mirror of
https://github.com/photonstorm/phaser
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1309 lines
36 KiB
JavaScript
1309 lines
36 KiB
JavaScript
/**
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* @author Richard Davey <rich@photonstorm.com>
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* @copyright 2016 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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/**
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* A collection of useful mathematical functions.
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*
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* These are normally accessed through `game.math`.
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*
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* @class Phaser.Math
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* @static
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* @see {@link Phaser.Utils}
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* @see {@link Phaser.ArrayUtils}
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*/
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Phaser.Math = {
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/**
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* Twice PI.
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* @property {number} Phaser.Math#PI2
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* @default ~6.283
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*/
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PI2: Math.PI * 2,
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/**
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* Degrees to Radians factor.
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* @property {number} Phaser.Math#DEG_TO_RAD
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*/
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DEG_TO_RAD: Math.PI / 180,
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/**
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* Degrees to Radians factor.
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* @property {number} Phaser.Math#RAD_TO_DEG
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*/
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RAD_TO_DEG: 180 / Math.PI,
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/**
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* Convert degrees to radians.
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*
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* @method Phaser.Math#degToRad
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* @param {number} degrees - Angle in degrees.
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* @return {number} Angle in radians.
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*/
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degToRad: function (degrees) {
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return degrees * Phaser.Math.DEG_TO_RAD;
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},
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/**
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* Convert radians to degrees.
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*
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* @method Phaser.Math#radToDeg
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* @param {number} radians - Angle in radians.
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* @return {number} Angle in degrees
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*/
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radToDeg: function (radians) {
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return radians * Phaser.Math.RAD_TO_DEG;
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},
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/**
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* Given a number, this function returns the closest number that is a power of two.
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* This function is from the Starling Framework.
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*
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* @method Phaser.Math#getNextPowerOfTwo
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* @param {number} value - The value to get the closest power of two from.
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* @return {number} The closest number that is a power of two.
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*/
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getNextPowerOfTwo: function (value) {
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if (value > 0 && (value & (value - 1)) === 0)
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{
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// http://goo.gl/D9kPj
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return value;
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}
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else
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{
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var result = 1;
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while (result < value)
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{
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result <<= 1;
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}
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return result;
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}
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},
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/**
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* Checks if the given dimensions make a power of two texture.
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*
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* @method Phaser.Math#isPowerOfTwo
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* @param {number} width - The width to check.
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* @param {number} height - The height to check.
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* @return {boolean} True if the width and height are a power of two.
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*/
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isPowerOfTwo: function (width, height) {
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return (width > 0 && (width & (width - 1)) === 0 && height > 0 && (height & (height - 1)) === 0);
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},
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/**
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* Returns a random float in the range `[min, max)`. If these parameters are not in order than they will be put in order.
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* Default is 0 for `min` and 1 for `max`.
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*
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* @method Phaser.Math#random
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* @param {number} [min=0] - The minimum value. Must be a Number.
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* @param {number} [max=1] - The maximum value. Must be a Number greater than `min`.
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* @return {number} A floating point number between min (inclusive) and max (exclusive).
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*/
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random: function (min, max)
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{
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if (min === undefined) { min = 0; }
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if (max === undefined) { max = 1; }
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if (min === max)
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{
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return min;
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}
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if (min < max)
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{
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var temp = min;
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min = max;
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max = temp;
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}
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return (Math.random() * (max - min) + min);
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},
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/**
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* Returns a random integer in the range `[min, max]`. If these parameters are not in order than they will be put in order.
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* Default is 0 for `min` and 1 for `max`.
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*
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* @method Phaser.Math#between
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* @param {number} [min=0] - The minimum value. Must be a Number.
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* @param {number} [max=1] - The maximum value. Must be a Number greater than `min`.
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* @return {number} An integer between min (inclusive) and max (inclusive).
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*/
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between: function (min, max)
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{
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if (min === undefined) { min = 0; }
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if (max === undefined) { max = 1; }
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if (min === max)
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{
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return min;
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}
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if (min < max)
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{
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var temp = min;
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min = max;
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max = temp;
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}
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min = Math.ceil(min);
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max = Math.floor(max);
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return Math.floor(Math.random() * (max - min + 1)) + min;
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},
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/**
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* Two number are fuzzyEqual if their difference is less than epsilon.
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*
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* @method Phaser.Math#fuzzyEqual
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* @param {number} a - The first number to compare.
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* @param {number} b - The second number to compare.
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* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
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* @return {boolean} True if |a-b|<epsilon
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*/
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fuzzyEqual: function (a, b, epsilon) {
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if (epsilon === undefined) { epsilon = 0.0001; }
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return Math.abs(a - b) < epsilon;
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},
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/**
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* `a` is fuzzyLessThan `b` if it is less than b + epsilon.
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*
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* @method Phaser.Math#fuzzyLessThan
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* @param {number} a - The first number to compare.
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* @param {number} b - The second number to compare.
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* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
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* @return {boolean} True if a<b+epsilon
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*/
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fuzzyLessThan: function (a, b, epsilon) {
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if (epsilon === undefined) { epsilon = 0.0001; }
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return a < b + epsilon;
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},
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/**
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* `a` is fuzzyGreaterThan `b` if it is more than b - epsilon.
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*
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* @method Phaser.Math#fuzzyGreaterThan
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* @param {number} a - The first number to compare.
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* @param {number} b - The second number to compare.
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* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
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* @return {boolean} True if a>b+epsilon
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*/
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fuzzyGreaterThan: function (a, b, epsilon) {
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if (epsilon === undefined) { epsilon = 0.0001; }
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return a > b - epsilon;
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},
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/**
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* Applies a fuzzy ceil to the given value.
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*
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* @method Phaser.Math#fuzzyCeil
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* @param {number} val - The value to ceil.
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* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
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* @return {number} ceiling(val-epsilon)
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*/
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fuzzyCeil: function (val, epsilon) {
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if (epsilon === undefined) { epsilon = 0.0001; }
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return Math.ceil(val - epsilon);
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},
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/**
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* Applies a fuzzy floor to the given value.
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*
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* @method Phaser.Math#fuzzyFloor
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* @param {number} val - The value to floor.
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* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
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* @return {number} floor(val+epsilon)
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*/
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fuzzyFloor: function (val, epsilon) {
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if (epsilon === undefined) { epsilon = 0.0001; }
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return Math.floor(val + epsilon);
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},
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/**
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* Averages all values passed to the function and returns the result.
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*
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* @method Phaser.Math#average
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* @params {...number} The numbers to average
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* @return {number} The average of all given values.
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*/
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average: function () {
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var sum = 0;
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var len = arguments.length;
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for (var i = 0; i < len; i++)
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{
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sum += (+arguments[i]);
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}
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return sum / len;
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},
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/**
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* @method Phaser.Math#shear
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* @param {number} n
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* @return {number} n mod 1
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*/
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shear: function (n) {
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return n % 1;
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},
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/**
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* Snap a value to nearest grid slice, using rounding.
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*
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* Example: if you have an interval gap of 5 and a position of 12... you will snap to 10 whereas 14 will snap to 15.
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*
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* @method Phaser.Math#snapTo
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* @param {number} input - The value to snap.
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* @param {number} gap - The interval gap of the grid.
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* @param {number} [start=0] - Optional starting offset for gap.
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* @return {number} The snapped value.
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*/
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snapTo: function (input, gap, start) {
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if (start === undefined) { start = 0; }
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if (gap === 0) {
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return input;
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}
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input -= start;
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input = gap * Math.round(input / gap);
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return start + input;
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},
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/**
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* Snap a value to nearest grid slice, using floor.
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*
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* Example: if you have an interval gap of 5 and a position of 12... you will snap to 10.
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* As will 14 snap to 10... but 16 will snap to 15.
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*
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* @method Phaser.Math#snapToFloor
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* @param {number} input - The value to snap.
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* @param {number} gap - The interval gap of the grid.
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* @param {number} [start=0] - Optional starting offset for gap.
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* @return {number} The snapped value.
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*/
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snapToFloor: function (input, gap, start) {
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if (start === undefined) { start = 0; }
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if (gap === 0) {
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return input;
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}
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input -= start;
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input = gap * Math.floor(input / gap);
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return start + input;
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},
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/**
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* Snap a value to nearest grid slice, using ceil.
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*
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* Example: if you have an interval gap of 5 and a position of 12... you will snap to 15.
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* As will 14 will snap to 15... but 16 will snap to 20.
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*
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* @method Phaser.Math#snapToCeil
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* @param {number} input - The value to snap.
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* @param {number} gap - The interval gap of the grid.
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* @param {number} [start=0] - Optional starting offset for gap.
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* @return {number} The snapped value.
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*/
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snapToCeil: function (input, gap, start) {
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if (start === undefined) { start = 0; }
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if (gap === 0) {
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return input;
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}
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input -= start;
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input = gap * Math.ceil(input / gap);
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return start + input;
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},
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/**
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* Round to some place comparative to a `base`, default is 10 for decimal place.
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* The `place` is represented by the power applied to `base` to get that place.
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*
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* e.g. 2000/7 ~= 285.714285714285714285714 ~= (bin)100011101.1011011011011011
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*
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* roundTo(2000/7,3) === 0
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* roundTo(2000/7,2) == 300
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* roundTo(2000/7,1) == 290
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* roundTo(2000/7,0) == 286
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* roundTo(2000/7,-1) == 285.7
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* roundTo(2000/7,-2) == 285.71
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* roundTo(2000/7,-3) == 285.714
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* roundTo(2000/7,-4) == 285.7143
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* roundTo(2000/7,-5) == 285.71429
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*
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* roundTo(2000/7,3,2) == 288 -- 100100000
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* roundTo(2000/7,2,2) == 284 -- 100011100
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* roundTo(2000/7,1,2) == 286 -- 100011110
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* roundTo(2000/7,0,2) == 286 -- 100011110
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* roundTo(2000/7,-1,2) == 285.5 -- 100011101.1
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* roundTo(2000/7,-2,2) == 285.75 -- 100011101.11
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* roundTo(2000/7,-3,2) == 285.75 -- 100011101.11
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* roundTo(2000/7,-4,2) == 285.6875 -- 100011101.1011
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* roundTo(2000/7,-5,2) == 285.71875 -- 100011101.10111
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*
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* Note what occurs when we round to the 3rd space (8ths place), 100100000, this is to be assumed
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* because we are rounding 100011.1011011011011011 which rounds up.
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*
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* @method Phaser.Math#roundTo
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* @param {number} value - The value to round.
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* @param {number} [place=0] - The place to round to.
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* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
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* @return {number} The rounded value.
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*/
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roundTo: function (value, place, base) {
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if (place === undefined) { place = 0; }
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if (base === undefined) { base = 10; }
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var p = Math.pow(base, -place);
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return Math.round(value * p) / p;
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},
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/**
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* Floors to some place comparative to a `base`, default is 10 for decimal place.
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* The `place` is represented by the power applied to `base` to get that place.
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*
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* @method Phaser.Math#floorTo
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* @param {number} value - The value to round.
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* @param {number} [place=0] - The place to round to.
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* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
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* @return {number} The rounded value.
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*/
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floorTo: function (value, place, base) {
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if (place === undefined) { place = 0; }
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if (base === undefined) { base = 10; }
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var p = Math.pow(base, -place);
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return Math.floor(value * p) / p;
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},
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/**
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* Ceils to some place comparative to a `base`, default is 10 for decimal place.
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* The `place` is represented by the power applied to `base` to get that place.
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*
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* @method Phaser.Math#ceilTo
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* @param {number} value - The value to round.
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* @param {number} [place=0] - The place to round to.
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* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
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* @return {number} The rounded value.
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*/
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ceilTo: function (value, place, base) {
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if (place === undefined) { place = 0; }
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if (base === undefined) { base = 10; }
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var p = Math.pow(base, -place);
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return Math.ceil(value * p) / p;
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},
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/**
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* Rotates currentAngle towards targetAngle, taking the shortest rotation distance.
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* The lerp argument is the amount to rotate by in this call.
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*
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* @method Phaser.Math#rotateToAngle
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* @param {number} currentAngle - The current angle, in radians.
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* @param {number} targetAngle - The target angle to rotate to, in radians.
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* @param {number} [lerp=0.05] - The lerp value to add to the current angle.
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* @return {number} The adjusted angle.
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*/
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rotateToAngle: function (currentAngle, targetAngle, lerp) {
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if (lerp === undefined) { lerp = 0.05; }
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if (currentAngle === targetAngle)
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{
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return currentAngle;
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}
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if (Math.abs(targetAngle - currentAngle) <= lerp || Math.abs(targetAngle - currentAngle) >= (Phaser.Math.PI2 - lerp))
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{
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currentAngle = targetAngle;
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}
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else
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{
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if (Math.abs(targetAngle - currentAngle) > Math.PI)
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{
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if (targetAngle < currentAngle)
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{
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targetAngle += Phaser.Math.PI2;
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}
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else
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{
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targetAngle -= Phaser.Math.PI2;
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}
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}
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if (targetAngle > currentAngle)
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{
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currentAngle += lerp;
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}
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else if (targetAngle < currentAngle)
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{
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currentAngle -= lerp;
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}
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}
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return currentAngle;
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},
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/**
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* Gets the shortest angle between `angle1` and `angle2`.
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* Both angles must be in the range -180 to 180, which is the same clamped
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* range that `sprite.angle` uses, so you can pass in two sprite angles to
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* this method, and get the shortest angle back between the two of them.
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*
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* The angle returned will be in the same range. If the returned angle is
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* greater than 0 then it's a counter-clockwise rotation, if < 0 then it's
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* a clockwise rotation.
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*
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* @method Phaser.Math#getShortestAngle
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* @param {number} angle1 - The first angle. In the range -180 to 180.
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* @param {number} angle2 - The second angle. In the range -180 to 180.
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* @return {number} The shortest angle, in degrees. If greater than zero it's a counter-clockwise rotation.
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*/
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getShortestAngle: function (angle1, angle2) {
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var difference = angle2 - angle1;
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if (difference === 0)
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{
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return 0;
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}
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var times = Math.floor((difference - (-180)) / 360);
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return difference - (times * 360);
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},
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/**
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* Find the angle of a segment from (x1, y1) -> (x2, y2).
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*
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* @method Phaser.Math#angleBetween
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* @param {number} x1 - The x coordinate of the first value.
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* @param {number} y1 - The y coordinate of the first value.
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* @param {number} x2 - The x coordinate of the second value.
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* @param {number} y2 - The y coordinate of the second value.
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* @return {number} The angle, in radians.
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*/
|
|
angleBetween: function (x1, y1, x2, y2) {
|
|
|
|
return Math.atan2(y2 - y1, x2 - x1);
|
|
|
|
},
|
|
|
|
/**
|
|
* Find the angle of a segment from (x1, y1) -> (x2, y2).
|
|
*
|
|
* The difference between this method and Math.angleBetween is that this assumes the y coordinate travels
|
|
* down the screen.
|
|
*
|
|
* @method Phaser.Math#angleBetweenY
|
|
* @param {number} x1 - The x coordinate of the first value.
|
|
* @param {number} y1 - The y coordinate of the first value.
|
|
* @param {number} x2 - The x coordinate of the second value.
|
|
* @param {number} y2 - The y coordinate of the second value.
|
|
* @return {number} The angle, in radians.
|
|
*/
|
|
angleBetweenY: function (x1, y1, x2, y2) {
|
|
|
|
return Math.atan2(x2 - x1, y2 - y1);
|
|
|
|
},
|
|
|
|
/**
|
|
* Find the angle of a segment from (point1.x, point1.y) -> (point2.x, point2.y).
|
|
*
|
|
* @method Phaser.Math#angleBetweenPoints
|
|
* @param {Phaser.Point} point1 - The first point.
|
|
* @param {Phaser.Point} point2 - The second point.
|
|
* @return {number} The angle between the two points, in radians.
|
|
*/
|
|
angleBetweenPoints: function (point1, point2) {
|
|
|
|
return Math.atan2(point2.y - point1.y, point2.x - point1.x);
|
|
|
|
},
|
|
|
|
/**
|
|
* Find the angle of a segment from (point1.x, point1.y) -> (point2.x, point2.y).
|
|
* @method Phaser.Math#angleBetweenPointsY
|
|
* @param {Phaser.Point} point1
|
|
* @param {Phaser.Point} point2
|
|
* @return {number} The angle, in radians.
|
|
*/
|
|
angleBetweenPointsY: function (point1, point2) {
|
|
|
|
return Math.atan2(point2.x - point1.x, point2.y - point1.y);
|
|
|
|
},
|
|
|
|
/**
|
|
* Reverses an angle.
|
|
* @method Phaser.Math#reverseAngle
|
|
* @param {number} angleRad - The angle to reverse, in radians.
|
|
* @return {number} The reverse angle, in radians.
|
|
*/
|
|
reverseAngle: function (angleRad) {
|
|
|
|
return this.normalizeAngle(angleRad + Math.PI, true);
|
|
|
|
},
|
|
|
|
/**
|
|
* Normalizes an angle to the [0,2pi) range.
|
|
* @method Phaser.Math#normalizeAngle
|
|
* @param {number} angleRad - The angle to normalize, in radians.
|
|
* @return {number} The angle, fit within the [0,2pi] range, in radians.
|
|
*/
|
|
normalizeAngle: function (angleRad) {
|
|
|
|
angleRad = angleRad % (2 * Math.PI);
|
|
return angleRad >= 0 ? angleRad : angleRad + 2 * Math.PI;
|
|
|
|
},
|
|
|
|
/**
|
|
* Adds the given amount to the value, but never lets the value go over the specified maximum.
|
|
*
|
|
* @method Phaser.Math#maxAdd
|
|
* @param {number} value - The value to add the amount to.
|
|
* @param {number} amount - The amount to add to the value.
|
|
* @param {number} max - The maximum the value is allowed to be.
|
|
* @return {number} The new value.
|
|
*/
|
|
maxAdd: function (value, amount, max) {
|
|
|
|
return Math.min(value + amount, max);
|
|
|
|
},
|
|
|
|
/**
|
|
* Subtracts the given amount from the value, but never lets the value go below the specified minimum.
|
|
*
|
|
* @method Phaser.Math#minSub
|
|
* @param {number} value - The base value.
|
|
* @param {number} amount - The amount to subtract from the base value.
|
|
* @param {number} min - The minimum the value is allowed to be.
|
|
* @return {number} The new value.
|
|
*/
|
|
minSub: function (value, amount, min) {
|
|
|
|
return Math.max(value - amount, min);
|
|
|
|
},
|
|
|
|
/**
|
|
* Ensures that the value always stays between min and max, by wrapping the value around.
|
|
*
|
|
* If `max` is not larger than `min` the result is 0.
|
|
*
|
|
* @method Phaser.Math#wrap
|
|
* @param {number} value - The value to wrap.
|
|
* @param {number} min - The minimum the value is allowed to be.
|
|
* @param {number} max - The maximum the value is allowed to be, should be larger than `min`.
|
|
* @return {number} The wrapped value.
|
|
*/
|
|
wrap: function (value, min, max) {
|
|
|
|
var range = max - min;
|
|
|
|
if (range <= 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
var result = (value - min) % range;
|
|
|
|
if (result < 0)
|
|
{
|
|
result += range;
|
|
}
|
|
|
|
return result + min;
|
|
|
|
},
|
|
|
|
/**
|
|
* Adds value to amount and ensures that the result always stays between 0 and max, by wrapping the value around.
|
|
*
|
|
* Values _must_ be positive integers, and are passed through Math.abs. See {@link Phaser.Math#wrap} for an alternative.
|
|
*
|
|
* @method Phaser.Math#wrapValue
|
|
* @param {number} value - The value to add the amount to.
|
|
* @param {number} amount - The amount to add to the value.
|
|
* @param {number} max - The maximum the value is allowed to be.
|
|
* @return {number} The wrapped value.
|
|
*/
|
|
wrapValue: function (value, amount, max) {
|
|
|
|
var diff;
|
|
value = Math.abs(value);
|
|
amount = Math.abs(amount);
|
|
max = Math.abs(max);
|
|
diff = (value + amount) % max;
|
|
|
|
return diff;
|
|
|
|
},
|
|
|
|
/**
|
|
* Returns true if the number given is odd.
|
|
*
|
|
* @method Phaser.Math#isOdd
|
|
* @param {integer} n - The number to check.
|
|
* @return {boolean} True if the given number is odd. False if the given number is even.
|
|
*/
|
|
isOdd: function (n) {
|
|
|
|
// Does not work with extremely large values
|
|
return !!(n & 1);
|
|
|
|
},
|
|
|
|
/**
|
|
* Returns true if the number given is even.
|
|
*
|
|
* @method Phaser.Math#isEven
|
|
* @param {integer} n - The number to check.
|
|
* @return {boolean} True if the given number is even. False if the given number is odd.
|
|
*/
|
|
isEven: function (n) {
|
|
|
|
// Does not work with extremely large values
|
|
return !(n & 1);
|
|
|
|
},
|
|
|
|
/**
|
|
* Variation of Math.min that can be passed either an array of numbers or the numbers as parameters.
|
|
*
|
|
* Prefer the standard `Math.min` function when appropriate.
|
|
*
|
|
* @method Phaser.Math#min
|
|
* @return {number} The lowest value from those given.
|
|
* @see {@link http://jsperf.com/math-s-min-max-vs-homemade}
|
|
*/
|
|
min: function () {
|
|
|
|
if (arguments.length === 1 && typeof arguments[0] === 'object')
|
|
{
|
|
var data = arguments[0];
|
|
}
|
|
else
|
|
{
|
|
var data = arguments;
|
|
}
|
|
|
|
for (var i = 1, min = 0, len = data.length; i < len; i++)
|
|
{
|
|
if (data[i] < data[min])
|
|
{
|
|
min = i;
|
|
}
|
|
}
|
|
|
|
return data[min];
|
|
|
|
},
|
|
|
|
/**
|
|
* Variation of Math.max that can be passed either an array of numbers or the numbers as parameters.
|
|
*
|
|
* Prefer the standard `Math.max` function when appropriate.
|
|
*
|
|
* @method Phaser.Math#max
|
|
* @return {number} The largest value from those given.
|
|
* @see {@link http://jsperf.com/math-s-min-max-vs-homemade}
|
|
*/
|
|
max: function () {
|
|
|
|
if (arguments.length === 1 && typeof arguments[0] === 'object')
|
|
{
|
|
var data = arguments[0];
|
|
}
|
|
else
|
|
{
|
|
var data = arguments;
|
|
}
|
|
|
|
for (var i = 1, max = 0, len = data.length; i < len; i++)
|
|
{
|
|
if (data[i] > data[max])
|
|
{
|
|
max = i;
|
|
}
|
|
}
|
|
|
|
return data[max];
|
|
|
|
},
|
|
|
|
/**
|
|
* Variation of Math.min that can be passed a property and either an array of objects or the objects as parameters.
|
|
* It will find the lowest matching property value from the given objects.
|
|
*
|
|
* @method Phaser.Math#minProperty
|
|
* @return {number} The lowest value from those given.
|
|
*/
|
|
minProperty: function (property) {
|
|
|
|
if (arguments.length === 2 && typeof arguments[1] === 'object')
|
|
{
|
|
var data = arguments[1];
|
|
}
|
|
else
|
|
{
|
|
var data = arguments.slice(1);
|
|
}
|
|
|
|
for (var i = 1, min = 0, len = data.length; i < len; i++)
|
|
{
|
|
if (data[i][property] < data[min][property])
|
|
{
|
|
min = i;
|
|
}
|
|
}
|
|
|
|
return data[min][property];
|
|
|
|
},
|
|
|
|
/**
|
|
* Variation of Math.max that can be passed a property and either an array of objects or the objects as parameters.
|
|
* It will find the largest matching property value from the given objects.
|
|
*
|
|
* @method Phaser.Math#maxProperty
|
|
* @return {number} The largest value from those given.
|
|
*/
|
|
maxProperty: function (property) {
|
|
|
|
if (arguments.length === 2 && typeof arguments[1] === 'object')
|
|
{
|
|
var data = arguments[1];
|
|
}
|
|
else
|
|
{
|
|
var data = arguments.slice(1);
|
|
}
|
|
|
|
for (var i = 1, max = 0, len = data.length; i < len; i++)
|
|
{
|
|
if (data[i][property] > data[max][property])
|
|
{
|
|
max = i;
|
|
}
|
|
}
|
|
|
|
return data[max][property];
|
|
|
|
},
|
|
|
|
/**
|
|
* Keeps an angle value between -180 and +180; or -PI and PI if radians.
|
|
*
|
|
* @method Phaser.Math#wrapAngle
|
|
* @param {number} angle - The angle value to wrap
|
|
* @param {boolean} [radians=false] - Set to `true` if the angle is given in radians, otherwise degrees is expected.
|
|
* @return {number} The new angle value; will be the same as the input angle if it was within bounds.
|
|
*/
|
|
wrapAngle: function (angle, radians) {
|
|
|
|
return radians ? this.wrap(angle, -Math.PI, Math.PI) : this.wrap(angle, -180, 180);
|
|
|
|
},
|
|
|
|
/**
|
|
* A Linear Interpolation Method, mostly used by Phaser.Tween.
|
|
*
|
|
* @method Phaser.Math#linearInterpolation
|
|
* @param {Array} v - The input array of values to interpolate between.
|
|
* @param {number} k - The percentage of interpolation, between 0 and 1.
|
|
* @return {number} The interpolated value
|
|
*/
|
|
linearInterpolation: function (v, k) {
|
|
|
|
var m = v.length - 1;
|
|
var f = m * k;
|
|
var i = Math.floor(f);
|
|
|
|
if (k < 0)
|
|
{
|
|
return this.linear(v[0], v[1], f);
|
|
}
|
|
|
|
if (k > 1)
|
|
{
|
|
return this.linear(v[m], v[m - 1], m - f);
|
|
}
|
|
|
|
return this.linear(v[i], v[i + 1 > m ? m : i + 1], f - i);
|
|
|
|
},
|
|
|
|
/**
|
|
* A Bezier Interpolation Method, mostly used by Phaser.Tween.
|
|
*
|
|
* @method Phaser.Math#bezierInterpolation
|
|
* @param {Array} v - The input array of values to interpolate between.
|
|
* @param {number} k - The percentage of interpolation, between 0 and 1.
|
|
* @return {number} The interpolated value
|
|
*/
|
|
bezierInterpolation: function (v, k) {
|
|
|
|
var b = 0;
|
|
var n = v.length - 1;
|
|
|
|
for (var i = 0; i <= n; i++)
|
|
{
|
|
b += Math.pow(1 - k, n - i) * Math.pow(k, i) * v[i] * this.bernstein(n, i);
|
|
}
|
|
|
|
return b;
|
|
|
|
},
|
|
|
|
/**
|
|
* A Catmull Rom Interpolation Method, mostly used by Phaser.Tween.
|
|
*
|
|
* @method Phaser.Math#catmullRomInterpolation
|
|
* @param {Array} v - The input array of values to interpolate between.
|
|
* @param {number} k - The percentage of interpolation, between 0 and 1.
|
|
* @return {number} The interpolated value
|
|
*/
|
|
catmullRomInterpolation: function (v, k) {
|
|
|
|
var m = v.length - 1;
|
|
var f = m * k;
|
|
var i = Math.floor(f);
|
|
|
|
if (v[0] === v[m])
|
|
{
|
|
if (k < 0)
|
|
{
|
|
i = Math.floor(f = m * (1 + k));
|
|
}
|
|
|
|
return this.catmullRom(v[(i - 1 + m) % m], v[i], v[(i + 1) % m], v[(i + 2) % m], f - i);
|
|
}
|
|
else
|
|
{
|
|
if (k < 0)
|
|
{
|
|
return v[0] - (this.catmullRom(v[0], v[0], v[1], v[1], -f) - v[0]);
|
|
}
|
|
|
|
if (k > 1)
|
|
{
|
|
return v[m] - (this.catmullRom(v[m], v[m], v[m - 1], v[m - 1], f - m) - v[m]);
|
|
}
|
|
|
|
return this.catmullRom(v[i ? i - 1 : 0], v[i], v[m < i + 1 ? m : i + 1], v[m < i + 2 ? m : i + 2], f - i);
|
|
}
|
|
|
|
},
|
|
|
|
/**
|
|
* Calculates a linear (interpolation) value over t.
|
|
*
|
|
* @method Phaser.Math#linear
|
|
* @param {number} p0
|
|
* @param {number} p1
|
|
* @param {number} t - A value between 0 and 1.
|
|
* @return {number}
|
|
*/
|
|
linear: function (p0, p1, t) {
|
|
|
|
return (p1 - p0) * t + p0;
|
|
|
|
},
|
|
|
|
/**
|
|
* @method Phaser.Math#bernstein
|
|
* @protected
|
|
* @param {number} n
|
|
* @param {number} i
|
|
* @return {number}
|
|
*/
|
|
bernstein: function (n, i) {
|
|
|
|
return this.factorial(n) / this.factorial(i) / this.factorial(n - i);
|
|
|
|
},
|
|
|
|
/**
|
|
* @method Phaser.Math#factorial
|
|
* @param {number} value - the number you want to evaluate
|
|
* @return {number}
|
|
*/
|
|
factorial: function (value) {
|
|
|
|
if (value === 0)
|
|
{
|
|
return 1;
|
|
}
|
|
|
|
var res = value;
|
|
|
|
while(--value)
|
|
{
|
|
res *= value;
|
|
}
|
|
|
|
return res;
|
|
|
|
},
|
|
|
|
/**
|
|
* Calculates a catmum rom value.
|
|
*
|
|
* @method Phaser.Math#catmullRom
|
|
* @protected
|
|
* @param {number} p0
|
|
* @param {number} p1
|
|
* @param {number} p2
|
|
* @param {number} p3
|
|
* @param {number} t
|
|
* @return {number}
|
|
*/
|
|
catmullRom: function (p0, p1, p2, p3, t) {
|
|
|
|
var v0 = (p2 - p0) * 0.5, v1 = (p3 - p1) * 0.5, t2 = t * t, t3 = t * t2;
|
|
|
|
return (2 * p1 - 2 * p2 + v0 + v1) * t3 + (-3 * p1 + 3 * p2 - 2 * v0 - v1) * t2 + v0 * t + p1;
|
|
|
|
},
|
|
|
|
/**
|
|
* The absolute difference between two values.
|
|
*
|
|
* @method Phaser.Math#difference
|
|
* @param {number} a - The first value to check.
|
|
* @param {number} b - The second value to check.
|
|
* @return {number} The absolute difference between the two values.
|
|
*/
|
|
difference: function (a, b) {
|
|
|
|
return Math.abs(a - b);
|
|
|
|
},
|
|
|
|
/**
|
|
* Round to the next whole number _away_ from zero.
|
|
*
|
|
* @method Phaser.Math#roundAwayFromZero
|
|
* @param {number} value - Any number.
|
|
* @return {integer} The rounded value of that number.
|
|
*/
|
|
roundAwayFromZero: function (value) {
|
|
|
|
// "Opposite" of truncate.
|
|
return (value > 0) ? Math.ceil(value) : Math.floor(value);
|
|
|
|
},
|
|
|
|
/**
|
|
* Generate a sine and cosine table simultaneously and extremely quickly.
|
|
* The parameters allow you to specify the length, amplitude and frequency of the wave.
|
|
* This generator is fast enough to be used in real-time.
|
|
* Code based on research by Franky of scene.at
|
|
*
|
|
* @method Phaser.Math#sinCosGenerator
|
|
* @param {number} length - The length of the wave
|
|
* @param {number} sinAmplitude - The amplitude to apply to the sine table (default 1.0) if you need values between say -+ 125 then give 125 as the value
|
|
* @param {number} cosAmplitude - The amplitude to apply to the cosine table (default 1.0) if you need values between say -+ 125 then give 125 as the value
|
|
* @param {number} frequency - The frequency of the sine and cosine table data
|
|
* @return {{sin:number[], cos:number[]}} Returns the table data.
|
|
*/
|
|
sinCosGenerator: function (length, sinAmplitude, cosAmplitude, frequency) {
|
|
|
|
if (sinAmplitude === undefined) { sinAmplitude = 1.0; }
|
|
if (cosAmplitude === undefined) { cosAmplitude = 1.0; }
|
|
if (frequency === undefined) { frequency = 1.0; }
|
|
|
|
var sin = sinAmplitude;
|
|
var cos = cosAmplitude;
|
|
var frq = frequency * Math.PI / length;
|
|
|
|
var cosTable = [];
|
|
var sinTable = [];
|
|
|
|
for (var c = 0; c < length; c++) {
|
|
|
|
cos -= sin * frq;
|
|
sin += cos * frq;
|
|
|
|
cosTable[c] = cos;
|
|
sinTable[c] = sin;
|
|
|
|
}
|
|
|
|
return { sin: sinTable, cos: cosTable, length: length };
|
|
|
|
},
|
|
|
|
/**
|
|
* Returns the euclidian distance between the two given set of coordinates.
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|
*
|
|
* @method Phaser.Math#distance
|
|
* @param {number} x1
|
|
* @param {number} y1
|
|
* @param {number} x2
|
|
* @param {number} y2
|
|
* @return {number} The distance between the two sets of coordinates.
|
|
*/
|
|
distance: function (x1, y1, x2, y2) {
|
|
|
|
var dx = x1 - x2;
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|
var dy = y1 - y2;
|
|
|
|
return Math.sqrt(dx * dx + dy * dy);
|
|
|
|
},
|
|
|
|
/**
|
|
* Returns the euclidean distance squared between the two given set of
|
|
* coordinates (cuts out a square root operation before returning).
|
|
*
|
|
* @method Phaser.Math#distanceSq
|
|
* @param {number} x1
|
|
* @param {number} y1
|
|
* @param {number} x2
|
|
* @param {number} y2
|
|
* @return {number} The distance squared between the two sets of coordinates.
|
|
*/
|
|
distanceSq: function (x1, y1, x2, y2) {
|
|
|
|
var dx = x1 - x2;
|
|
var dy = y1 - y2;
|
|
|
|
return dx * dx + dy * dy;
|
|
|
|
},
|
|
|
|
/**
|
|
* Returns the distance between the two given set of coordinates at the power given.
|
|
*
|
|
* @method Phaser.Math#distancePow
|
|
* @param {number} x1
|
|
* @param {number} y1
|
|
* @param {number} x2
|
|
* @param {number} y2
|
|
* @param {number} [pow=2]
|
|
* @return {number} The distance between the two sets of coordinates.
|
|
*/
|
|
distancePow: function (x1, y1, x2, y2, pow) {
|
|
|
|
if (pow === undefined) { pow = 2; }
|
|
|
|
return Math.sqrt(Math.pow(x2 - x1, pow) + Math.pow(y2 - y1, pow));
|
|
|
|
},
|
|
|
|
/**
|
|
* Force a value within the boundaries by clamping it to the range `min`, `max`.
|
|
*
|
|
* @method Phaser.Math#clamp
|
|
* @param {float} v - The value to be clamped.
|
|
* @param {float} min - The minimum bounds.
|
|
* @param {float} max - The maximum bounds.
|
|
* @return {number} The clamped value.
|
|
*/
|
|
clamp: function (v, min, max) {
|
|
|
|
if (v < min)
|
|
{
|
|
return min;
|
|
}
|
|
else if (max < v)
|
|
{
|
|
return max;
|
|
}
|
|
else
|
|
{
|
|
return v;
|
|
}
|
|
|
|
},
|
|
|
|
/**
|
|
* Clamp `x` to the range `[a, Infinity)`.
|
|
* Roughly the same as `Math.max(x, a)`, except for NaN handling.
|
|
*
|
|
* @method Phaser.Math#clampBottom
|
|
* @param {number} x
|
|
* @param {number} a
|
|
* @return {number}
|
|
*/
|
|
clampBottom: function (x, a) {
|
|
|
|
return x < a ? a : x;
|
|
|
|
},
|
|
|
|
/**
|
|
* Checks if two values are within the given tolerance of each other.
|
|
*
|
|
* @method Phaser.Math#within
|
|
* @param {number} a - The first number to check
|
|
* @param {number} b - The second number to check
|
|
* @param {number} tolerance - The tolerance. Anything equal to or less than this is considered within the range.
|
|
* @return {boolean} True if a is <= tolerance of b.
|
|
* @see {@link Phaser.Math.fuzzyEqual}
|
|
*/
|
|
within: function (a, b, tolerance) {
|
|
|
|
return (Math.abs(a - b) <= tolerance);
|
|
|
|
},
|
|
|
|
/**
|
|
* Linear mapping from range <a1, a2> to range <b1, b2>
|
|
*
|
|
* @method Phaser.Math#mapLinear
|
|
* @param {number} x - The value to map
|
|
* @param {number} a1 - First endpoint of the range <a1, a2>
|
|
* @param {number} a2 - Final endpoint of the range <a1, a2>
|
|
* @param {number} b1 - First endpoint of the range <b1, b2>
|
|
* @param {number} b2 - Final endpoint of the range <b1, b2>
|
|
* @return {number}
|
|
*/
|
|
mapLinear: function (x, a1, a2, b1, b2) {
|
|
|
|
return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 );
|
|
|
|
},
|
|
|
|
/**
|
|
* Smoothstep function as detailed at http://en.wikipedia.org/wiki/Smoothstep
|
|
*
|
|
* @method Phaser.Math#smoothstep
|
|
* @param {float} x - The input value.
|
|
* @param {float} min - The left edge. Should be smaller than the right edge.
|
|
* @param {float} max - The right edge.
|
|
* @return {float} A value between 0 and 1.
|
|
*/
|
|
smoothstep: function (x, min, max) {
|
|
|
|
// Scale, bias and saturate x to 0..1 range
|
|
x = Math.max(0, Math.min(1, (x - min) / (max - min)));
|
|
|
|
// Evaluate polynomial
|
|
return x * x * (3 - 2 * x);
|
|
|
|
},
|
|
|
|
/**
|
|
* Smootherstep function as detailed at http://en.wikipedia.org/wiki/Smoothstep
|
|
*
|
|
* @method Phaser.Math#smootherstep
|
|
* @param {float} x - The input value.
|
|
* @param {float} min - The left edge. Should be smaller than the right edge.
|
|
* @param {float} max - The right edge.
|
|
* @return {float} A value between 0 and 1.
|
|
*/
|
|
smootherstep: function (x, min, max) {
|
|
|
|
x = Math.max(0, Math.min(1, (x - min) / (max - min)));
|
|
|
|
return x * x * x * (x * (x * 6 - 15) + 10);
|
|
|
|
},
|
|
|
|
/**
|
|
* A value representing the sign of the value: -1 for negative, +1 for positive, 0 if value is 0.
|
|
*
|
|
* This works differently from `Math.sign` for values of NaN and -0, etc.
|
|
*
|
|
* @method Phaser.Math#sign
|
|
* @param {number} x
|
|
* @return {integer} An integer in {-1, 0, 1}
|
|
*/
|
|
sign: function (x) {
|
|
|
|
return ( x < 0 ) ? -1 : ( ( x > 0 ) ? 1 : 0 );
|
|
|
|
},
|
|
|
|
/**
|
|
* Work out what percentage value `a` is of value `b` using the given base.
|
|
*
|
|
* @method Phaser.Math#percent
|
|
* @param {number} a - The value to work out the percentage for.
|
|
* @param {number} b - The value you wish to get the percentage of.
|
|
* @param {number} [base=0] - The base value.
|
|
* @return {number} The percentage a is of b, between 0 and 1.
|
|
*/
|
|
percent: function (a, b, base) {
|
|
|
|
if (base === undefined) { base = 0; }
|
|
|
|
if (a > b || base > b)
|
|
{
|
|
return 1;
|
|
}
|
|
else if (a < base || base > a)
|
|
{
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
return (a - base) / b;
|
|
}
|
|
|
|
}
|
|
|
|
};
|