vec[2] - vec2[2];
return dest;
};
/**
* Performs a vector multiplication
*
* @param {vec3} vec First operand
* @param {vec3} vec2 Second operand
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.multiply = function (vec, vec2, dest) {
if (!dest || vec === dest) {
vec[0] *= vec2[0];
vec[1] *= vec2[1];
vec[2] *= vec2[2];
return vec;
}
dest[0] = vec[0] * vec2[0];
dest[1] = vec[1] * vec2[1];
dest[2] = vec[2] * vec2[2];
return dest;
};
/**
* Negates the components of a vec3
*
* @param {vec3} vec vec3 to negate
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.negate = function (vec, dest) {
if (!dest) { dest = vec; }
dest[0] = -vec[0];
dest[1] = -vec[1];
dest[2] = -vec[2];
return dest;
};
/**
* Multiplies the components of a vec3 by a scalar value
*
* @param {vec3} vec vec3 to scale
* @param {number} val Value to scale by
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.scale = function (vec, val, dest) {
if (!dest || vec === dest) {
vec[0] *= val;
vec[1] *= val;
vec[2] *= val;
return vec;
}
dest[0] = vec[0] * val;
dest[1] = vec[1] * val;
dest[2] = vec[2] * val;
return dest;
};
/**
* Generates a unit vector of the same direction as the provided vec3
* If vector length is 0, returns [0, 0, 0]
*
* @param {vec3} vec vec3 to normalize
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.normalize = function (vec, dest) {
if (!dest) { dest = vec; }
var x = vec[0], y = vec[1], z = vec[2],
len = Math.sqrt(x * x + y * y + z * z);
if (!len) {
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
return dest;
} else if (len === 1) {
dest[0] = x;
dest[1] = y;
dest[2] = z;
return dest;
}
len = 1 / len;
dest[0] = x * len;
dest[1] = y * len;
dest[2] = z * len;
return dest;
};
/**
* Generates the cross product of two vec3s
*
* @param {vec3} vec First operand
* @param {vec3} vec2 Second operand
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.cross = function (vec, vec2, dest) {
if (!dest) { dest = vec; }
var x = vec[0], y = vec[1], z = vec[2],
x2 = vec2[0], y2 = vec2[1], z2 = vec2[2];
dest[0] = y * z2 - z * y2;
dest[1] = z * x2 - x * z2;
dest[2] = x * y2 - y * x2;
return dest;
};
/**
* Caclulates the length of a vec3
*
* @param {vec3} vec vec3 to calculate length of
*
* @returns {number} Length of vec
*/
vec3.length = function (vec) {
var x = vec[0], y = vec[1], z = vec[2];
return Math.sqrt(x * x + y * y + z * z);
};
/**
* Caclulates the squared length of a vec3
*
* @param {vec3} vec vec3 to calculate squared length of
*
* @returns {number} Squared Length of vec
*/
vec3.squaredLength = function (vec) {
var x = vec[0], y = vec[1], z = vec[2];
return x * x + y * y + z * z;
};
/**
* Caclulates the dot product of two vec3s
*
* @param {vec3} vec First operand
* @param {vec3} vec2 Second operand
*
* @returns {number} Dot product of vec and vec2
*/
vec3.dot = function (vec, vec2) {
return vec[0] * vec2[0] + vec[1] * vec2[1] + vec[2] * vec2[2];
};
/**
* Generates a unit vector pointing from one vector to another
*
* @param {vec3} vec Origin vec3
* @param {vec3} vec2 vec3 to point to
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.direction = function (vec, vec2, dest) {
if (!dest) { dest = vec; }
var x = vec[0] - vec2[0],
y = vec[1] - vec2[1],
z = vec[2] - vec2[2],
len = Math.sqrt(x * x + y * y + z * z);
if (!len) {
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
return dest;
}
len = 1 / len;
dest[0] = x * len;
dest[1] = y * len;
dest[2] = z * len;
return dest;
};
/**
* Performs a linear interpolation between two vec3
*
* @param {vec3} vec First vector
* @param {vec3} vec2 Second vector
* @param {number} lerp Interpolation amount between the two inputs
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.lerp = function (vec, vec2, lerp, dest) {
if (!dest) { dest = vec; }
dest[0] = vec[0] + lerp * (vec2[0] - vec[0]);
dest[1] = vec[1] + lerp * (vec2[1] - vec[1]);
dest[2] = vec[2] + lerp * (vec2[2] - vec[2]);
return dest;
};
/**
* Calculates the euclidian distance between two vec3
*
* Params:
* @param {vec3} vec First vector
* @param {vec3} vec2 Second vector
*
* @returns {number} Distance between vec and vec2
*/
vec3.dist = function (vec, vec2) {
var x = vec2[0] - vec[0],
y = vec2[1] - vec[1],
z = vec2[2] - vec[2];
return Math.sqrt(x*x + y*y + z*z);
};
// Pre-allocated to prevent unecessary garbage collection
var unprojectMat = null;
var unprojectVec = new MatrixArray(4);
/**
* Projects the specified vec3 from screen space into object space
* Based on the <a href="http://webcvs.freedesktop.org/mesa/Mesa/src/glu/mesa/project.c?revision=1.4&view=markup">Mesa gluUnProject implementation</a>
*
* @param {vec3} vec Screen-space vector to project
* @param {mat4} view View matrix
* @param {mat4} proj Projection matrix
* @param {vec4} viewport Viewport as given to gl.viewport [x, y, width, height]
* @param {vec3} [dest] vec3 receiving unprojected result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
vec3.unproject = function (vec, view, proj, viewport, dest) {
if (!dest) { dest = vec; }
if(!unprojectMat) {
unprojectMat = mat4.create();
}
var m = unprojectMat;
var v = unprojectVec;
v[0] = (vec[0] - viewport[0]) * 2.0 / viewport[2] - 1.0;
v[1] = (vec[1] - viewport[1]) * 2.0 / viewport[3] - 1.0;
v[2] = 2.0 * vec[2] - 1.0;
v[3] = 1.0;
mat4.multiply(proj, view, m);
if(!mat4.inverse(m)) { return null; }
mat4.multiplyVec4(m, v);
if(v[3] === 0.0) { return null; }
dest[0] = v[0] / v[3];
dest[1] = v[1] / v[3];
dest[2] = v[2] / v[3];
return dest;
};
var xUnitVec3 = vec3.createFrom(1,0,0);
var yUnitVec3 = vec3.createFrom(0,1,0);
var zUnitVec3 = vec3.createFrom(0,0,1);
var tmpvec3 = vec3.create();
/**
* Generates a quaternion of rotation between two given normalized vectors
*
* @param {vec3} a Normalized source vector
* @param {vec3} b Normalized target vector
* @param {quat4} [dest] quat4 receiving operation result.
*
* @returns {quat4} dest if specified, a new quat4 otherwise
*/
vec3.rotationTo = function (a, b, dest) {
if (!dest) { dest = quat4.create(); }
var d = vec3.dot(a, b);
var axis = tmpvec3;
if (d >= 1.0) {
quat4.set(identityQuat4, dest);
} else if (d < (0.000001 - 1.0)) {
vec3.cross(xUnitVec3, a, axis);
if (vec3.length(axis) < 0.000001)
vec3.cross(yUnitVec3, a, axis);
if (vec3.length(axis) < 0.000001)
vec3.cross(zUnitVec3, a, axis);
vec3.normalize(axis);
quat4.fromAngleAxis(Math.PI, axis, dest);
} else {
var s = Math.sqrt((1.0 + d) * 2.0);
var sInv = 1.0 / s;
vec3.cross(a, b, axis);
dest[0] = axis[0] * sInv;
dest[1] = axis[1] * sInv;
dest[2] = axis[2] * sInv;
dest[3] = s * 0.5;
quat4.normalize(dest);
}
if (dest[3] > 1.0) dest[3] = 1.0;
else if (dest[3] < -1.0) dest[3] = -1.0;
return dest;
};
/**
* Returns a string representation of a vector
*
* @param {vec3} vec Vector to represent as a string
*
* @returns {string} String representation of vec
*/
vec3.str = function (vec) {
return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ']';
};
/**
* @class 3x3 Matrix
* @name mat3
*/
var mat3 = {};
/**
* Creates a new instance of a mat3 using the default array type
* Any javascript array-like object containing at least 9 numeric elements can serve as a mat3
*
* @param {mat3} [mat] mat3 containing values to initialize with
*
* @returns {mat3} New mat3
*/
mat3.create = function (mat) {
var dest = new MatrixArray(9);
if (mat) {
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[8] = mat[8];
} else {
dest[0] = dest[1] =
dest[2] = dest[3] =
dest[4] = dest[5] =
dest[6] = dest[7] =
dest[8] = 0;
}
return dest;
};
/**
* Creates a new instance of a mat3, initializing it with the given arguments
*
* @param {number} m00
* @param {number} m01
* @param {number} m02
* @param {number} m10
* @param {number} m11
* @param {number} m12
* @param {number} m20
* @param {number} m21
* @param {number} m22
* @returns {mat3} New mat3
*/
mat3.createFrom = function (m00, m01, m02, m10, m11, m12, m20, m21, m22) {
var dest = new MatrixArray(9);
dest[0] = m00;
dest[1] = m01;
dest[2] = m02;
dest[3] = m10;
dest[4] = m11;
dest[5] = m12;
dest[6] = m20;
dest[7] = m21;
dest[8] = m22;
return dest;
};
/**
* Calculates the determinant of a mat3
*
* @param {mat3} mat mat3 to calculate determinant of
*
* @returns {Number} determinant of mat
*/
mat3.determinant = function (mat) {
var a00 = mat[0], a01 = mat[1], a02 = mat[2],
a10 = mat[3], a11 = mat[4], a12 = mat[5],
a20 = mat[6], a21 = mat[7], a22 = mat[8];
return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
};
/**
* Calculates the inverse matrix of a mat3
*
* @param {mat3} mat mat3 to calculate inverse of
* @param {mat3} [dest] mat3 receiving inverse matrix. If not specified result is written to mat
*
* @param {mat3} dest is specified, mat otherwise, null if matrix cannot be inverted
*/
mat3.inverse = function (mat, dest) {
var a00 = mat[0], a01 = mat[1], a02 = mat[2],
a10 = mat[3], a11 = mat[4], a12 = mat[5],
a20 = mat[6], a21 = mat[7], a22 = mat[8],
b01 = a22 * a11 - a12 * a21,
b11 = -a22 * a10 + a12 * a20,
b21 = a21 * a10 - a11 * a20,
d = a00 * b01 + a01 * b11 + a02 * b21,
id;
if (!d) { return null; }
id = 1 / d;
if (!dest) { dest = mat3.create(); }
dest[0] = b01 * id;
dest[1] = (-a22 * a01 + a02 * a21) * id;
dest[2] = (a12 * a01 - a02 * a11) * id;
dest[3] = b11 * id;
dest[4] = (a22 * a00 - a02 * a20) * id;
dest[5] = (-a12 * a00 + a02 * a10) * id;
dest[6] = b21 * id;
dest[7] = (-a21 * a00 + a01 * a20) * id;
dest[8] = (a11 * a00 - a01 * a10) * id;
return dest;
};
/**
* Performs a matrix multiplication
*
* @param {mat3} mat First operand
* @param {mat3} mat2 Second operand
* @param {mat3} [dest] mat3 receiving operation result. If not specified result is written to mat
*
* @returns {mat3} dest if specified, mat otherwise
*/
mat3.multiply = function (mat, mat2, dest) {
if (!dest) { dest = mat; }
// Cache the matrix values (makes for huge speed increases!)
var a00 = mat[0], a01 = mat[1], a02 = mat[2],
a10 = mat[3], a11 = mat[4], a12 = mat[5],
a20 = mat[6], a21 = mat[7], a22 = mat[8],
b00 = mat2[0], b01 = mat2[1], b02 = mat2[2],
b10 = mat2[3], b11 = mat2[4], b12 = mat2[5],
b20 = mat2[6], b21 = mat2[7], b22 = mat2[8];
dest[0] = b00 * a00 + b01 * a10 + b02 * a20;
dest[1] = b00 * a01 + b01 * a11 + b02 * a21;
dest[2] = b00 * a02 + b01 * a12 + b02 * a22;
dest[3] = b10 * a00 + b11 * a10 + b12 * a20;
dest[4] = b10 * a01 + b11 * a11 + b12 * a21;
dest[5] = b10 * a02 + b11 * a12 + b12 * a22;
dest[6] = b20 * a00 + b21 * a10 + b22 * a20;
dest[7] = b20 * a01 + b21 * a11 + b22 * a21;
dest[8] = b20 * a02 + b21 * a12 + b22 * a22;
return dest;
};
/**
* Transforms the vec2 according to the given mat3.
*
* @param {mat3} matrix mat3 to multiply against
* @param {vec2} vec the vector to multiply
* @param {vec2} [dest] an optional receiving vector. If not given, vec is used.
*
* @returns {vec2} The multiplication result
**/
mat3.multiplyVec2 = function(matrix, vec, dest) {
if (!dest) dest = vec;
var x = vec[0], y = vec[1];
dest[0] = x * matrix[0] + y * matrix[3] + matrix[6];
dest[1] = x * matrix[1] + y * matrix[4] + matrix[7];
return dest;
};
/**
* Transforms the vec3 according to the given mat3
*
* @param {mat3} matrix mat3 to multiply against
* @param {vec3} vec the vector to multiply
* @param {vec3} [dest] an optional receiving vector. If not given, vec is used.
*
* @returns {vec3} The multiplication result
**/
mat3.multiplyVec3 = function(matrix, vec, dest) {
if (!dest) dest = vec;
var x = vec[0], y = vec[1], z = vec[2];
dest[0] = x * matrix[0] + y * matrix[3] + z * matrix[6];
dest[1] = x * matrix[1] + y * matrix[4] + z * matrix[7];
dest[2] = x * matrix[2] + y * matrix[5] + z * matrix[8];
return dest;
};
/**
* Copies the values of one mat3 to another
*
* @param {mat3} mat mat3 containing values to copy
* @param {mat3} dest mat3 receiving copied values
*
* @returns {mat3} dest
*/
mat3.set = function (mat, dest) {
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[8] = mat[8];
return dest;
};
/**
* Compares two matrices for equality within a certain margin of error
*
* @param {mat3} a First matrix
* @param {mat3} b Second matrix
*
* @returns {Boolean} True if a is equivalent to b
*/
mat3.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON &&
Math.abs(a[3] - b[3]) < FLOAT_EPSILON &&
Math.abs(a[4] - b[4]) < FLOAT_EPSILON &&
Math.abs(a[5] - b[5]) < FLOAT_EPSILON &&
Math.abs(a[6] - b[6]) < FLOAT_EPSILON &&
Math.abs(a[7] - b[7]) < FLOAT_EPSILON &&
Math.abs(a[8] - b[8]) < FLOAT_EPSILON
);
};
/**
* Sets a mat3 to an identity matrix
*
* @param {mat3} dest mat3 to set
*
* @returns dest if specified, otherwise a new mat3
*/
mat3.identity = function (dest) {
if (!dest) { dest = mat3.create(); }
dest[0] = 1;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
dest[4] = 1;
dest[5] = 0;
dest[6] = 0;
dest[7] = 0;
dest[8] = 1;
return dest;
};
/**
* Transposes a mat3 (flips the values over the diagonal)
*
* Params:
* @param {mat3} mat mat3 to transpose
* @param {mat3} [dest] mat3 receiving transposed values. If not specified result is written to mat
*
* @returns {mat3} dest is specified, mat otherwise
*/
mat3.transpose = function (mat, dest) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (!dest || mat === dest) {
var a01 = mat[1], a02 = mat[2],
a12 = mat[5];
mat[1] = mat[3];
mat[2] = mat[6];
mat[3] = a01;
mat[5] = mat[7];
mat[6] = a02;
mat[7] = a12;
return mat;
}
dest[0] = mat[0];
dest[1] = mat[3];
dest[2] = mat[6];
dest[3] = mat[1];
dest[4] = mat[4];
dest[5] = mat[7];
dest[6] = mat[2];
dest[7] = mat[5];
dest[8] = mat[8];
return dest;
};
/**
* Copies the elements of a mat3 into the upper 3x3 elements of a mat4
*
* @param {mat3} mat mat3 containing values to copy
* @param {mat4} [dest] mat4 receiving copied values
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat3.toMat4 = function (mat, dest) {
if (!dest) { dest = mat4.create(); }
dest[15] = 1;
dest[14] = 0;
dest[13] = 0;
dest[12] = 0;
dest[11] = 0;
dest[10] = mat[8];
dest[9] = mat[7];
dest[8] = mat[6];
dest[7] = 0;
dest[6] = mat[5];
dest[5] = mat[4];
dest[4] = mat[3];
dest[3] = 0;
dest[2] = mat[2];
dest[1] = mat[1];
dest[0] = mat[0];
return dest;
};
/**
* Returns a string representation of a mat3
*
* @param {mat3} mat mat3 to represent as a string
*
* @param {string} String representation of mat
*/
mat3.str = function (mat) {
return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] +
', ' + mat[3] + ', ' + mat[4] + ', ' + mat[5] +
', ' + mat[6] + ', ' + mat[7] + ', ' + mat[8] + ']';
};
/**
* @class 4x4 Matrix
* @name mat4
*/
var mat4 = {};
/**
* Creates a new instance of a mat4 using the default array type
* Any javascript array-like object containing at least 16 numeric elements can serve as a mat4
*
* @param {mat4} [mat] mat4 containing values to initialize with
*
* @returns {mat4} New mat4
*/
mat4.create = function (mat) {
var dest = new MatrixArray(16);
if (mat) {
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[8] = mat[8];
dest[9] = mat[9];
dest[10] = mat[10];
dest[11] = mat[11];
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
}
return dest;
};
/**
* Creates a new instance of a mat4, initializing it with the given arguments
*
* @param {number} m00
* @param {number} m01
* @param {number} m02
* @param {number} m03
* @param {number} m10
* @param {number} m11
* @param {number} m12
* @param {number} m13
* @param {number} m20
* @param {number} m21
* @param {number} m22
* @param {number} m23
* @param {number} m30
* @param {number} m31
* @param {number} m32
* @param {number} m33
* @returns {mat4} New mat4
*/
mat4.createFrom = function (m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
var dest = new MatrixArray(16);
dest[0] = m00;
dest[1] = m01;
dest[2] = m02;
dest[3] = m03;
dest[4] = m10;
dest[5] = m11;
dest[6] = m12;
dest[7] = m13;
dest[8] = m20;
dest[9] = m21;
dest[10] = m22;
dest[11] = m23;
dest[12] = m30;
dest[13] = m31;
dest[14] = m32;
dest[15] = m33;
return dest;
};
/**
* Copies the values of one mat4 to another
*
* @param {mat4} mat mat4 containing values to copy
* @param {mat4} dest mat4 receiving copied values
*
* @returns {mat4} dest
*/
mat4.set = function (mat, dest) {
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[8] = mat[8];
dest[9] = mat[9];
dest[10] = mat[10];
dest[11] = mat[11];
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
return dest;
};
/**
* Compares two matrices for equality within a certain margin of error
*
* @param {mat4} a First matrix
* @param {mat4} b Second matrix
*
* @returns {Boolean} True if a is equivalent to b
*/
mat4.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON &&
Math.abs(a[3] - b[3]) < FLOAT_EPSILON &&
Math.abs(a[4] - b[4]) < FLOAT_EPSILON &&
Math.abs(a[5] - b[5]) < FLOAT_EPSILON &&
Math.abs(a[6] - b[6]) < FLOAT_EPSILON &&
Math.abs(a[7] - b[7]) < FLOAT_EPSILON &&
Math.abs(a[8] - b[8]) < FLOAT_EPSILON &&
Math.abs(a[9] - b[9]) < FLOAT_EPSILON &&
Math.abs(a[10] - b[10]) < FLOAT_EPSILON &&
Math.abs(a[11] - b[11]) < FLOAT_EPSILON &&
Math.abs(a[12] - b[12]) < FLOAT_EPSILON &&
Math.abs(a[13] - b[13]) < FLOAT_EPSILON &&
Math.abs(a[14] - b[14]) < FLOAT_EPSILON &&
Math.abs(a[15] - b[15]) < FLOAT_EPSILON
);
};
/**
* Sets a mat4 to an identity matrix
*
* @param {mat4} dest mat4 to set
*
* @returns {mat4} dest
*/
mat4.identity = function (dest) {
if (!dest) { dest = mat4.create(); }
dest[0] = 1;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
dest[4] = 0;
dest[5] = 1;
dest[6] = 0;
dest[7] = 0;
dest[8] = 0;
dest[9] = 0;
dest[10] = 1;
dest[11] = 0;
dest[12] = 0;
dest[13] = 0;
dest[14] = 0;
dest[15] = 1;
return dest;
};
/**
* Transposes a mat4 (flips the values over the diagonal)
*
* @param {mat4} mat mat4 to transpose
* @param {mat4} [dest] mat4 receiving transposed values. If not specified result is written to mat
*
* @param {mat4} dest is specified, mat otherwise
*/
mat4.transpose = function (mat, dest) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (!dest || mat === dest) {
var a01 = mat[1], a02 = mat[2], a03 = mat[3],
a12 = mat[6], a13 = mat[7],
a23 = mat[11];
mat[1] = mat[4];
mat[2] = mat[8];
mat[3] = mat[12];
mat[4] = a01;
mat[6] = mat[9];
mat[7] = mat[13];
mat[8] = a02;
mat[9] = a12;
mat[11] = mat[14];
mat[12] = a03;
mat[13] = a13;
mat[14] = a23;
return mat;
}
dest[0] = mat[0];
dest[1] = mat[4];
dest[2] = mat[8];
dest[3] = mat[12];
dest[4] = mat[1];
dest[5] = mat[5];
dest[6] = mat[9];
dest[7] = mat[13];
dest[8] = mat[2];
dest[9] = mat[6];
dest[10] = mat[10];
dest[11] = mat[14];
dest[12] = mat[3];
dest[13] = mat[7];
dest[14] = mat[11];
dest[15] = mat[15];
return dest;
};
/**
* Calculates the determinant of a mat4
*
* @param {mat4} mat mat4 to calculate determinant of
*
* @returns {number} determinant of mat
*/
mat4.determinant = function (mat) {
// Cache the matrix values (makes for huge speed increases!)
var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3],
a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7],
a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11],
a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
return (a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 +
a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 +
a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 +
a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 +
a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 +
a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33);
};
/**
* Calculates the inverse matrix of a mat4
*
* @param {mat4} mat mat4 to calculate inverse of
* @param {mat4} [dest] mat4 receiving inverse matrix. If not specified result is written to mat
*
* @param {mat4} dest is specified, mat otherwise, null if matrix cannot be inverted
*/
mat4.inverse = function (mat, dest) {
if (!dest) { dest = mat; }
// Cache the matrix values (makes for huge speed increases!)
var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3],
a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7],
a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11],
a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[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,
d = (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06),
invDet;
// Calculate the determinant
if (!d) { return null; }
invDet = 1 / d;
dest[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet;
dest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet;
dest[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet;
dest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet;
dest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet;
dest[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet;
dest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet;
dest[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet;
dest[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet;
dest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet;
dest[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet;
dest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet;
dest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet;
dest[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet;
dest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet;
dest[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet;
return dest;
};
/**
* Copies the upper 3x3 elements of a mat4 into another mat4
*
* @param {mat4} mat mat4 containing values to copy
* @param {mat4} [dest] mat4 receiving copied values
*
* @returns {mat4} dest is specified, a new mat4 otherwise
*/
mat4.toRotationMat = function (mat, dest) {
if (!dest) { dest = mat4.create(); }
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[8] = mat[8];
dest[9] = mat[9];
dest[10] = mat[10];
dest[11] = mat[11];
dest[12] = 0;
dest[13] = 0;
dest[14] = 0;
dest[15] = 1;
return dest;
};
/**
* Copies the upper 3x3 elements of a mat4 into a mat3
*
* @param {mat4} mat mat4 containing values to copy
* @param {mat3} [dest] mat3 receiving copied values
*
* @returns {mat3} dest is specified, a new mat3 otherwise
*/
mat4.toMat3 = function (mat, dest) {
if (!dest) { dest = mat3.create(); }
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[4];
dest[4] = mat[5];
dest[5] = mat[6];
dest[6] = mat[8];
dest[7] = mat[9];
dest[8] = mat[10];
return dest;
};
/**
* Calculates the inverse of the upper 3x3 elements of a mat4 and copies the result into a mat3
* The resulting matrix is useful for calculating transformed normals
*
* Params:
* @param {mat4} mat mat4 containing values to invert and copy
* @param {mat3} [dest] mat3 receiving values
*
* @returns {mat3} dest is specified, a new mat3 otherwise, null if the matrix cannot be inverted
*/
mat4.toInverseMat3 = function (mat, dest) {
// Cache the matrix values (makes for huge speed increases!)
var a00 = mat[0], a01 = mat[1], a02 = mat[2],
a10 = mat[4], a11 = mat[5], a12 = mat[6],
a20 = mat[8], a21 = mat[9], a22 = mat[10],
b01 = a22 * a11 - a12 * a21,
b11 = -a22 * a10 + a12 * a20,
b21 = a21 * a10 - a11 * a20,
d = a00 * b01 + a01 * b11 + a02 * b21,
id;
if (!d) { return null; }
id = 1 / d;
if (!dest) { dest = mat3.create(); }
dest[0] = b01 * id;
dest[1] = (-a22 * a01 + a02 * a21) * id;
dest[2] = (a12 * a01 - a02 * a11) * id;
dest[3] = b11 * id;
dest[4] = (a22 * a00 - a02 * a20) * id;
dest[5] = (-a12 * a00 + a02 * a10) * id;
dest[6] = b21 * id;
dest[7] = (-a21 * a00 + a01 * a20) * id;
dest[8] = (a11 * a00 - a01 * a10) * id;
return dest;
};
/**
* Performs a matrix multiplication
*
* @param {mat4} mat First operand
* @param {mat4} mat2 Second operand
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.multiply = function (mat, mat2, dest) {
if (!dest) { dest = mat; }
// Cache the matrix values (makes for huge speed increases!)
var a00 = mat[ 0], a01 = mat[ 1], a02 = mat[ 2], a03 = mat[3];
var a10 = mat[ 4], a11 = mat[ 5], a12 = mat[ 6], a13 = mat[7];
var a20 = mat[ 8], a21 = mat[ 9], a22 = mat[10], a23 = mat[11];
var a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
// Cache only the current line of the second matrix
var b0 = mat2[0], b1 = mat2[1], b2 = mat2[2], b3 = mat2[3];
dest[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
dest[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
dest[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
dest[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = mat2[4];
b1 = mat2[5];
b2 = mat2[6];
b3 = mat2[7];
dest[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
dest[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
dest[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
dest[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = mat2[8];
b1 = mat2[9];
b2 = mat2[10];
b3 = mat2[11];
dest[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
dest[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
dest[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
dest[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = mat2[12];
b1 = mat2[13];
b2 = mat2[14];
b3 = mat2[15];
dest[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
dest[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
dest[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
dest[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
return dest;
};
/**
* Transforms a vec3 with the given matrix
* 4th vector component is implicitly '1'
*
* @param {mat4} mat mat4 to transform the vector with
* @param {vec3} vec vec3 to transform
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns {vec3} dest if specified, vec otherwise
*/
mat4.multiplyVec3 = function (mat, vec, dest) {
if (!dest) { dest = vec; }
var x = vec[0], y = vec[1], z = vec[2];
dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12];
dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13];
dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14];
return dest;
};
/**
* Transforms a vec4 with the given matrix
*
* @param {mat4} mat mat4 to transform the vector with
* @param {vec4} vec vec4 to transform
* @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec
*
* @returns {vec4} dest if specified, vec otherwise
*/
mat4.multiplyVec4 = function (mat, vec, dest) {
if (!dest) { dest = vec; }
var x = vec[0], y = vec[1], z = vec[2], w = vec[3];
dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12] * w;
dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13] * w;
dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14] * w;
dest[3] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15] * w;
return dest;
};
/**
* Translates a matrix by the given vector
*
* @param {mat4} mat mat4 to translate
* @param {vec3} vec vec3 specifying the translation
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.translate = function (mat, vec, dest) {
var x = vec[0], y = vec[1], z = vec[2],
a00, a01, a02, a03,
a10, a11, a12, a13,
a20, a21, a22, a23;
if (!dest || mat === dest) {
mat[12] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12];
mat[13] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13];
mat[14] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14];
mat[15] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15];
return mat;
}
a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3];
a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7];
a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11];
dest[0] = a00; dest[1] = a01; dest[2] = a02; dest[3] = a03;
dest[4] = a10; dest[5] = a11; dest[6] = a12; dest[7] = a13;
dest[8] = a20; dest[9] = a21; dest[10] = a22; dest[11] = a23;
dest[12] = a00 * x + a10 * y + a20 * z + mat[12];
dest[13] = a01 * x + a11 * y + a21 * z + mat[13];
dest[14] = a02 * x + a12 * y + a22 * z + mat[14];
dest[15] = a03 * x + a13 * y + a23 * z + mat[15];
return dest;
};
/**
* Scales a matrix by the given vector
*
* @param {mat4} mat mat4 to scale
* @param {vec3} vec vec3 specifying the scale for each axis
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @param {mat4} dest if specified, mat otherwise
*/
mat4.scale = function (mat, vec, dest) {
var x = vec[0], y = vec[1], z = vec[2];
if (!dest || mat === dest) {
mat[0] *= x;
mat[1] *= x;
mat[2] *= x;
mat[3] *= x;
mat[4] *= y;
mat[5] *= y;
mat[6] *= y;
mat[7] *= y;
mat[8] *= z;
mat[9] *= z;
mat[10] *= z;
mat[11] *= z;
return mat;
}
dest[0] = mat[0] * x;
dest[1] = mat[1] * x;
dest[2] = mat[2] * x;
dest[3] = mat[3] * x;
dest[4] = mat[4] * y;
dest[5] = mat[5] * y;
dest[6] = mat[6] * y;
dest[7] = mat[7] * y;
dest[8] = mat[8] * z;
dest[9] = mat[9] * z;
dest[10] = mat[10] * z;
dest[11] = mat[11] * z;
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
return dest;
};
/**
* Rotates a matrix by the given angle around the specified axis
* If rotating around a primary axis (X,Y,Z) one of the specialized rotation functions should be used instead for performance
*
* @param {mat4} mat mat4 to rotate
* @param {number} angle Angle (in radians) to rotate
* @param {vec3} axis vec3 representing the axis to rotate around
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.rotate = function (mat, angle, axis, dest) {
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 (!len) { return null; }
if (len !== 1) {
len = 1 / len;
x *= len;
y *= len;
z *= len;
}
s = Math.sin(angle);
c = Math.cos(angle);
t = 1 - c;
a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3];
a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7];
a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[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;
if (!dest) {
dest = mat;
} else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
}
// Perform rotation-specific matrix multiplication
dest[0] = a00 * b00 + a10 * b01 + a20 * b02;
dest[1] = a01 * b00 + a11 * b01 + a21 * b02;
dest[2] = a02 * b00 + a12 * b01 + a22 * b02;
dest[3] = a03 * b00 + a13 * b01 + a23 * b02;
dest[4] = a00 * b10 + a10 * b11 + a20 * b12;
dest[5] = a01 * b10 + a11 * b11 + a21 * b12;
dest[6] = a02 * b10 + a12 * b11 + a22 * b12;
dest[7] = a03 * b10 + a13 * b11 + a23 * b12;
dest[8] = a00 * b20 + a10 * b21 + a20 * b22;
dest[9] = a01 * b20 + a11 * b21 + a21 * b22;
dest[10] = a02 * b20 + a12 * b21 + a22 * b22;
dest[11] = a03 * b20 + a13 * b21 + a23 * b22;
return dest;
};
/**
* Rotates a matrix by the given angle around the X axis
*
* @param {mat4} mat mat4 to rotate
* @param {number} angle Angle (in radians) to rotate
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.rotateX = function (mat, angle, dest) {
var s = Math.sin(angle),
c = Math.cos(angle),
a10 = mat[4],
a11 = mat[5],
a12 = mat[6],
a13 = mat[7],
a20 = mat[8],
a21 = mat[9],
a22 = mat[10],
a23 = mat[11];
if (!dest) {
dest = mat;
} else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
}
// Perform axis-specific matrix multiplication
dest[4] = a10 * c + a20 * s;
dest[5] = a11 * c + a21 * s;
dest[6] = a12 * c + a22 * s;
dest[7] = a13 * c + a23 * s;
dest[8] = a10 * -s + a20 * c;
dest[9] = a11 * -s + a21 * c;
dest[10] = a12 * -s + a22 * c;
dest[11] = a13 * -s + a23 * c;
return dest;
};
/**
* Rotates a matrix by the given angle around the Y axis
*
* @param {mat4} mat mat4 to rotate
* @param {number} angle Angle (in radians) to rotate
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.rotateY = function (mat, angle, dest) {
var s = Math.sin(angle),
c = Math.cos(angle),
a00 = mat[0],
a01 = mat[1],
a02 = mat[2],
a03 = mat[3],
a20 = mat[8],
a21 = mat[9],
a22 = mat[10],
a23 = mat[11];
if (!dest) {
dest = mat;
} else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows
dest[4] = mat[4];
dest[5] = mat[5];
dest[6] = mat[6];
dest[7] = mat[7];
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
}
// Perform axis-specific matrix multiplication
dest[0] = a00 * c + a20 * -s;
dest[1] = a01 * c + a21 * -s;
dest[2] = a02 * c + a22 * -s;
dest[3] = a03 * c + a23 * -s;
dest[8] = a00 * s + a20 * c;
dest[9] = a01 * s + a21 * c;
dest[10] = a02 * s + a22 * c;
dest[11] = a03 * s + a23 * c;
return dest;
};
/**
* Rotates a matrix by the given angle around the Z axis
*
* @param {mat4} mat mat4 to rotate
* @param {number} angle Angle (in radians) to rotate
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat
*
* @returns {mat4} dest if specified, mat otherwise
*/
mat4.rotateZ = function (mat, angle, dest) {
var s = Math.sin(angle),
c = Math.cos(angle),
a00 = mat[0],
a01 = mat[1],
a02 = mat[2],
a03 = mat[3],
a10 = mat[4],
a11 = mat[5],
a12 = mat[6],
a13 = mat[7];
if (!dest) {
dest = mat;
} else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row
dest[8] = mat[8];
dest[9] = mat[9];
dest[10] = mat[10];
dest[11] = mat[11];
dest[12] = mat[12];
dest[13] = mat[13];
dest[14] = mat[14];
dest[15] = mat[15];
}
// Perform axis-specific matrix multiplication
dest[0] = a00 * c + a10 * s;
dest[1] = a01 * c + a11 * s;
dest[2] = a02 * c + a12 * s;
dest[3] = a03 * c + a13 * s;
dest[4] = a00 * -s + a10 * c;
dest[5] = a01 * -s + a11 * c;
dest[6] = a02 * -s + a12 * c;
dest[7] = a03 * -s + a13 * c;
return dest;
};
/**
* Generates a frustum matrix with the given bounds
*
* @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
* @param {mat4} [dest] mat4 frustum matrix will be written into
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat4.frustum = function (left, right, bottom, top, near, far, dest) {
if (!dest) { dest = mat4.create(); }
var rl = (right - left),
tb = (top - bottom),
fn = (far - near);
dest[0] = (near * 2) / rl;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
dest[4] = 0;
dest[5] = (near * 2) / tb;
dest[6] = 0;
dest[7] = 0;
dest[8] = (right + left) / rl;
dest[9] = (top + bottom) / tb;
dest[10] = -(far + near) / fn;
dest[11] = -1;
dest[12] = 0;
dest[13] = 0;
dest[14] = -(far * near * 2) / fn;
dest[15] = 0;
return dest;
};
/**
* Generates a perspective projection matrix with the given bounds
*
* @param {number} fovy Vertical field of view
* @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
* @param {mat4} [dest] mat4 frustum matrix will be written into
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat4.perspective = function (fovy, aspect, near, far, dest) {
var top = near * Math.tan(fovy * Math.PI / 360.0),
right = top * aspect;
return mat4.frustum(-right, right, -top, top, near, far, dest);
};
/**
* Generates a orthogonal projection matrix with the given bounds
*
* @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
* @param {mat4} [dest] mat4 frustum matrix will be written into
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat4.ortho = function (left, right, bottom, top, near, far, dest) {
if (!dest) { dest = mat4.create(); }
var rl = (right - left),
tb = (top - bottom),
fn = (far - near);
dest[0] = 2 / rl;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
dest[4] = 0;
dest[5] = 2 / tb;
dest[6] = 0;
dest[7] = 0;
dest[8] = 0;
dest[9] = 0;
dest[10] = -2 / fn;
dest[11] = 0;
dest[12] = -(left + right) / rl;
dest[13] = -(top + bottom) / tb;
dest[14] = -(far + near) / fn;
dest[15] = 1;
return dest;
};
/**
* Generates a look-at matrix with the given eye position, focal point, and up axis
*
* @param {vec3} eye Position of the viewer
* @param {vec3} center Point the viewer is looking at
* @param {vec3} up vec3 pointing "up"
* @param {mat4} [dest] mat4 frustum matrix will be written into
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat4.lookAt = function (eye, center, up, dest) {
if (!dest) { dest = mat4.create(); }
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 (eyex === centerx && eyey === centery && eyez === centerz) {
return mat4.identity(dest);
}
//vec3.direction(eye, center, z);
z0 = eyex - centerx;
z1 = eyey - centery;
z2 = eyez - centerz;
// normalize (no check needed for 0 because of early return)
len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
z0 *= len;
z1 *= len;
z2 *= len;
//vec3.normalize(vec3.cross(up, z, x));
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;
}
//vec3.normalize(vec3.cross(z, x, y));
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;
}
dest[0] = x0;
dest[1] = y0;
dest[2] = z0;
dest[3] = 0;
dest[4] = x1;
dest[5] = y1;
dest[6] = z1;
dest[7] = 0;
dest[8] = x2;
dest[9] = y2;
dest[10] = z2;
dest[11] = 0;
dest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
dest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
dest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
dest[15] = 1;
return dest;
};
/**
* 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 {quat4} quat Rotation quaternion
* @param {vec3} vec Translation vector
* @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to a new mat4
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
mat4.fromRotationTranslation = function (quat, vec, dest) {
if (!dest) { dest = mat4.create(); }
// Quaternion math
var x = quat[0], y = quat[1], z = quat[2], w = quat[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;
dest[0] = 1 - (yy + zz);
dest[1] = xy + wz;
dest[2] = xz - wy;
dest[3] = 0;
dest[4] = xy - wz;
dest[5] = 1 - (xx + zz);
dest[6] = yz + wx;
dest[7] = 0;
dest[8] = xz + wy;
dest[9] = yz - wx;
dest[10] = 1 - (xx + yy);
dest[11] = 0;
dest[12] = vec[0];
dest[13] = vec[1];
dest[14] = vec[2];
dest[15] = 1;
return dest;
};
/**
* Returns a string representation of a mat4
*
* @param {mat4} mat mat4 to represent as a string
*
* @returns {string} String representation of mat
*/
mat4.str = function (mat) {
return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] +
', ' + mat[4] + ', ' + mat[5] + ', ' + mat[6] + ', ' + mat[7] +
', ' + mat[8] + ', ' + mat[9] + ', ' + mat[10] + ', ' + mat[11] +
', ' + mat[12] + ', ' + mat[13] + ', ' + mat[14] + ', ' + mat[15] + ']';
};
/**
* @class Quaternion
* @name quat4
*/
var quat4 = {};
/**
* Creates a new instance of a quat4 using the default array type
* Any javascript array containing at least 4 numeric elements can serve as a quat4
*
* @param {quat4} [quat] quat4 containing values to initialize with
*
* @returns {quat4} New quat4
*/
quat4.create = function (quat) {
var dest = new MatrixArray(4);
if (quat) {
dest[0] = quat[0];
dest[1] = quat[1];
dest[2] = quat[2];
dest[3] = quat[3];
} else {
dest[0] = dest[1] = dest[2] = dest[3] = 0;
}
return dest;
};
/**
* Creates a new instance of a quat4, initializing it with the given arguments
*
* @param {number} x X value
* @param {number} y Y value
* @param {number} z Z value
* @param {number} w W value
* @returns {quat4} New quat4
*/
quat4.createFrom = function (x, y, z, w) {
var dest = new MatrixArray(4);
dest[0] = x;
dest[1] = y;
dest[2] = z;
dest[3] = w;
return dest;
};
/**
* Copies the values of one quat4 to another
*
* @param {quat4} quat quat4 containing values to copy
* @param {quat4} dest quat4 receiving copied values
*
* @returns {quat4} dest
*/
quat4.set = function (quat, dest) {
dest[0] = quat[0];
dest[1] = quat[1];
dest[2] = quat[2];
dest[3] = quat[3];
return dest;
};
/**
* Compares two quaternions for equality within a certain margin of error
*
* @param {quat4} a First vector
* @param {quat4} b Second vector
*
* @returns {Boolean} True if a is equivalent to b
*/
quat4.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON &&
Math.abs(a[3] - b[3]) < FLOAT_EPSILON
);
};
/**
* Creates a new identity Quat4
*
* @param {quat4} [dest] quat4 receiving copied values
*
* @returns {quat4} dest is specified, new quat4 otherwise
*/
quat4.identity = function (dest) {
if (!dest) { dest = quat4.create(); }
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
dest[3] = 1;
return dest;
};
var identityQuat4 = quat4.identity();
/**
* Calculates the W component of a quat4 from the X, Y, and Z components.
* Assumes that quaternion is 1 unit in length.
* Any existing W component will be ignored.
*
* @param {quat4} quat quat4 to calculate W component of
* @param {quat4} [dest] quat4 receiving calculated values. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.calculateW = function (quat, dest) {
var x = quat[0], y = quat[1], z = quat[2];
if (!dest || quat === dest) {
quat[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
return quat;
}
dest[0] = x;
dest[1] = y;
dest[2] = z;
dest[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
return dest;
};
/**
* Calculates the dot product of two quaternions
*
* @param {quat4} quat First operand
* @param {quat4} quat2 Second operand
*
* @return {number} Dot product of quat and quat2
*/
quat4.dot = function(quat, quat2){
return quat[0]*quat2[0] + quat[1]*quat2[1] + quat[2]*quat2[2] + quat[3]*quat2[3];
};
/**
* Calculates the inverse of a quat4
*
* @param {quat4} quat quat4 to calculate inverse of
* @param {quat4} [dest] quat4 receiving inverse values. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.inverse = function(quat, dest) {
var q0 = quat[0], q1 = quat[1], q2 = quat[2], q3 = quat[3],
dot = q0*q0 + q1*q1 + q2*q2 + q3*q3,
invDot = dot ? 1.0/dot : 0;
// TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
if(!dest || quat === dest) {
quat[0] *= -invDot;
quat[1] *= -invDot;
quat[2] *= -invDot;
quat[3] *= invDot;
return quat;
}
dest[0] = -quat[0]*invDot;
dest[1] = -quat[1]*invDot;
dest[2] = -quat[2]*invDot;
dest[3] = quat[3]*invDot;
return dest;
};
/**
* Calculates the conjugate of a quat4
* If the quaternion is normalized, this function is faster than quat4.inverse and produces the same result.
*
* @param {quat4} quat quat4 to calculate conjugate of
* @param {quat4} [dest] quat4 receiving conjugate values. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.conjugate = function (quat, dest) {
if (!dest || quat === dest) {
quat[0] *= -1;
quat[1] *= -1;
quat[2] *= -1;
return quat;
}
dest[0] = -quat[0];
dest[1] = -quat[1];
dest[2] = -quat[2];
dest[3] = quat[3];
return dest;
};
/**
* Calculates the length of a quat4
*
* Params:
* @param {quat4} quat quat4 to calculate length of
*
* @returns Length of quat
*/
quat4.length = function (quat) {
var x = quat[0], y = quat[1], z = quat[2], w = quat[3];
return Math.sqrt(x * x + y * y + z * z + w * w);
};
/**
* Generates a unit quaternion of the same direction as the provided quat4
* If quaternion length is 0, returns [0, 0, 0, 0]
*
* @param {quat4} quat quat4 to normalize
* @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.normalize = function (quat, dest) {
if (!dest) { dest = quat; }
var x = quat[0], y = quat[1], z = quat[2], w = quat[3],
len = Math.sqrt(x * x + y * y + z * z + w * w);
if (len === 0) {
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
return dest;
}
len = 1 / len;
dest[0] = x * len;
dest[1] = y * len;
dest[2] = z * len;
dest[3] = w * len;
return dest;
};
/**
* Performs quaternion addition
*
* @param {quat4} quat First operand
* @param {quat4} quat2 Second operand
* @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.add = function (quat, quat2, dest) {
if(!dest || quat === dest) {
quat[0] += quat2[0];
quat[1] += quat2[1];
quat[2] += quat2[2];
quat[3] += quat2[3];
return quat;
}
dest[0] = quat[0]+quat2[0];
dest[1] = quat[1]+quat2[1];
dest[2] = quat[2]+quat2[2];
dest[3] = quat[3]+quat2[3];
return dest;
};
/**
* Performs a quaternion multiplication
*
* @param {quat4} quat First operand
* @param {quat4} quat2 Second operand
* @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.multiply = function (quat, quat2, dest) {
if (!dest) { dest = quat; }
var qax = quat[0], qay = quat[1], qaz = quat[2], qaw = quat[3],
qbx = quat2[0], qby = quat2[1], qbz = quat2[2], qbw = quat2[3];
dest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
dest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
dest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
dest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
return dest;
};
/**
* Transforms a vec3 with the given quaternion
*
* @param {quat4} quat quat4 to transform the vector with
* @param {vec3} vec vec3 to transform
* @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec
*
* @returns dest if specified, vec otherwise
*/
quat4.multiplyVec3 = function (quat, vec, dest) {
if (!dest) { dest = vec; }
var x = vec[0], y = vec[1], z = vec[2],
qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[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
dest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
dest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
dest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
return dest;
};
/**
* Multiplies the components of a quaternion by a scalar value
*
* @param {quat4} quat to scale
* @param {number} val Value to scale by
* @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.scale = function (quat, val, dest) {
if(!dest || quat === dest) {
quat[0] *= val;
quat[1] *= val;
quat[2] *= val;
quat[3] *= val;
return quat;
}
dest[0] = quat[0]*val;
dest[1] = quat[1]*val;
dest[2] = quat[2]*val;
dest[3] = quat[3]*val;
return dest;
};
/**
* Calculates a 3x3 matrix from the given quat4
*
* @param {quat4} quat quat4 to create matrix from
* @param {mat3} [dest] mat3 receiving operation result
*
* @returns {mat3} dest if specified, a new mat3 otherwise
*/
quat4.toMat3 = function (quat, dest) {
if (!dest) { dest = mat3.create(); }
var x = quat[0], y = quat[1], z = quat[2], w = quat[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;
dest[0] = 1 - (yy + zz);
dest[1] = xy + wz;
dest[2] = xz - wy;
dest[3] = xy - wz;
dest[4] = 1 - (xx + zz);
dest[5] = yz + wx;
dest[6] = xz + wy;
dest[7] = yz - wx;
dest[8] = 1 - (xx + yy);
return dest;
};
/**
* Calculates a 4x4 matrix from the given quat4
*
* @param {quat4} quat quat4 to create matrix from
* @param {mat4} [dest] mat4 receiving operation result
*
* @returns {mat4} dest if specified, a new mat4 otherwise
*/
quat4.toMat4 = function (quat, dest) {
if (!dest) { dest = mat4.create(); }
var x = quat[0], y = quat[1], z = quat[2], w = quat[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;
dest[0] = 1 - (yy + zz);
dest[1] = xy + wz;
dest[2] = xz - wy;
dest[3] = 0;
dest[4] = xy - wz;
dest[5] = 1 - (xx + zz);
dest[6] = yz + wx;
dest[7] = 0;
dest[8] = xz + wy;
dest[9] = yz - wx;
dest[10] = 1 - (xx + yy);
dest[11] = 0;
dest[12] = 0;
dest[13] = 0;
dest[14] = 0;
dest[15] = 1;
return dest;
};
/**
* Performs a spherical linear interpolation between two quat4
*
* @param {quat4} quat First quaternion
* @param {quat4} quat2 Second quaternion
* @param {number} slerp Interpolation amount between the two inputs
* @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat
*
* @returns {quat4} dest if specified, quat otherwise
*/
quat4.slerp = function (quat, quat2, slerp, dest) {
if (!dest) { dest = quat; }
var cosHalfTheta = quat[0] * quat2[0] + quat[1] * quat2[1] + quat[2] * quat2[2] + quat[3] * quat2[3],
halfTheta,
sinHalfTheta,
ratioA,
ratioB;
if (Math.abs(cosHalfTheta) >= 1.0) {
if (dest !== quat) {
dest[0] = quat[0];
dest[1] = quat[1];
dest[2] = quat[2];
dest[3] = quat[3];
}
return dest;
}
halfTheta = Math.acos(cosHalfTheta);
sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta * cosHalfTheta);
if (Math.abs(sinHalfTheta) < 0.001) {
dest[0] = (quat[0] * 0.5 + quat2[0] * 0.5);
dest[1] = (quat[1] * 0.5 + quat2[1] * 0.5);
dest[2] = (quat[2] * 0.5 + quat2[2] * 0.5);
dest[3] = (quat[3] * 0.5 + quat2[3] * 0.5);
return dest;
}
ratioA = Math.sin((1 - slerp) * halfTheta) / sinHalfTheta;
ratioB = Math.sin(slerp * halfTheta) / sinHalfTheta;
dest[0] = (quat[0] * ratioA + quat2[0] * ratioB);
dest[1] = (quat[1] * ratioA + quat2[1] * ratioB);
dest[2] = (quat[2] * ratioA + quat2[2] * ratioB);
dest[3] = (quat[3] * ratioA + quat2[3] * ratioB);
return dest;
};
/**
* Creates a quaternion from the given 3x3 rotation matrix.
* If dest is omitted, a new quaternion will be created.
*
* @param {mat3} mat the rotation matrix
* @param {quat4} [dest] an optional receiving quaternion
*
* @returns {quat4} the quaternion constructed from the rotation matrix
*
*/
quat4.fromRotationMatrix = function(mat, dest) {
if (!dest) dest = quat4.create();
// Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
// article "Quaternion Calculus and Fast Animation".
var fTrace = mat[0] + mat[4] + mat[8];
var fRoot;
if ( fTrace > 0.0 ) {
// |w| > 1/2, may as well choose w > 1/2
fRoot = Math.sqrt(fTrace + 1.0); // 2w
dest[3] = 0.5 * fRoot;
fRoot = 0.5/fRoot; // 1/(4w)
dest[0] = (mat[7]-mat[5])*fRoot;
dest[1] = (mat[2]-mat[6])*fRoot;
dest[2] = (mat[3]-mat[1])*fRoot;
} else {
// |w| <= 1/2
var s_iNext = quat4.fromRotationMatrix.s_iNext = quat4.fromRotationMatrix.s_iNext || [1,2,0];
var i = 0;
if ( mat[4] > mat[0] )
i = 1;
if ( mat[8] > mat[i*3+i] )
i = 2;
var j = s_iNext[i];
var k = s_iNext[j];
fRoot = Math.sqrt(mat[i*3+i]-mat[j*3+j]-mat[k*3+k] + 1.0);
dest[i] = 0.5 * fRoot;
fRoot = 0.5 / fRoot;
dest[3] = (mat[k*3+j] - mat[j*3+k]) * fRoot;
dest[j] = (mat[j*3+i] + mat[i*3+j]) * fRoot;
dest[k] = (mat[k*3+i] + mat[i*3+k]) * fRoot;
}
return dest;
};
/**
* Alias. See the description for quat4.fromRotationMatrix().
*/
mat3.toQuat4 = quat4.fromRotationMatrix;
(function() {
var mat = mat3.create();
/**
* Creates a quaternion from the 3 given vectors. They must be perpendicular
* to one another and represent the X, Y and Z axes.
*
* If dest is omitted, a new quat4 will be created.
*
* Example: The default OpenGL orientation has a view vector [0, 0, -1],
* right vector [1, 0, 0], and up vector [0, 1, 0]. A quaternion representing
* this orientation could be constructed with:
*
* quat = quat4.fromAxes([0, 0, -1], [1, 0, 0], [0, 1, 0], quat4.create());
*
* @param {vec3} view the view vector, or direction the object is pointing in
* @param {vec3} right the right vector, or direction to the "right" of the object
* @param {vec3} up the up vector, or direction towards the object's "up"
* @param {quat4} [dest] an optional receiving quat4
*
* @returns {quat4} dest
**/
quat4.fromAxes = function(view, right, up, dest) {
mat[0] = right[0];
mat[3] = right[1];
mat[6] = right[2];
mat[1] = up[0];
mat[4] = up[1];
mat[7] = up[2];
mat[2] = view[0];
mat[5] = view[1];
mat[8] = view[2];
return quat4.fromRotationMatrix(mat, dest);
};
})();
/**
* Sets a quat4 to the Identity and returns it.
*
* @param {quat4} [dest] quat4 to set. If omitted, a
* new quat4 will be created.
*
* @returns {quat4} dest
*/
quat4.identity = function(dest) {
if (!dest) dest = quat4.create();
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
dest[3] = 1;
return dest;
};
/**
* Sets a quat4 from the given angle and rotation axis,
* then returns it. If dest is not given, a new quat4 is created.
*
* @param {Number} angle the angle in radians
* @param {vec3} axis the axis around which to rotate
* @param {quat4} [dest] the optional quat4 to store the result
*
* @returns {quat4} dest
**/
quat4.fromAngleAxis = function(angle, axis, dest) {
// The quaternion representing the rotation is
// q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k)
if (!dest) dest = quat4.create();
var half = angle * 0.5;
var s = Math.sin(half);
dest[3] = Math.cos(half);
dest[0] = s * axis[0];
dest[1] = s * axis[1];
dest[2] = s * axis[2];
return dest;
};
/**
* Stores the angle and axis in a vec4, where the XYZ components represent
* the axis and the W (4th) component is the angle in radians.
*
* If dest is not given, src will be modified in place and returned, after
* which it should not be considered not a quaternion (just an axis and angle).
*
* @param {quat4} quat the quaternion whose angle and axis to store
* @param {vec4} [dest] the optional vec4 to receive the data
*
* @returns {vec4} dest
*/
quat4.toAngleAxis = function(src, dest) {
if (!dest) dest = src;
// The quaternion representing the rotation is
// q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k)
var sqrlen = src[0]*src[0]+src[1]*src[1]+src[2]*src[2];
if (sqrlen > 0)
{
dest[3] = 2 * Math.acos(src[3]);
var invlen = glMath.invsqrt(sqrlen);
dest[0] = src[0]*invlen;
dest[1] = src[1]*invlen;
dest[2] = src[2]*invlen;
} else {
// angle is 0 (mod 2*pi), so any axis will do
dest[3] = 0;
dest[0] = 1;
dest[1] = 0;
dest[2] = 0;
}
return dest;
};
/**
* Returns a string representation of a quaternion
*
* @param {quat4} quat quat4 to represent as a string
*
* @returns {string} String representation of quat
*/
quat4.str = function (quat) {
return '[' + quat[0] + ', ' + quat[1] + ', ' + quat[2] + ', ' + quat[3] + ']';
};
/**
* @class 2 Dimensional Vector
* @name vec2
*/
var vec2 = {};
/**
* Creates a new vec2, initializing it from vec if vec
* is given.
*
* @param {vec2} [vec] the vector's initial contents
* @returns {vec2} a new 2D vector
*/
vec2.create = function(vec) {
var dest = new MatrixArray(2);
if (vec) {
dest[0] = vec[0];
dest[1] = vec[1];
} else {
dest[0] = 0;
dest[1] = 0;
}
return dest;
};
/**
* Creates a new instance of a vec2, initializing it with the given arguments
*
* @param {number} x X value
* @param {number} y Y value
* @returns {vec2} New vec2
*/
vec2.createFrom = function (x, y) {
var dest = new MatrixArray(2);
dest[0] = x;
dest[1] = y;
return dest;
};
/**
* Adds the vec2's together. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec2} vecA the first operand
* @param {vec2} vecB the second operand
* @param {vec2} [dest] the optional receiving vector
* @returns {vec2} dest
*/
vec2.add = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] + vecB[0];
dest[1] = vecA[1] + vecB[1];
return dest;
};
/**
* Subtracts vecB from vecA. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec2} vecA the first operand
* @param {vec2} vecB the second operand
* @param {vec2} [dest] the optional receiving vector
* @returns {vec2} dest
*/
vec2.subtract = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] - vecB[0];
dest[1] = vecA[1] - vecB[1];
return dest;
};
/**
* Multiplies vecA with vecB. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec2} vecA the first operand
* @param {vec2} vecB the second operand
* @param {vec2} [dest] the optional receiving vector
* @returns {vec2} dest
*/
vec2.multiply = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] * vecB[0];
dest[1] = vecA[1] * vecB[1];
return dest;
};
/**
* Divides vecA by vecB. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec2} vecA the first operand
* @param {vec2} vecB the second operand
* @param {vec2} [dest] the optional receiving vector
* @returns {vec2} dest
*/
vec2.divide = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] / vecB[0];
dest[1] = vecA[1] / vecB[1];
return dest;
};
/**
* Scales vecA by some scalar number. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecA.
*
* This is the same as multiplying each component of vecA
* by the given scalar.
*
* @param {vec2} vecA the vector to be scaled
* @param {Number} scalar the amount to scale the vector by
* @param {vec2} [dest] the optional receiving vector
* @returns {vec2} dest
*/
vec2.scale = function(vecA, scalar, dest) {
if (!dest) dest = vecA;
dest[0] = vecA[0] * scalar;
dest[1] = vecA[1] * scalar;
return dest;
};
/**
* Calculates the euclidian distance between two vec2
*
* Params:
* @param {vec2} vecA First vector
* @param {vec2} vecB Second vector
*
* @returns {number} Distance between vecA and vecB
*/
vec2.dist = function (vecA, vecB) {
var x = vecB[0] - vecA[0],
y = vecB[1] - vecA[1];
return Math.sqrt(x*x + y*y);
};
/**
* Copies the values of one vec2 to another
*
* @param {vec2} vec vec2 containing values to copy
* @param {vec2} dest vec2 receiving copied values
*
* @returns {vec2} dest
*/
vec2.set = function (vec, dest) {
dest[0] = vec[0];
dest[1] = vec[1];
return dest;
};
/**
* Compares two vectors for equality within a certain margin of error
*
* @param {vec2} a First vector
* @param {vec2} b Second vector
*
* @returns {Boolean} True if a is equivalent to b
*/
vec2.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON
);
};
/**
* Negates the components of a vec2
*
* @param {vec2} vec vec2 to negate
* @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec
*
* @returns {vec2} dest if specified, vec otherwise
*/
vec2.negate = function (vec, dest) {
if (!dest) { dest = vec; }
dest[0] = -vec[0];
dest[1] = -vec[1];
return dest;
};
/**
* Normlize a vec2
*
* @param {vec2} vec vec2 to normalize
* @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec
*
* @returns {vec2} dest if specified, vec otherwise
*/
vec2.normalize = function (vec, dest) {
if (!dest) { dest = vec; }
var mag = vec[0] * vec[0] + vec[1] * vec[1];
if (mag > 0) {
mag = Math.sqrt(mag);
dest[0] = vec[0] / mag;
dest[1] = vec[1] / mag;
} else {
dest[0] = dest[1] = 0;
}
return dest;
};
/**
* Computes the cross product of two vec2's. Note that the cross product must by definition
* produce a 3D vector. If a dest vector is given, it will contain the resultant 3D vector.
* Otherwise, a scalar number will be returned, representing the vector's Z coordinate, since
* its X and Y must always equal 0.
*
* Examples:
* var crossResult = vec3.create();
* vec2.cross([1, 2], [3, 4], crossResult);
* //=> [0, 0, -2]
*
* vec2.cross([1, 2], [3, 4]);
* //=> -2
*
* See http://stackoverflow.com/questions/243945/calculating-a-2d-vectors-cross-product
* for some interesting facts.
*
* @param {vec2} vecA left operand
* @param {vec2} vecB right operand
* @param {vec2} [dest] optional vec2 receiving result. If not specified a scalar is returned
*
*/
vec2.cross = function (vecA, vecB, dest) {
var z = vecA[0] * vecB[1] - vecA[1] * vecB[0];
if (!dest) return z;
dest[0] = dest[1] = 0;
dest[2] = z;
return dest;
};
/**
* Caclulates the length of a vec2
*
* @param {vec2} vec vec2 to calculate length of
*
* @returns {Number} Length of vec
*/
vec2.length = function (vec) {
var x = vec[0], y = vec[1];
return Math.sqrt(x * x + y * y);
};
/**
* Caclulates the squared length of a vec2
*
* @param {vec2} vec vec2 to calculate squared length of
*
* @returns {Number} Squared Length of vec
*/
vec2.squaredLength = function (vec) {
var x = vec[0], y = vec[1];
return x * x + y * y;
};
/**
* Caclulates the dot product of two vec2s
*
* @param {vec2} vecA First operand
* @param {vec2} vecB Second operand
*
* @returns {Number} Dot product of vecA and vecB
*/
vec2.dot = function (vecA, vecB) {
return vecA[0] * vecB[0] + vecA[1] * vecB[1];
};
/**
* Generates a 2D unit vector pointing from one vector to another
*
* @param {vec2} vecA Origin vec2
* @param {vec2} vecB vec2 to point to
* @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA
*
* @returns {vec2} dest if specified, vecA otherwise
*/
vec2.direction = function (vecA, vecB, dest) {
if (!dest) { dest = vecA; }
var x = vecA[0] - vecB[0],
y = vecA[1] - vecB[1],
len = x * x + y * y;
if (!len) {
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
return dest;
}
len = 1 / Math.sqrt(len);
dest[0] = x * len;
dest[1] = y * len;
return dest;
};
/**
* Performs a linear interpolation between two vec2
*
* @param {vec2} vecA First vector
* @param {vec2} vecB Second vector
* @param {Number} lerp Interpolation amount between the two inputs
* @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA
*
* @returns {vec2} dest if specified, vecA otherwise
*/
vec2.lerp = function (vecA, vecB, lerp, dest) {
if (!dest) { dest = vecA; }
dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]);
dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]);
return dest;
};
/**
* Returns a string representation of a vector
*
* @param {vec2} vec Vector to represent as a string
*
* @returns {String} String representation of vec
*/
vec2.str = function (vec) {
return '[' + vec[0] + ', ' + vec[1] + ']';
};
/**
* @class 2x2 Matrix
* @name mat2
*/
var mat2 = {};
/**
* Creates a new 2x2 matrix. If src is given, the new matrix
* is initialized to those values.
*
* @param {mat2} [src] the seed values for the new matrix, if any
* @returns {mat2} a new matrix
*/
mat2.create = function(src) {
var dest = new MatrixArray(4);
if (src) {
dest[0] = src[0];
dest[1] = src[1];
dest[2] = src[2];
dest[3] = src[3];
} else {
dest[0] = dest[1] = dest[2] = dest[3] = 0;
}
return dest;
};
/**
* Creates a new instance of a mat2, initializing it with the given arguments
*
* @param {number} m00
* @param {number} m01
* @param {number} m10
* @param {number} m11
* @returns {mat2} New mat2
*/
mat2.createFrom = function (m00, m01, m10, m11) {
var dest = new MatrixArray(4);
dest[0] = m00;
dest[1] = m01;
dest[2] = m10;
dest[3] = m11;
return dest;
};
/**
* Copies the values of one mat2 to another
*
* @param {mat2} mat mat2 containing values to copy
* @param {mat2} dest mat2 receiving copied values
*
* @returns {mat2} dest
*/
mat2.set = function (mat, dest) {
dest[0] = mat[0];
dest[1] = mat[1];
dest[2] = mat[2];
dest[3] = mat[3];
return dest;
};
/**
* Compares two matrices for equality within a certain margin of error
*
* @param {mat2} a First matrix
* @param {mat2} b Second matrix
*
* @returns {Boolean} True if a is equivalent to b
*/
mat2.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON &&
Math.abs(a[3] - b[3]) < FLOAT_EPSILON
);
};
/**
* Sets a mat2 to an identity matrix
*
* @param {mat2} [dest] mat2 to set. If omitted a new one will be created.
*
* @returns {mat2} dest
*/
mat2.identity = function (dest) {
if (!dest) { dest = mat2.create(); }
dest[0] = 1;
dest[1] = 0;
dest[2] = 0;
dest[3] = 1;
return dest;
};
/**
* Transposes a mat2 (flips the values over the diagonal)
*
* @param {mat2} mat mat2 to transpose
* @param {mat2} [dest] mat2 receiving transposed values. If not specified result is written to mat
*
* @param {mat2} dest if specified, mat otherwise
*/
mat2.transpose = function (mat, dest) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (!dest || mat === dest) {
var a00 = mat[1];
mat[1] = mat[2];
mat[2] = a00;
return mat;
}
dest[0] = mat[0];
dest[1] = mat[2];
dest[2] = mat[1];
dest[3] = mat[3];
return dest;
};
/**
* Calculates the determinant of a mat2
*
* @param {mat2} mat mat2 to calculate determinant of
*
* @returns {Number} determinant of mat
*/
mat2.determinant = function (mat) {
return mat[0] * mat[3] - mat[2] * mat[1];
};
/**
* Calculates the inverse matrix of a mat2
*
* @param {mat2} mat mat2 to calculate inverse of
* @param {mat2} [dest] mat2 receiving inverse matrix. If not specified result is written to mat
*
* @param {mat2} dest is specified, mat otherwise, null if matrix cannot be inverted
*/
mat2.inverse = function (mat, dest) {
if (!dest) { dest = mat; }
var a0 = mat[0], a1 = mat[1], a2 = mat[2], a3 = mat[3];
var det = a0 * a3 - a2 * a1;
if (!det) return null;
det = 1.0 / det;
dest[0] = a3 * det;
dest[1] = -a1 * det;
dest[2] = -a2 * det;
dest[3] = a0 * det;
return dest;
};
/**
* Performs a matrix multiplication
*
* @param {mat2} matA First operand
* @param {mat2} matB Second operand
* @param {mat2} [dest] mat2 receiving operation result. If not specified result is written to matA
*
* @returns {mat2} dest if specified, matA otherwise
*/
mat2.multiply = function (matA, matB, dest) {
if (!dest) { dest = matA; }
var a11 = matA[0],
a12 = matA[1],
a21 = matA[2],
a22 = matA[3];
dest[0] = a11 * matB[0] + a12 * matB[2];
dest[1] = a11 * matB[1] + a12 * matB[3];
dest[2] = a21 * matB[0] + a22 * matB[2];
dest[3] = a21 * matB[1] + a22 * matB[3];
return dest;
};
/**
* Rotates a 2x2 matrix by an angle
*
* @param {mat2} mat The matrix to rotate
* @param {Number} angle The angle in radians
* @param {mat2} [dest] Optional mat2 receiving the result. If omitted mat will be used.
*
* @returns {mat2} dest if specified, mat otherwise
*/
mat2.rotate = function (mat, angle, dest) {
if (!dest) { dest = mat; }
var a11 = mat[0],
a12 = mat[1],
a21 = mat[2],
a22 = mat[3],
s = Math.sin(angle),
c = Math.cos(angle);
dest[0] = a11 * c + a12 * s;
dest[1] = a11 * -s + a12 * c;
dest[2] = a21 * c + a22 * s;
dest[3] = a21 * -s + a22 * c;
return dest;
};
/**
* Multiplies the vec2 by the given 2x2 matrix
*
* @param {mat2} matrix the 2x2 matrix to multiply against
* @param {vec2} vec the vector to multiply
* @param {vec2} [dest] an optional receiving vector. If not given, vec is used.
*
* @returns {vec2} The multiplication result
**/
mat2.multiplyVec2 = function(matrix, vec, dest) {
if (!dest) dest = vec;
var x = vec[0], y = vec[1];
dest[0] = x * matrix[0] + y * matrix[1];
dest[1] = x * matrix[2] + y * matrix[3];
return dest;
};
/**
* Scales the mat2 by the dimensions in the given vec2
*
* @param {mat2} matrix the 2x2 matrix to scale
* @param {vec2} vec the vector containing the dimensions to scale by
* @param {vec2} [dest] an optional receiving mat2. If not given, matrix is used.
*
* @returns {mat2} dest if specified, matrix otherwise
**/
mat2.scale = function(matrix, vec, dest) {
if (!dest) { dest = matrix; }
var a11 = matrix[0],
a12 = matrix[1],
a21 = matrix[2],
a22 = matrix[3],
b11 = vec[0],
b22 = vec[1];
dest[0] = a11 * b11;
dest[1] = a12 * b22;
dest[2] = a21 * b11;
dest[3] = a22 * b22;
return dest;
};
/**
* Returns a string representation of a mat2
*
* @param {mat2} mat mat2 to represent as a string
*
* @param {String} String representation of mat
*/
mat2.str = function (mat) {
return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] + ']';
};
/**
* @class 4 Dimensional Vector
* @name vec4
*/
var vec4 = {};
/**
* Creates a new vec4, initializing it from vec if vec
* is given.
*
* @param {vec4} [vec] the vector's initial contents
* @returns {vec4} a new 2D vector
*/
vec4.create = function(vec) {
var dest = new MatrixArray(4);
if (vec) {
dest[0] = vec[0];
dest[1] = vec[1];
dest[2] = vec[2];
dest[3] = vec[3];
} else {
dest[0] = 0;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
}
return dest;
};
/**
* Creates a new instance of a vec4, initializing it with the given arguments
*
* @param {number} x X value
* @param {number} y Y value
* @param {number} z Z value
* @param {number} w W value
* @returns {vec4} New vec4
*/
vec4.createFrom = function (x, y, z, w) {
var dest = new MatrixArray(4);
dest[0] = x;
dest[1] = y;
dest[2] = z;
dest[3] = w;
return dest;
};
/**
* Adds the vec4's together. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec4} vecA the first operand
* @param {vec4} vecB the second operand
* @param {vec4} [dest] the optional receiving vector
* @returns {vec4} dest
*/
vec4.add = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] + vecB[0];
dest[1] = vecA[1] + vecB[1];
dest[2] = vecA[2] + vecB[2];
dest[3] = vecA[3] + vecB[3];
return dest;
};
/**
* Subtracts vecB from vecA. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec4} vecA the first operand
* @param {vec4} vecB the second operand
* @param {vec4} [dest] the optional receiving vector
* @returns {vec4} dest
*/
vec4.subtract = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] - vecB[0];
dest[1] = vecA[1] - vecB[1];
dest[2] = vecA[2] - vecB[2];
dest[3] = vecA[3] - vecB[3];
return dest;
};
/**
* Multiplies vecA with vecB. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec4} vecA the first operand
* @param {vec4} vecB the second operand
* @param {vec4} [dest] the optional receiving vector
* @returns {vec4} dest
*/
vec4.multiply = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] * vecB[0];
dest[1] = vecA[1] * vecB[1];
dest[2] = vecA[2] * vecB[2];
dest[3] = vecA[3] * vecB[3];
return dest;
};
/**
* Divides vecA by vecB. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecB.
*
* @param {vec4} vecA the first operand
* @param {vec4} vecB the second operand
* @param {vec4} [dest] the optional receiving vector
* @returns {vec4} dest
*/
vec4.divide = function(vecA, vecB, dest) {
if (!dest) dest = vecB;
dest[0] = vecA[0] / vecB[0];
dest[1] = vecA[1] / vecB[1];
dest[2] = vecA[2] / vecB[2];
dest[3] = vecA[3] / vecB[3];
return dest;
};
/**
* Scales vecA by some scalar number. If dest is given, the result
* is stored there. Otherwise, the result is stored in vecA.
*
* This is the same as multiplying each component of vecA
* by the given scalar.
*
* @param {vec4} vecA the vector to be scaled
* @param {Number} scalar the amount to scale the vector by
* @param {vec4} [dest] the optional receiving vector
* @returns {vec4} dest
*/
vec4.scale = function(vecA, scalar, dest) {
if (!dest) dest = vecA;
dest[0] = vecA[0] * scalar;
dest[1] = vecA[1] * scalar;
dest[2] = vecA[2] * scalar;
dest[3] = vecA[3] * scalar;
return dest;
};
/**
* Copies the values of one vec4 to another
*
* @param {vec4} vec vec4 containing values to copy
* @param {vec4} dest vec4 receiving copied values
*
* @returns {vec4} dest
*/
vec4.set = function (vec, dest) {
dest[0] = vec[0];
dest[1] = vec[1];
dest[2] = vec[2];
dest[3] = vec[3];
return dest;
};
/**
* Compares two vectors for equality within a certain margin of error
*
* @param {vec4} a First vector
* @param {vec4} b Second vector
*
* @returns {Boolean} True if a is equivalent to b
*/
vec4.equal = function (a, b) {
return a === b || (
Math.abs(a[0] - b[0]) < FLOAT_EPSILON &&
Math.abs(a[1] - b[1]) < FLOAT_EPSILON &&
Math.abs(a[2] - b[2]) < FLOAT_EPSILON &&
Math.abs(a[3] - b[3]) < FLOAT_EPSILON
);
};
/**
* Negates the components of a vec4
*
* @param {vec4} vec vec4 to negate
* @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec
*
* @returns {vec4} dest if specified, vec otherwise
*/
vec4.negate = function (vec, dest) {
if (!dest) { dest = vec; }
dest[0] = -vec[0];
dest[1] = -vec[1];
dest[2] = -vec[2];
dest[3] = -vec[3];
return dest;
};
/**
* Caclulates the length of a vec2
*
* @param {vec2} vec vec2 to calculate length of
*
* @returns {Number} Length of vec
*/
vec4.length = function (vec) {
var x = vec[0], y = vec[1], z = vec[2], w = vec[3];
return Math.sqrt(x * x + y * y + z * z + w * w);
};
/**
* Caclulates the squared length of a vec4
*
* @param {vec4} vec vec4 to calculate squared length of
*
* @returns {Number} Squared Length of vec
*/
vec4.squaredLength = function (vec) {
var x = vec[0], y = vec[1], z = vec[2], w = vec[3];
return x * x + y * y + z * z + w * w;
};
/**
* Performs a linear interpolation between two vec4
*
* @param {vec4} vecA First vector
* @param {vec4} vecB Second vector
* @param {Number} lerp Interpolation amount between the two inputs
* @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vecA
*
* @returns {vec4} dest if specified, vecA otherwise
*/
vec4.lerp = function (vecA, vecB, lerp, dest) {
if (!dest) { dest = vecA; }
dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]);
dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]);
dest[2] = vecA[2] + lerp * (vecB[2] - vecA[2]);
dest[3] = vecA[3] + lerp * (vecB[3] - vecA[3]);
return dest;
};
/**
* Returns a string representation of a vector
*
* @param {vec4} vec Vector to represent as a string
*
* @returns {String} String representation of vec
*/
vec4.str = function (vec) {
return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ', ' + vec[3] + ']';
};
/*
* Exports
*/
if(root) {
root.glMatrixArrayType = MatrixArray;
root.MatrixArray = MatrixArray;
root.setMatrixArrayType = setMatrixArrayType;
root.determineMatrixArrayType = determineMatrixArrayType;
root.glMath = glMath;
root.vec2 = vec2;
root.vec3 = vec3;
root.vec4 = vec4;
root.mat2 = mat2;
root.mat3 = mat3;
root.mat4 = mat4;
root.quat4 = quat4;
}
return {
glMatrixArrayType: MatrixArray,
MatrixArray: MatrixArray,
setMatrixArrayType: setMatrixArrayType,
determineMatrixArrayType: determineMatrixArrayType,
glMath: glMath,
vec2: vec2,
vec3: vec3,
vec4: vec4,
mat2: mat2,
mat3: mat3,
mat4: mat4,
quat4: quat4
};
}));