mirror of
https://github.com/photonstorm/phaser
synced 2024-12-24 12:03:36 +00:00
766 lines
18 KiB
JavaScript
766 lines
18 KiB
JavaScript
/**
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* @author Richard Davey <rich@photonstorm.com>
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* @copyright 2018 Photon Storm Ltd.
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* @license {@link https://github.com/photonstorm/phaser/blob/master/license.txt|MIT License}
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*/
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// Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji
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// and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl
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var Class = require('../utils/Class');
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var Vector3 = require('./Vector3');
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var Matrix3 = require('./Matrix3');
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var EPSILON = 0.000001;
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// Some shared 'private' arrays
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var siNext = new Int8Array([ 1, 2, 0 ]);
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var tmp = new Float32Array([ 0, 0, 0 ]);
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var xUnitVec3 = new Vector3(1, 0, 0);
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var yUnitVec3 = new Vector3(0, 1, 0);
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var tmpvec = new Vector3();
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var tmpMat3 = new Matrix3();
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/**
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* @classdesc
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* A quaternion.
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*
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* @class Quaternion
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* @memberof Phaser.Math
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* @constructor
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* @since 3.0.0
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*
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* @param {number} [x] - The x component.
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* @param {number} [y] - The y component.
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* @param {number} [z] - The z component.
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* @param {number} [w] - The w component.
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*/
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var Quaternion = new Class({
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initialize:
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function Quaternion (x, y, z, w)
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{
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/**
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* The x component of this Quaternion.
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*
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* @name Phaser.Math.Quaternion#x
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* @type {number}
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* @default 0
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* @since 3.0.0
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*/
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/**
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* The y component of this Quaternion.
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*
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* @name Phaser.Math.Quaternion#y
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* @type {number}
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* @default 0
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* @since 3.0.0
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*/
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/**
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* The z component of this Quaternion.
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*
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* @name Phaser.Math.Quaternion#z
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* @type {number}
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* @default 0
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* @since 3.0.0
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*/
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/**
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* The w component of this Quaternion.
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*
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* @name Phaser.Math.Quaternion#w
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* @type {number}
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* @default 0
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* @since 3.0.0
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*/
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if (typeof x === 'object')
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{
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this.x = x.x || 0;
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this.y = x.y || 0;
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this.z = x.z || 0;
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this.w = x.w || 0;
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}
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else
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{
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this.x = x || 0;
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this.y = y || 0;
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this.z = z || 0;
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this.w = w || 0;
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}
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},
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/**
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* Copy the components of a given Quaternion or Vector into this Quaternion.
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*
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* @method Phaser.Math.Quaternion#copy
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} src - The Quaternion or Vector to copy the components from.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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copy: function (src)
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{
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this.x = src.x;
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this.y = src.y;
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this.z = src.z;
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this.w = src.w;
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return this;
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},
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/**
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* Set the components of this Quaternion.
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*
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* @method Phaser.Math.Quaternion#set
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* @since 3.0.0
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*
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* @param {(number|object)} [x=0] - The x component, or an object containing x, y, z, and w components.
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* @param {number} [y=0] - The y component.
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* @param {number} [z=0] - The z component.
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* @param {number} [w=0] - The w component.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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set: function (x, y, z, w)
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{
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if (typeof x === 'object')
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{
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this.x = x.x || 0;
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this.y = x.y || 0;
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this.z = x.z || 0;
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this.w = x.w || 0;
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}
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else
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{
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this.x = x || 0;
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this.y = y || 0;
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this.z = z || 0;
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this.w = w || 0;
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}
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return this;
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},
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/**
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* Add a given Quaternion or Vector to this Quaternion. Addition is component-wise.
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*
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* @method Phaser.Math.Quaternion#add
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} v - The Quaternion or Vector to add to this Quaternion.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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add: function (v)
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{
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this.x += v.x;
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this.y += v.y;
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this.z += v.z;
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this.w += v.w;
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return this;
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},
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/**
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* Subtract a given Quaternion or Vector from this Quaternion. Subtraction is component-wise.
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*
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* @method Phaser.Math.Quaternion#subtract
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} v - The Quaternion or Vector to subtract from this Quaternion.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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subtract: function (v)
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{
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this.x -= v.x;
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this.y -= v.y;
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this.z -= v.z;
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this.w -= v.w;
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return this;
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},
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/**
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* Scale this Quaternion by the given value.
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*
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* @method Phaser.Math.Quaternion#scale
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* @since 3.0.0
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*
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* @param {number} scale - The value to scale this Quaternion by.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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scale: function (scale)
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{
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this.x *= scale;
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this.y *= scale;
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this.z *= scale;
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this.w *= scale;
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return this;
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},
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/**
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* Calculate the length of this Quaternion.
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*
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* @method Phaser.Math.Quaternion#length
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* @since 3.0.0
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*
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* @return {number} The length of this Quaternion.
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*/
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length: function ()
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{
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var x = this.x;
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var y = this.y;
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var z = this.z;
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var w = this.w;
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return Math.sqrt(x * x + y * y + z * z + w * w);
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},
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/**
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* Calculate the length of this Quaternion squared.
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*
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* @method Phaser.Math.Quaternion#lengthSq
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* @since 3.0.0
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*
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* @return {number} The length of this Quaternion, squared.
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*/
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lengthSq: function ()
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{
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var x = this.x;
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var y = this.y;
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var z = this.z;
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var w = this.w;
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return x * x + y * y + z * z + w * w;
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},
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/**
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* Normalize this Quaternion.
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*
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* @method Phaser.Math.Quaternion#normalize
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* @since 3.0.0
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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normalize: function ()
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{
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var x = this.x;
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var y = this.y;
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var z = this.z;
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var w = this.w;
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var len = x * x + y * y + z * z + w * w;
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if (len > 0)
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{
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len = 1 / Math.sqrt(len);
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this.x = x * len;
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this.y = y * len;
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this.z = z * len;
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this.w = w * len;
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}
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return this;
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},
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/**
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* Calculate the dot product of this Quaternion and the given Quaternion or Vector.
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*
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* @method Phaser.Math.Quaternion#dot
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} v - The Quaternion or Vector to dot product with this Quaternion.
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*
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* @return {number} The dot product of this Quaternion and the given Quaternion or Vector.
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*/
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dot: function (v)
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{
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return this.x * v.x + this.y * v.y + this.z * v.z + this.w * v.w;
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},
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/**
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* Linearly interpolate this Quaternion towards the given Quaternion or Vector.
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*
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* @method Phaser.Math.Quaternion#lerp
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} v - The Quaternion or Vector to interpolate towards.
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* @param {number} [t=0] - The percentage of interpolation.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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lerp: function (v, t)
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{
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if (t === undefined) { t = 0; }
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var ax = this.x;
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var ay = this.y;
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var az = this.z;
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var aw = this.w;
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this.x = ax + t * (v.x - ax);
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this.y = ay + t * (v.y - ay);
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this.z = az + t * (v.z - az);
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this.w = aw + t * (v.w - aw);
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return this;
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},
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/**
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* [description]
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*
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* @method Phaser.Math.Quaternion#rotationTo
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* @since 3.0.0
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*
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* @param {Phaser.Math.Vector3} a - [description]
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* @param {Phaser.Math.Vector3} b - [description]
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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rotationTo: function (a, b)
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{
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var dot = a.x * b.x + a.y * b.y + a.z * b.z;
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if (dot < -0.999999)
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{
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if (tmpvec.copy(xUnitVec3).cross(a).length() < EPSILON)
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{
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tmpvec.copy(yUnitVec3).cross(a);
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}
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tmpvec.normalize();
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return this.setAxisAngle(tmpvec, Math.PI);
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}
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else if (dot > 0.999999)
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{
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this.x = 0;
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this.y = 0;
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this.z = 0;
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this.w = 1;
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return this;
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}
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else
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{
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tmpvec.copy(a).cross(b);
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this.x = tmpvec.x;
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this.y = tmpvec.y;
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this.z = tmpvec.z;
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this.w = 1 + dot;
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return this.normalize();
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}
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},
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/**
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* Set the axes of this Quaternion.
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*
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* @method Phaser.Math.Quaternion#setAxes
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* @since 3.0.0
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*
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* @param {Phaser.Math.Vector3} view - The view axis.
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* @param {Phaser.Math.Vector3} right - The right axis.
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* @param {Phaser.Math.Vector3} up - The upwards axis.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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setAxes: function (view, right, up)
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{
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var m = tmpMat3.val;
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m[0] = right.x;
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m[3] = right.y;
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m[6] = right.z;
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m[1] = up.x;
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m[4] = up.y;
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m[7] = up.z;
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m[2] = -view.x;
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m[5] = -view.y;
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m[8] = -view.z;
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return this.fromMat3(tmpMat3).normalize();
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},
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/**
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* Reset this Matrix to an identity (default) Quaternion.
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*
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* @method Phaser.Math.Quaternion#identity
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* @since 3.0.0
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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identity: function ()
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{
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this.x = 0;
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this.y = 0;
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this.z = 0;
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this.w = 1;
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return this;
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},
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/**
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* Set the axis angle of this Quaternion.
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*
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* @method Phaser.Math.Quaternion#setAxisAngle
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* @since 3.0.0
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*
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* @param {Phaser.Math.Vector3} axis - The axis.
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* @param {number} rad - The angle in radians.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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setAxisAngle: function (axis, rad)
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{
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rad = rad * 0.5;
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var s = Math.sin(rad);
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this.x = s * axis.x;
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this.y = s * axis.y;
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this.z = s * axis.z;
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this.w = Math.cos(rad);
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return this;
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},
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/**
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* Multiply this Quaternion by the given Quaternion or Vector.
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*
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* @method Phaser.Math.Quaternion#multiply
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} b - The Quaternion or Vector to multiply this Quaternion by.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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multiply: function (b)
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{
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var ax = this.x;
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var ay = this.y;
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var az = this.z;
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var aw = this.w;
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var bx = b.x;
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var by = b.y;
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var bz = b.z;
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var bw = b.w;
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this.x = ax * bw + aw * bx + ay * bz - az * by;
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this.y = ay * bw + aw * by + az * bx - ax * bz;
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this.z = az * bw + aw * bz + ax * by - ay * bx;
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this.w = aw * bw - ax * bx - ay * by - az * bz;
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return this;
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},
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/**
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* Smoothly linearly interpolate this Quaternion towards the given Quaternion or Vector.
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*
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* @method Phaser.Math.Quaternion#slerp
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* @since 3.0.0
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*
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* @param {(Phaser.Math.Quaternion|Phaser.Math.Vector4)} b - The Quaternion or Vector to interpolate towards.
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* @param {number} t - The percentage of interpolation.
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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slerp: function (b, t)
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{
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// benchmarks: http://jsperf.com/quaternion-slerp-implementations
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var ax = this.x;
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var ay = this.y;
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var az = this.z;
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var aw = this.w;
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var bx = b.x;
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var by = b.y;
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var bz = b.z;
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var bw = b.w;
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// calc cosine
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var cosom = ax * bx + ay * by + az * bz + aw * bw;
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// adjust signs (if necessary)
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if (cosom < 0)
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{
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cosom = -cosom;
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bx = - bx;
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by = - by;
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bz = - bz;
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bw = - bw;
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}
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// "from" and "to" quaternions are very close
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// ... so we can do a linear interpolation
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var scale0 = 1 - t;
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var scale1 = t;
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// calculate coefficients
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if ((1 - cosom) > EPSILON)
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{
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// standard case (slerp)
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var omega = Math.acos(cosom);
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var sinom = Math.sin(omega);
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scale0 = Math.sin((1.0 - t) * omega) / sinom;
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scale1 = Math.sin(t * omega) / sinom;
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}
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// calculate final values
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this.x = scale0 * ax + scale1 * bx;
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this.y = scale0 * ay + scale1 * by;
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this.z = scale0 * az + scale1 * bz;
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this.w = scale0 * aw + scale1 * bw;
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return this;
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},
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/**
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* Invert this Quaternion.
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*
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* @method Phaser.Math.Quaternion#invert
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* @since 3.0.0
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*
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* @return {Phaser.Math.Quaternion} This Quaternion.
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*/
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invert: function ()
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{
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var a0 = this.x;
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var a1 = this.y;
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var a2 = this.z;
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var a3 = this.w;
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var dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
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var invDot = (dot) ? 1 / dot : 0;
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// TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
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this.x = -a0 * invDot;
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this.y = -a1 * invDot;
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this.z = -a2 * invDot;
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this.w = a3 * invDot;
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|
|
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return this;
|
|
},
|
|
|
|
/**
|
|
* Convert this Quaternion into its conjugate.
|
|
*
|
|
* Sets the x, y and z components.
|
|
*
|
|
* @method Phaser.Math.Quaternion#conjugate
|
|
* @since 3.0.0
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
conjugate: function ()
|
|
{
|
|
this.x = -this.x;
|
|
this.y = -this.y;
|
|
this.z = -this.z;
|
|
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Rotate this Quaternion on the X axis.
|
|
*
|
|
* @method Phaser.Math.Quaternion#rotateX
|
|
* @since 3.0.0
|
|
*
|
|
* @param {number} rad - The rotation angle in radians.
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
rotateX: function (rad)
|
|
{
|
|
rad *= 0.5;
|
|
|
|
var ax = this.x;
|
|
var ay = this.y;
|
|
var az = this.z;
|
|
var aw = this.w;
|
|
|
|
var bx = Math.sin(rad);
|
|
var bw = Math.cos(rad);
|
|
|
|
this.x = ax * bw + aw * bx;
|
|
this.y = ay * bw + az * bx;
|
|
this.z = az * bw - ay * bx;
|
|
this.w = aw * bw - ax * bx;
|
|
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Rotate this Quaternion on the Y axis.
|
|
*
|
|
* @method Phaser.Math.Quaternion#rotateY
|
|
* @since 3.0.0
|
|
*
|
|
* @param {number} rad - The rotation angle in radians.
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
rotateY: function (rad)
|
|
{
|
|
rad *= 0.5;
|
|
|
|
var ax = this.x;
|
|
var ay = this.y;
|
|
var az = this.z;
|
|
var aw = this.w;
|
|
|
|
var by = Math.sin(rad);
|
|
var bw = Math.cos(rad);
|
|
|
|
this.x = ax * bw - az * by;
|
|
this.y = ay * bw + aw * by;
|
|
this.z = az * bw + ax * by;
|
|
this.w = aw * bw - ay * by;
|
|
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Rotate this Quaternion on the Z axis.
|
|
*
|
|
* @method Phaser.Math.Quaternion#rotateZ
|
|
* @since 3.0.0
|
|
*
|
|
* @param {number} rad - The rotation angle in radians.
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
rotateZ: function (rad)
|
|
{
|
|
rad *= 0.5;
|
|
|
|
var ax = this.x;
|
|
var ay = this.y;
|
|
var az = this.z;
|
|
var aw = this.w;
|
|
|
|
var bz = Math.sin(rad);
|
|
var bw = Math.cos(rad);
|
|
|
|
this.x = ax * bw + ay * bz;
|
|
this.y = ay * bw - ax * bz;
|
|
this.z = az * bw + aw * bz;
|
|
this.w = aw * bw - az * bz;
|
|
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Create a unit (or rotation) Quaternion from its x, y, and z components.
|
|
*
|
|
* Sets the w component.
|
|
*
|
|
* @method Phaser.Math.Quaternion#calculateW
|
|
* @since 3.0.0
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
calculateW: function ()
|
|
{
|
|
var x = this.x;
|
|
var y = this.y;
|
|
var z = this.z;
|
|
|
|
this.w = -Math.sqrt(1.0 - x * x - y * y - z * z);
|
|
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Convert the given Matrix into this Quaternion.
|
|
*
|
|
* @method Phaser.Math.Quaternion#fromMat3
|
|
* @since 3.0.0
|
|
*
|
|
* @param {Phaser.Math.Matrix3} mat - The Matrix to convert from.
|
|
*
|
|
* @return {Phaser.Math.Quaternion} This Quaternion.
|
|
*/
|
|
fromMat3: function (mat)
|
|
{
|
|
// benchmarks:
|
|
// http://jsperf.com/typed-array-access-speed
|
|
// http://jsperf.com/conversion-of-3x3-matrix-to-quaternion
|
|
|
|
// Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
|
|
// article "Quaternion Calculus and Fast Animation".
|
|
var m = mat.val;
|
|
var fTrace = m[0] + m[4] + m[8];
|
|
var fRoot;
|
|
|
|
if (fTrace > 0)
|
|
{
|
|
// |w| > 1/2, may as well choose w > 1/2
|
|
fRoot = Math.sqrt(fTrace + 1.0); // 2w
|
|
|
|
this.w = 0.5 * fRoot;
|
|
|
|
fRoot = 0.5 / fRoot; // 1/(4w)
|
|
|
|
this.x = (m[7] - m[5]) * fRoot;
|
|
this.y = (m[2] - m[6]) * fRoot;
|
|
this.z = (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 = siNext[i];
|
|
var k = siNext[j];
|
|
|
|
// This isn't quite as clean without array access
|
|
fRoot = Math.sqrt(m[i * 3 + i] - m[j * 3 + j] - m[k * 3 + k] + 1);
|
|
tmp[i] = 0.5 * fRoot;
|
|
|
|
fRoot = 0.5 / fRoot;
|
|
|
|
tmp[j] = (m[j * 3 + i] + m[i * 3 + j]) * fRoot;
|
|
tmp[k] = (m[k * 3 + i] + m[i * 3 + k]) * fRoot;
|
|
|
|
this.x = tmp[0];
|
|
this.y = tmp[1];
|
|
this.z = tmp[2];
|
|
this.w = (m[k * 3 + j] - m[j * 3 + k]) * fRoot;
|
|
}
|
|
|
|
return this;
|
|
}
|
|
|
|
});
|
|
|
|
module.exports = Quaternion;
|