/**
* Phaser - GameMath
*
* @desc Adds a set of extra Math functions and extends a few commonly used ones.
* Includes methods written by Dylan Engelman and Adam Saltsman.
*
* @version 1.0 - 17th March 2013
* @author Richard Davey
*/
class GameMath {
constructor(game: Game) {
this._game = game;
}
private _game: Game;
public static PI: number = 3.141592653589793; //number pi
public static PI_2: number = 1.5707963267948965; //PI / 2 OR 90 deg
public static PI_4: number = 0.7853981633974483; //PI / 4 OR 45 deg
public static PI_8: number = 0.39269908169872413; //PI / 8 OR 22.5 deg
public static PI_16: number = 0.19634954084936206; //PI / 16 OR 11.25 deg
public static TWO_PI: number = 6.283185307179586; //2 * PI OR 180 deg
public static THREE_PI_2: number = 4.7123889803846895; //3 * PI_2 OR 270 deg
public static E: number = 2.71828182845905; //number e
public static LN10: number = 2.302585092994046; //ln(10)
public static LN2: number = 0.6931471805599453; //ln(2)
public static LOG10E: number = 0.4342944819032518; //logB10(e)
public static LOG2E: number = 1.442695040888963387; //logB2(e)
public static SQRT1_2: number = 0.7071067811865476; //sqrt( 1 / 2 )
public static SQRT2: number = 1.4142135623730951; //sqrt( 2 )
public static DEG_TO_RAD: number = 0.017453292519943294444444444444444; //PI / 180;
public static RAD_TO_DEG: number = 57.295779513082325225835265587527; // 180.0 / PI;
public static B_16: number = 65536;//2^16
public static B_31: number = 2147483648;//2^31
public static B_32: number = 4294967296;//2^32
public static B_48: number = 281474976710656;//2^48
public static B_53: number = 9007199254740992;//2^53 !!NOTE!! largest accurate double floating point whole value
public static B_64: number = 18446744073709551616;//2^64 !!NOTE!! Not accurate see B_53
public static ONE_THIRD: number = 0.333333333333333333333333333333333; // 1.0/3.0;
public static TWO_THIRDS: number = 0.666666666666666666666666666666666; // 2.0/3.0;
public static ONE_SIXTH: number = 0.166666666666666666666666666666666; // 1.0/6.0;
public static COS_PI_3: number = 0.86602540378443864676372317075294;//COS( PI / 3 )
public static SIN_2PI_3: number = 0.03654595;// SIN( 2*PI/3 )
public static CIRCLE_ALPHA: number = 0.5522847498307933984022516322796; //4*(Math.sqrt(2)-1)/3.0;
public static ON: bool = true;
public static OFF: bool = false;
public static SHORT_EPSILON: number = 0.1;//round integer epsilon
public static PERC_EPSILON: number = 0.001;//percentage epsilon
public static EPSILON: number = 0.0001;//single float average epsilon
public static LONG_EPSILON: number = 0.00000001;//arbitrary 8 digit epsilon
public computeMachineEpsilon(): number {
// Machine epsilon ala Eispack
var fourThirds: number = 4.0 / 3.0;
var third: number = fourThirds - 1.0;
var one: number = third + third + third;
return Math.abs(1.0 - one);
}
public fuzzyEqual(a: number, b: number, epsilon: number = 0.0001): bool {
return Math.abs(a - b) < epsilon;
}
public fuzzyLessThan(a: number, b: number, epsilon: number = 0.0001): bool {
return a < b + epsilon;
}
public fuzzyGreaterThan(a: number, b: number, epsilon: number = 0.0001): bool {
return a > b - epsilon;
}
public fuzzyCeil(val: number, epsilon: number = 0.0001): number {
return Math.ceil(val - epsilon);
}
public fuzzyFloor(val: number, epsilon: number = 0.0001): number {
return Math.floor(val + epsilon);
}
public average(...args: any[]): number {
var avg: number = 0;
for (var i = 0; i < args.length; i++)
{
avg += args[i];
}
return avg / args.length;
}
public slam(value: number, target: number, epsilon: number = 0.0001): number {
return (Math.abs(value - target) < epsilon) ? target : value;
}
/**
* ratio of value to a range
*/
public percentageMinMax(val: number, max: number, min: number = 0): number {
val -= min;
max -= min;
if (!max) return 0;
else return val / max;
}
/**
* a value representing the sign of the value.
* -1 for negative, +1 for positive, 0 if value is 0
*/
public sign(n: number): number {
if (n) return n / Math.abs(n);
else return 0;
}
public truncate(n: number): number {
return (n > 0) ? Math.floor(n) : Math.ceil(n);
}
public shear(n: number): number {
return n % 1;
}
/**
* wrap a value around a range, similar to modulus with a floating minimum
*/
public wrap(val: number, max: number, min: number = 0): number {
val -= min;
max -= min;
if (max == 0) return min;
val %= max;
val += min;
while (val < min)
val += max;
return val;
}
/**
* arithmetic version of wrap... need to decide which is more efficient
*/
public arithWrap(value: number, max: number, min: number = 0): number {
max -= min;
if (max == 0) return min;
return value - max * Math.floor((value - min) / max);
}
/**
* force a value within the boundaries of two values
*
* if max < min, min is returned
*/
public clamp(input: number, max: number, min: number = 0): number {
return Math.max(min, Math.min(max, input));
}
/**
* 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
*/
public snapTo(input: number, gap: number, start: number = 0): number {
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
*/
public snapToFloor(input: number, gap: number, start: number = 0): number {
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
*/
public snapToCeil(input: number, gap: number, start: number = 0): number {
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.
*/
public snapToInArray(input: number, arr: number[], sort?: bool = true): number {
if (sort) arr.sort();
if (input < arr[0]) return arr[0];
var i: number = 1;
while (arr[i] < input)
i++;
var low: number = arr[i - 1];
var high: number = (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.
*/
public roundTo(value: number, place: number = 0, base: number = 10): number {
var p: number = Math.pow(base, -place);
return Math.round(value * p) / p;
}
public floorTo(value: number, place: number = 0, base: number = 10): number {
var p: number = Math.pow(base, -place);
return Math.floor(value * p) / p;
}
public ceilTo(value: number, place: number = 0, base: number = 10): number {
var p: number = Math.pow(base, -place);
return Math.ceil(value * p) / p;
}
/**
* a one dimensional linear interpolation of a value.
*/
public interpolateFloat(a: number, b: number, weight: number): number {
return (b - a) * weight + a;
}
/**
* convert radians to degrees
*/
public radiansToDegrees(angle: number): number {
return angle * GameMath.RAD_TO_DEG;
}
/**
* convert degrees to radians
*/
public degreesToRadians(angle: number): number {
return angle * GameMath.DEG_TO_RAD;
}
/**
* Find the angle of a segment from (x1, y1) -> (x2, y2 )
*/
public angleBetween(x1: number, y1: number, x2: number, y2: number): number {
return Math.atan2(y2 - y1, x2 - x1);
}
/**
* set an angle with in the bounds of -PI to PI
*/
public normalizeAngle(angle: number, radians: bool = true): number {
var rd: number = (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
*/
public nearestAngleBetween(a1: number, a2: number, radians: bool = true): number {
var rd: number = (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;
}
/**
* normalizes independent and then sets dep to the nearest value respective to independent
*
* for instance if dep=-170 and ind=170 then 190 will be returned as an alternative to -170
*/
public normalizeAngleToAnother(dep: number, ind: number, radians: bool = true): number {
return ind + this.nearestAngleBetween(ind, dep, radians);
}
/**
* normalize independent and dependent and then set dependent to an angle relative to 'after/clockwise' independent
*
* for instance dep=-170 and ind=170, then 190 will be reutrned as alternative to -170
*/
public normalizeAngleAfterAnother(dep: number, ind: number, radians: bool = true): number {
dep = this.normalizeAngle(dep - ind, radians);
return ind + dep;
}
/**
* normalizes indendent and dependent and then sets dependent to an angle relative to 'before/counterclockwise' independent
*
* for instance dep = 190 and ind = 170, then -170 will be returned as an alternative to 190
*/
public normalizeAngleBeforeAnother(dep: number, ind: number, radians: bool = true): number {
dep = this.normalizeAngle(ind - dep, radians);
return ind - dep;
}
/**
* interpolate across the shortest arc between two angles
*/
public interpolateAngles(a1: number, a2: number, weight: number, radians: bool = true, ease = null): number {
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);
}
/**
* Compute the logarithm of any value of any base
*
* a logarithm is the exponent that some constant (base) would have to be raised to
* to be equal to value.
*
* i.e.
* 4 ^ x = 16
* can be rewritten as to solve for x
* logB4(16) = x
* which with this function would be
* LoDMath.logBaseOf(16,4)
*
* which would return 2, because 4^2 = 16
*/
public logBaseOf(value: number, base: number): number {
return Math.log(value) / Math.log(base);
}
/**
* Greatest Common Denominator using Euclid's algorithm
*/
public GCD(m: number, n: number): number {
var r: number;
//make sure positive, GCD is always positive
m = Math.abs(m);
n = Math.abs(n);
//m must be >= n
if (m < n)
{
r = m;
m = n;
n = r;
}
//now start loop
while (true)
{
r = m % n;
if (!r) return n;
m = n;
n = r;
}
return 1;
}
/**
* Lowest Common Multiple
*/
public LCM(m: number, n: number): number {
return (m * n) / this.GCD(m, n);
}
/**
* Factorial - N!
*
* simple product series
*
* by definition:
* 0! == 1
*/
public factorial(value: number): number {
if (value == 0) return 1;
var res: number = value;
while (--value)
{
res *= value;
}
return res;
}
/**
* gamma function
*
* defined: gamma(N) == (N - 1)!
*/
public gammaFunction(value: number): number {
return this.factorial(value - 1);
}
/**
* falling factorial
*
* defined: (N)! / (N - x)!
*
* written subscript: (N)x OR (base)exp
*/
public fallingFactorial(base: number, exp: number): number {
return this.factorial(base) / this.factorial(base - exp);
}
/**
* rising factorial
*
* defined: (N + x - 1)! / (N - 1)!
*
* written superscript N^(x) OR base^(exp)
*/
public risingFactorial(base: number, exp: number): number {
//expanded from gammaFunction for speed
return this.factorial(base + exp - 1) / this.factorial(base - 1);
}
/**
* binomial coefficient
*
* defined: N! / (k!(N-k)!)
* reduced: N! / (N-k)! == (N)k (fallingfactorial)
* reduced: (N)k / k!
*/
public binCoef(n: number, k: number): number {
return this.fallingFactorial(n, k) / this.factorial(k);
}
/**
* rising binomial coefficient
*
* as one can notice in the analysis of binCoef(...) that
* binCoef is the (N)k divided by k!. Similarly rising binCoef
* is merely N^(k) / k!
*/
public risingBinCoef(n: number, k: number): number {
return this.risingFactorial(n, k) / this.factorial(k);
}
/**
* Generate a random boolean 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
*/
public chanceRoll(chance: number = 50): bool {
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
*/
public maxAdd(value: number, amount: number, max: number): number {
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
*/
public minSub(value: number, amount: number, min: number): number {
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
*/
public wrapValue(value: number, amount: number, max: number): number {
var diff: number;
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
*/
public randomSign(): number {
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.
*/
public isOdd(n: number): bool {
if (n & 1)
{
return true;
}
else
{
return false;
}
}
/**
* 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.
*/
public isEven(n: number): bool {
if (n & 1)
{
return false;
}
else
{
return true;
}
}
/**
* 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
*/
public wrapAngle(angle: number): number {
var result: number = 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
*/
public angleLimit(angle: number, min: number, max: number): number {
var result: number = angle;
if (angle > max)
{
result = max;
}
else if (angle < min)
{
result = min;
}
return result;
}
/**
* @method linear
* @param {Any} v
* @param {Any} k
* @static
*/
public linearInterpolation(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 Bezier
* @param {Any} v
* @param {Any} k
* @static
*/
public bezierInterpolation(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 CatmullRom
* @param {Any} v
* @param {Any} k
* @static
*/
public catmullRomInterpolation(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
* @static
*/
public linear(p0, p1, t) {
return (p1 - p0) * t + p0;
}
/**
* @method Bernstein
* @param {Any} n
* @param {Any} i
* @static
*/
public bernstein(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
* @static
*/
public catmullRom(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;
}
public difference(a: number, b: number): number {
return Math.abs(a - b);
}
/**
* A tween-like function that takes a starting velocity
* and some other factors and returns an altered velocity.
*
* @param Velocity Any component of velocity (e.g. 20).
* @param Acceleration Rate at which the velocity is changing.
* @param Drag Really kind of a deceleration, this is how much the velocity changes if Acceleration is not set.
* @param Max An absolute value cap for the velocity.
*
* @return The altered Velocity value.
*/
public computeVelocity(Velocity: number, Acceleration: number = 0, Drag: number = 0, Max: number = 10000): number {
if (Acceleration !== 0)
{
Velocity += Acceleration * this._game.time.elapsed;
}
else if (Drag !== 0)
{
var drag: number = Drag * this._game.time.elapsed;
if (Velocity - drag > 0)
{
Velocity = Velocity - drag;
}
else if (Velocity + drag < 0)
{
Velocity += drag;
}
else
{
Velocity = 0;
}
}
if ((Velocity != 0) && (Max != 10000))
{
if (Velocity > Max)
{
Velocity = Max;
}
else if (Velocity < -Max)
{
Velocity = -Max;
}
}
return Velocity;
}
/**
* Given the angle and speed calculate the velocity and return it as a Point
*
* @param angle The angle (in degrees) calculated in clockwise positive direction (down = 90 degrees positive, right = 0 degrees positive, up = 90 degrees negative)
* @param speed The speed it will move, in pixels per second sq
*
* @return A Point where Point.x contains the velocity x value and Point.y contains the velocity y value
*/
public velocityFromAngle(angle: number, speed: number): Point {
var a: number = this.degreesToRadians(angle);
return new Point((Math.cos(a) * speed), (Math.sin(a) * speed));
}
/**
* The global random number generator seed (for deterministic behavior in recordings and saves).
*/
public globalSeed: number = Math.random();
/**
* Generates a random number. Deterministic, meaning safe
* to use if you want to record replays in random environments.
*
* @return A Number between 0 and 1.
*/
public random(): number {
return this.globalSeed = this.srand(this.globalSeed);
}
/**
* Generates a random number based on the seed provided.
*
* @param Seed A number between 0 and 1, used to generate a predictable random number (very optional).
*
* @return A Number between 0 and 1.
*/
public srand(Seed: number): number {
return ((69621 * (Seed * 0x7FFFFFFF)) % 0x7FFFFFFF) / 0x7FFFFFFF;
}
/**
* Fetch a random entry from the given array.
* Will return null if random selection is missing, or array has no entries.
* FlxG.getRandom() is deterministic and safe for use with replays/recordings.
* HOWEVER, FlxU.getRandom() is NOT deterministic and unsafe for use with replays/recordings.
*
* @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.
*/
public getRandom(Objects, StartIndex: number = 0, Length: number = 0) {
if (Objects != null)
{
var l: number = 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.
*/
public floor(Value: number): number {
var n: number = 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.
*/
public ceil(Value: number): number {
var n: number = Value|0;
return (Value > 0) ? ((n != Value) ? (n + 1) : (n)) : (n);
}
}