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1389 lines (1116 loc) · 36.7 KB
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/**
* @author Richard Davey <rich@photonstorm.com>
* @copyright 2014 Photon Storm Ltd.
* @license {@link https://github.com/photonstorm/phaser/blob/master/license.txt|MIT License}
*/
/**
* A collection of mathematical methods.
*
* @class Phaser.Math
*/
Phaser.Math = {
/**
* = 2 π
* @method Phaser.Math#PI2
*/
PI2: Math.PI * 2,
/**
* Two number are fuzzyEqual if their difference is less than ε.
* @method Phaser.Math#fuzzyEqual
* @param {number} a
* @param {number} b
* @param {number} epsilon
* @return {boolean} True if |a-b|<ε
*/
fuzzyEqual: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.abs(a - b) < epsilon;
},
/**
* a is fuzzyLessThan b if it is less than b + ε.
* @method Phaser.Math#fuzzyLessThan
* @param {number} a
* @param {number} b
* @param {number} epsilon
* @return {boolean} True if a<b+ε
*/
fuzzyLessThan: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return a < b + epsilon;
},
/**
* a is fuzzyGreaterThan b if it is more than b - ε.
* @method Phaser.Math#fuzzyGreaterThan
* @param {number} a
* @param {number} b
* @param {number} epsilon
* @return {boolean} True if a>b+ε
*/
fuzzyGreaterThan: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return a > b - epsilon;
},
/**
* @method Phaser.Math#fuzzyCeil
* @param {number} val
* @param {number} epsilon
* @return {boolean} ceiling(val-ε)
*/
fuzzyCeil: function (val, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.ceil(val - epsilon);
},
/**
* @method Phaser.Math#fuzzyFloor
* @param {number} val
* @param {number} epsilon
* @return {boolean} floor(val-ε)
*/
fuzzyFloor: function (val, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.floor(val + epsilon);
},
/**
* Averages all values passed to the function and returns the result. You can pass as many parameters as you like.
* @method Phaser.Math#average
* @return {number} The average of all given values.
*/
average: function () {
var args = [];
for (var _i = 0; _i < (arguments.length - 0); _i++) {
args[_i] = arguments[_i + 0];
}
var avg = 0;
for (var i = 0; i < args.length; i++) {
avg += args[i];
}
return avg / args.length;
},
/**
* @method Phaser.Math#truncate
* @param {number} n
* @return {number}
*/
truncate: function (n) {
return (n > 0) ? Math.floor(n) : Math.ceil(n);
},
/**
* @method Phaser.Math#shear
* @param {number} n
* @return {number} n mod 1
*/
shear: function (n) {
return n % 1;
},
/**
* Snap a value to nearest grid slice, using rounding.
*
* 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.
*
* @method Phaser.Math#snapTo
* @param {number} input - The value to snap.
* @param {number} gap - The interval gap of the grid.
* @param {number} [start] - Optional starting offset for gap.
* @return {number}
*/
snapTo: function (input, gap, start) {
if (typeof start === "undefined") { start = 0; }
if (gap === 0) {
return input;
}
input -= start;
input = gap * Math.round(input / gap);
return start + input;
},
/**
* Snap a value to nearest grid slice, using floor.
*
* Example: if you have an interval gap of 5 and a position of 12... you will snap to 10. As will 14 snap to 10... but 16 will snap to 15
*
* @method Phaser.Math#snapToFloor
* @param {number} input - The value to snap.
* @param {number} gap - The interval gap of the grid.
* @param {number} [start] - Optional starting offset for gap.
* @return {number}
*/
snapToFloor: function (input, gap, start) {
if (typeof start === "undefined") { start = 0; }
if (gap === 0) {
return input;
}
input -= start;
input = gap * Math.floor(input / gap);
return start + input;
},
/**
* Snap a value to nearest grid slice, using ceil.
*
* Example: if you have an interval gap of 5 and a position of 12... you will snap to 15. As will 14 will snap to 15... but 16 will snap to 20.
*
* @method Phaser.Math#snapToCeil
* @param {number} input - The value to snap.
* @param {number} gap - The interval gap of the grid.
* @param {number} [start] - Optional starting offset for gap.
* @return {number}
*/
snapToCeil: function (input, gap, start) {
if (typeof start === "undefined") { start = 0; }
if (gap === 0) {
return input;
}
input -= start;
input = gap * Math.ceil(input / gap);
return start + input;
},
/**
* Snaps a value to the nearest value in an array.
* @method Phaser.Math#snapToInArray
* @param {number} input
* @param {array} arr
* @param {boolean} sort - True if the array needs to be sorted.
* @return {number}
*/
snapToInArray: function (input, arr, sort) {
if (typeof sort === "undefined") { sort = true; }
if (sort) {
arr.sort();
}
if (input < arr[0]) {
return arr[0];
}
var i = 1;
while (arr[i] < input) {
i++;
}
var low = arr[i - 1];
var high = (i < arr.length) ? arr[i] : Number.POSITIVE_INFINITY;
return ((high - input) <= (input - low)) ? high : low;
},
/**
* Round to some place comparative to a 'base', default is 10 for decimal place.
*
* 'place' is represented by the power applied to 'base' to get that place
* e.g.
* 2000/7 ~= 285.714285714285714285714 ~= (bin)100011101.1011011011011011
*
* roundTo(2000/7,3) === 0
* roundTo(2000/7,2) == 300
* roundTo(2000/7,1) == 290
* roundTo(2000/7,0) == 286
* roundTo(2000/7,-1) == 285.7
* roundTo(2000/7,-2) == 285.71
* roundTo(2000/7,-3) == 285.714
* roundTo(2000/7,-4) == 285.7143
* roundTo(2000/7,-5) == 285.71429
*
* roundTo(2000/7,3,2) == 288 -- 100100000
* roundTo(2000/7,2,2) == 284 -- 100011100
* roundTo(2000/7,1,2) == 286 -- 100011110
* roundTo(2000/7,0,2) == 286 -- 100011110
* roundTo(2000/7,-1,2) == 285.5 -- 100011101.1
* roundTo(2000/7,-2,2) == 285.75 -- 100011101.11
* roundTo(2000/7,-3,2) == 285.75 -- 100011101.11
* roundTo(2000/7,-4,2) == 285.6875 -- 100011101.1011
* roundTo(2000/7,-5,2) == 285.71875 -- 100011101.10111
*
* Note what occurs when we round to the 3rd space (8ths place), 100100000, this is to be assumed
* because we are rounding 100011.1011011011011011 which rounds up.
*
* @method Phaser.Math#roundTo
* @param {number} value - The value to round.
* @param {number} place - The place to round to.
* @param {number} base - The base to round in... default is 10 for decimal.
* @return {number}
*/
roundTo: function (value, place, base) {
if (typeof place === "undefined") { place = 0; }
if (typeof base === "undefined") { base = 10; }
var p = Math.pow(base, -place);
return Math.round(value * p) / p;
},
/**
* @method Phaser.Math#floorTo
* @param {number} value - The value to round.
* @param {number} place - The place to round to.
* @param {number} base - The base to round in... default is 10 for decimal.
* @return {number}
*/
floorTo: function (value, place, base) {
if (typeof place === "undefined") { place = 0; }
if (typeof base === "undefined") { base = 10; }
var p = Math.pow(base, -place);
return Math.floor(value * p) / p;
},
/**
* @method Phaser.Math#ceilTo
* @param {number} value - The value to round.
* @param {number} place - The place to round to.
* @param {number} base - The base to round in... default is 10 for decimal.
* @return {number}
*/
ceilTo: function (value, place, base) {
if (typeof place === "undefined") { place = 0; }
if (typeof base === "undefined") { base = 10; }
var p = Math.pow(base, -place);
return Math.ceil(value * p) / p;
},
/**
* A one dimensional linear interpolation of a value.
* @method Phaser.Math#interpolateFloat
* @param {number} a
* @param {number} b
* @param {number} weight
* @return {number}
*/
interpolateFloat: function (a, b, weight) {
return (b - a) * weight + a;
},
/**
* Find the angle of a segment from (x1, y1) -> (x2, y2).
* @method Phaser.Math#angleBetween
* @param {number} x1
* @param {number} y1
* @param {number} x2
* @param {number} y2
* @return {number}
*/
angleBetween: function (x1, y1, x2, y2) {
return Math.atan2(y2 - y1, x2 - x1);
},
/**
* Find the angle of a segment from (point1.x, point1.y) -> (point2.x, point2.y).
* @method Phaser.Math#angleBetweenPoints
* @param {Phaser.Point} point1
* @param {Phaser.Point} point2
* @return {number}
*/
angleBetweenPoints: function (point1, point2) {
return Math.atan2(point2.y - point1.y, point2.x - point1.x);
},
/**
* Reverses an angle.
* @method Phaser.Math#reverseAngle
* @param {number} angleRad - The angle to reverse, in radians.
* @return {number} Returns 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} Returns 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;
},
/**
* Normalizes a latitude to the [-90,90] range. Latitudes above 90 or below -90 are capped, not wrapped.
* @method Phaser.Math#normalizeLatitude
* @param {number} lat - The latitude to normalize, in degrees.
* @return {number} Returns the latitude, fit within the [-90,90] range.
*/
normalizeLatitude: function (lat) {
return Math.max(-90, Math.min(90, lat));
},
/**
* Normalizes a longitude to the [-180,180] range. Longitudes above 180 or below -180 are wrapped.
* @method Phaser.Math#normalizeLongitude
* @param {number} lng - The longitude to normalize, in degrees.
* @return {number} Returns the longitude, fit within the [-180,180] range.
*/
normalizeLongitude: function (lng) {
if (lng % 360 == 180)
{
return 180;
}
lng = lng % 360;
return lng < -180 ? lng + 360 : lng > 180 ? lng - 360 : lng;
},
/**
* Closest angle between two angles from a1 to a2 absolute value the return for exact angle
* @method Phaser.Math#nearestAngleBetween
* @param {number} a1
* @param {number} a2
* @param {boolean} radians - True if angle sizes are expressed in radians.
* @return {number}
nearestAngleBetween: function (a1, a2, radians) {
if (typeof radians === "undefined") { radians = true; }
var rd = (radians) ? Math.PI : 180;
a1 = this.normalizeAngle(a1, radians);
a2 = this.normalizeAngle(a2, radians);
if (a1 < -rd / 2 && a2 > rd / 2)
{
a1 += rd * 2;
}
if (a2 < -rd / 2 && a1 > rd / 2)
{
a2 += rd * 2;
}
return a2 - a1;
},
*/
/**
* Interpolate across the shortest arc between two angles.
* @method Phaser.Math#interpolateAngles
* @param {number} a1 - Description.
* @param {number} a2 - Description.
* @param {number} weight - Description.
* @param {boolean} radians - True if angle sizes are expressed in radians.
* @param {Description} ease - Description.
* @return {number}
interpolateAngles: function (a1, a2, weight, radians, ease) {
if (typeof radians === "undefined") { radians = true; }
if (typeof ease === "undefined") { ease = null; }
a1 = this.normalizeAngle(a1, radians);
a2 = this.normalizeAngleToAnother(a2, a1, radians);
return (typeof ease === 'function') ? ease(weight, a1, a2 - a1, 1) : this.interpolateFloat(a1, a2, weight);
},
*/
/**
* Generate a random bool result based on the chance value.
* <p>
* Returns true or false based on the chance value (default 50%). For example if you wanted a player to have a 30% chance
* of getting a bonus, call chanceRoll(30) - true means the chance passed, false means it failed.
* </p>
* @method Phaser.Math#chanceRoll
* @param {number} chance - The chance of receiving the value. A number between 0 and 100 (effectively 0% to 100%).
* @return {boolean} True if the roll passed, or false otherwise.
*/
chanceRoll: function (chance) {
if (typeof chance === "undefined") { chance = 50; }
if (chance <= 0)
{
return false;
}
else if (chance >= 100)
{
return true;
}
else
{
if (Math.random() * 100 >= chance)
{
return false;
}
else
{
return true;
}
}
},
/**
* Returns an Array containi
992E
ng the numbers from min to max (inclusive).
*
* @method Phaser.Math#numberArray
* @param {number} min - The minimum value the array starts with.
* @param {number} max - The maximum value the array contains.
* @return {array} The array of number values.
*/
numberArray: function (min, max) {
var result = [];
for (var i = min; i <= max; i++)
{
result.push(i);
}
return result;
},
/**
* 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}
*/
maxAdd: function (value, amount, max) {
value += amount;
if (value > max)
{
value = max;
}
return value;
},
/**
* 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) {
value -= amount;
if (value < min)
{
value = min;
}
return value;
},
/**
* Ensures that the value always stays between min and max, by wrapping the value around.
* max should be larger than min, or the function will return 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.
* @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.
*
* @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;
},
/**
* Ensures the given value is between min and max inclusive.
*
* @method Phaser.Math#limitValue
* @param {number} value - The value to limit.
* @param {number} min - The minimum the value can be.
* @param {number} max - The maximum the value can be.
* @return {number} The limited value.
*/
limitValue: function(value, min, max) {
return value < min ? min : value > max ? max : value;
},
/**
* Randomly returns either a 1 or -1.
*
* @method Phaser.Math#randomSign
* @return {number} 1 or -1
*/
randomSign: function () {
return (Math.random() > 0.5) ? 1 : -1;
},
/**
* Returns true if the number given is odd.
*
* @method Phaser.Math#isOdd
* @param {number} n - The number to check.
* @return {boolean} True if the given number is odd. False if the given number is even.
*/
isOdd: function (n) {
return (n & 1);
},
/**
* Returns true if the number given is even.
*
* @method Phaser.Math#isEven
* @param {number} n - The number to check.
* @return {boolean} True if the given number is even. False if the given number is odd.
*/
isEven: function (n) {
if (n & 1)
{
return false;
}
else
{
return true;
}
},
/**
* Updated version of Math.min that can be passed either an array of numbers or the numbers as parameters.
* See http://jsperf.com/math-s-min-max-vs-homemade/5
*
* @method Phaser.Math#min
* @return {number} The lowest value from those given.
*/
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];
},
/**
* Updated version of Math.max that can be passed either an array of numbers or the numbers as parameters.
*
* @method Phaser.Math#max
* @return {number} The largest value from those given.
*/
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];
},
/**
* Updated version 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];
},
/**
* Updated version 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.
*
* @method Phaser.Math#wrapAngle
* @param {number} angle - The angle value to check
* @param {boolean} radians - True if angle is given in radians.
* @return {number} The new angle value, returns the same as the input angle if it was within bounds.
*/
wrapAngle: function (angle, radians) {
var radianFactor = (radians) ? Math.PI / 180 : 1;
return this.wrap(angle, -180 * radianFactor, 180 * radianFactor);
},
/**
* Keeps an angle value between the given min and max values.
*
* @method Phaser.Math#angleLimit
* @param {number} angle - The angle value to check. Must be between -180 and +180.
* @param {number} min - The minimum angle that is allowed (must be -180 or greater).
* @param {number} max - The maximum angle that is allowed (must be 180 or less).
* @return {number} The new angle value, returns the same as the input angle if it was within bounds
*/
angleLimit: function (angle, min, max) {
var result = angle;
if (angle > max)
{
result = max;
}
else if (angle < min)
{
result = min;
}
return result;
},
/**
* A Linear Interpolation Method, mostly used by Phaser.Tween.
* @method Phaser.Math#linearInterpolation
* @param {Array} v
* @param {number} k
* @return {number}
*/
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
* @param {number} k
* @return {number}
*/
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
* @param {number} k
* @return {number}
*/
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);
}
},
/**
* Description.
* @method Phaser.Math#Linear
* @param {number} p0
* @param {number} p1
* @param {number} t
* @return {number}
*/
linear: function (p0, p1, t) {
return (p1 - p0) * t + p0;
},
/**
* @method Phaser.Math#bernstein
* @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;
},
/**
* Description.
* @method Phaser.Math#catmullRom
* @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;
},
/**
* @method Phaser.Math#difference
* @param {number} a
* @param {number} b
* @return {number}
*/
difference: function (a, b) {
return Math.abs(a - b);
},
/**
* Fetch a random entry from the given array.
* Will return null if random selection is missing, or array has no entries.
*
* @method Phaser.Math#getRandom
* @param {array} objects - An array of objects.
* @param {number} startIndex - Optional offset off the front of the array. Default value is 0, or the beginning of the array.
* @param {number} length - Optional restriction on the number of values you want to randomly select from.
* @return {object} The random object that was selected.
*/
getRandom: function (objects, startIndex, length) {