Phaser.Math = {
PI2: Math.PI * 2,
fuzzyEqual: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.abs(a - b) < epsilon;
},
fuzzyLessThan: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return a < b + epsilon;
},
fuzzyGreaterThan: function (a, b, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return a > b - epsilon;
},
fuzzyCeil: function (val, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.ceil(val - epsilon);
},
fuzzyFloor: function (val, epsilon) {
if (typeof epsilon === "undefined") { epsilon = 0.0001; }
return Math.floor(val + epsilon);
},
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;
},
truncate: function (n) {
return (n > 0) ? Math.floor(n) : Math.ceil(n);
},
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. Where as 14 will snap to 15
*
* @param input - the value to snap
* @param gap - the interval gap of the grid
* @param [start] - optional starting offset for gap
*/
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
*
* @param input - the value to snap
* @param gap - the interval gap of the grid
* @param [start] - optional starting offset for gap
*/
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
*
* @param input - the value to snap
* @param gap - the interval gap of the grid
* @param [start] - optional starting offset for gap
*/
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.
*/
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;
},
/**
* roundTo 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
*
* @param value - the value to round
* @param place - the place to round to
* @param base - the base to round in... default is 10 for decimal
*
* 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.
*/
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;
},
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;
},
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.
*/
interpolateFloat: function (a, b, weight) {
return (b - a) * weight + a;
},
/**
* Find the angle of a segment from (x1, y1) -> (x2, y2 )
*/
angleBetween: function (x1, y1, x2, y2) {
return Math.atan2(y2 - y1, x2 - x1);
},
/**
* set an angle within the bounds of -PI to PI
*/
normalizeAngle: function (angle, radians) {
if (typeof radians === "undefined") { radians = true; }
var rd = (radians) ? GameMath.PI : 180;
return this.wrap(angle, rd, -rd);
},
/**
* closest angle between two angles from a1 to a2
* absolute value the return for exact angle
*/
nearestAngleBetween: function (a1, a2, radians) {
if (typeof radians === "undefined") { radians = true; }
var rd = (radians) ? GameMath.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
*/
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
*
* 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.
*
* @param chance The chance of receiving the value. A number between 0 and 100 (effectively 0% to 100%)
* @return true if the roll passed, or false
*/
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;
}
}
},
/**
* Adds the given amount to the value, but never lets the value go over the specified maximum
*
* @param value The value to add the amount to
* @param amount The amount to add to the value
* @param max The maximum the value is allowed to be
* @return The new value
*/
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
*
* @param value The base value
* @param amount The amount to subtract from the base value
* @param min The minimum the value is allowed to be
* @return The new value
*/
minSub: function (value, amount, min) {
value -= amount;
if (value < min)
{
value = min;
}
return value;
},
/**
* 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
*
* @param value The value to add the amount to
* @param amount The amount to add to the value
* @param max The maximum the value is allowed to be
* @return 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;
},
/**
* Randomly returns either a 1 or -1
*
* @return 1 or -1
*/
randomSign: function () {
return (Math.random() > 0.5) ? 1 : -1;
},
/**
* Returns true if the number given is odd.
*
* @param n The number to check
*
* @return 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.
*
* @param n The number to check
*
* @return 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;
}
},
/**
* Significantly faster version of Math.max
* See http://jsperf.com/math-s-min-max-vs-homemade/5
*
* @return The highest value from those given.
*/
max: function () {
for (var i = 1, max = 0, len = arguments.length; i < len; i++)
{
if (arguments[max] < arguments[i]) {
max = i;
}
}
return arguments[max];
},
/**
* Significantly faster version of Math.min
* See http://jsperf.com/math-s-min-max-vs-homemade/5
*
* @return The lowest value from those given.
*/
min: function () {
for (var i =1 , min = 0, len = arguments.length; i < len; i++)
{
if (arguments[i] < arguments[min]){
min = i;
}
}
return arguments[min];
},
/**
* Keeps an angle value between -180 and +180
* Should be called whenever the angle is updated on the Sprite to stop it from going insane.
*
* @param angle The angle value to check
*
* @return The new angle value, returns the same as the input angle if it was within bounds
*/
wrapAngle: function (angle) {
var result = angle;
// Nothing needs to change
if (angle >= -180 && angle <= 180)
{
return angle;
}
// Else normalise it to -180, 180
result = (angle + 180) % 360;
if (result < 0)
{
result += 360;
}
return result - 180;
},
/**
* Keeps an angle value between the given min and max values
*
* @param angle The angle value to check. Must be between -180 and +180
* @param min The minimum angle that is allowed (must be -180 or greater)
* @param max The maximum angle that is allowed (must be 180 or less)
*
* @return 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;
},
/**
* @method linearInterpolation
* @param {Any} v
* @param {Any} k
* @public
*/
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);
},
/**
* @method bezierInterpolation
* @param {Any} v
* @param {Any} k
* @public
*/
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;
},
/**
* @method catmullRomInterpolation
* @param {Any} v
* @param {Any} k
* @public
*/
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);
}
},
/**
* @method Linear
* @param {Any} p0
* @param {Any} p1
* @param {Any} t
* @public
*/
linear: function (p0, p1, t) {
return (p1 - p0) * t + p0;
},
/**
* @method bernstein
* @param {Any} n
* @param {Any} i
* @public
*/
bernstein: function (n, i) {
return this.factorial(n) / this.factorial(i) / this.factorial(n - i);
},
/**
* @method catmullRom
* @param {Any} p0
* @param {Any} p1
* @param {Any} p2
* @param {Any} p3
* @param {Any} t
* @public
*/
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;
},
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.
*
* @param objects An array of objects.
* @param startIndex Optional offset off the front of the array. Default value is 0, or the beginning of the array.
* @param length Optional restriction on the number of values you want to randomly select from.
*
* @return The random object that was selected.
*/
getRandom: function (objects, startIndex, length) {
if (typeof startIndex === "undefined") { startIndex = 0; }
if (typeof length === "undefined") { length = 0; }
if (objects != null) {
var l = length;
if ((l == 0) || (l > objects.length - startIndex))
{
l = objects.length - startIndex;
}
if (l > 0)
{
return objects[startIndex + Math.floor(Math.random() * l)];
}
}
return null;
},
/**
* Round down to the next whole number. E.g. floor(1.7) == 1, and floor(-2.7) == -2.
*
* @param Value Any number.
*
* @return The rounded value of that number.
*/
floor: function (value) {
var n = value | 0;
return (value > 0) ? (n) : ((n != value) ? (n - 1) : (n));
},
/**
* Round up to the next whole number. E.g. ceil(1.3) == 2, and ceil(-2.3) == -3.
*
* @param Value Any number.
*
* @return The rounded value of that number.
*/
ceil: function (value) {
var n = value | 0;
return (value > 0) ? ((n != value) ? (n + 1) : (n)) : (n);
},
/**
* Generate a sine and cosine table simultaneously and extremely quickly. Based on research by Franky of scene.at
*
* The parameters allow you to specify the length, amplitude and frequency of the wave. Once you have called this function
* you should get the results via getSinTable() and getCosTable(). This generator is fast enough to be used in real-time.
*
* @param length The length of the wave
* @param 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 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 frequency The frequency of the sine and cosine table data
* @return Returns the sine table
* @see getSinTable
* @see getCosTable
*/
sinCosGenerator: function (length, sinAmplitude, cosAmplitude, frequency) {
if (typeof sinAmplitude === "undefined") { sinAmplitude = 1.0; }
if (typeof cosAmplitude === "undefined") { cosAmplitude = 1.0; }
if (typeof 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 };
},
/**
* Removes the top element from the stack and re-inserts it onto the bottom, then returns it.
* The original stack is modified in the process.
* This effectively moves the position of the data from the start to the end of the table.
* @return The value.
*/
shift: function (stack) {
var s = stack.shift();
stack.push(s);
return s;
},
/**
* Shuffles the data in the given array into a new order
* @param array The array to shuffle
* @return The array
*/
shuffleArray: function (array) {
for (var i = array.length - 1; i > 0; i--) {
var j = Math.floor(Math.random() * (i + 1));
var temp = array[i];
array[i] = array[j];
array[j] = temp;
}
return array;
},
/**
* Returns the distance between the two given set of coordinates.
* @method distance
* @param {Number} x1
* @param {Number} y1
* @param {Number} x2
* @param {Number} y2
* @return {Number} The distance between this Point object and the destination Point object.
**/
distance: function (x1, y1, x2, y2) {
var dx = x1 - x2;
var dy = y1 - y2;
return Math.sqrt(dx * dx + dy * dy);
},
distanceRounded: function (x1, y1, x2, y2) {
return Math.round(Phaser.Math.distance(x1, y1, x2, y2));
},
/**
* force a value within the boundaries of two values
*
* Clamp value to range
*/
clamp: function ( x, a, b ) {
return ( x < a ) ? a : ( ( x > b ) ? b : x );
},
// Clamp value to range to range
mapLinear: function ( x, a1, a2, b1, b2 ) {
return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 );
},
// http://en.wikipedia.org/wiki/Smoothstep
smoothstep: function ( x, min, max ) {
if ( x <= min ) return 0;
if ( x >= max ) return 1;
x = ( x - min )/( max - min );
return x*x*(3 - 2*x);
},
smootherstep: function ( x, min, max ) {
if ( x <= min ) return 0;
if ( x >= max ) return 1;
x = ( 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
*/
sign: function ( x ) {
return ( x < 0 ) ? -1 : ( ( x > 0 ) ? 1 : 0 );
},
degToRad: function() {
var degreeToRadiansFactor = Math.PI / 180;
return function ( degrees ) {
return degrees * degreeToRadiansFactor;
};
}(),
radToDeg: function() {
var radianToDegreesFactor = 180 / Math.PI;
return function ( radians ) {
return radians * radianToDegreesFactor;
};
}()
};