/// /** * Phaser - GameMath * * Adds a set of extra Math functions used through-out Phaser. * Includes methods written by Dylan Engelman and Adam Saltsman. */ module Phaser { export class GameMath { constructor(game: Game) { this.game = game; GameMath.sinA = []; GameMath.cosA = []; for (var i = 0; i < 360; i++) { GameMath.sinA.push(Math.sin(this.degreesToRadians(i))); GameMath.cosA.push(Math.cos(this.degreesToRadians(i))); } } public game: Game; // Pre-calculated tables containing Math.sin(angle) and Math.cos(angle) from -180 to 180 // So sinA[sprite.rotation] would be the same as Math.sin(sprite.rotation) without a call to Math.sin static sinA: number[]; static cosA: number[]; static PI: number = 3.141592653589793; //number pi static PI_2: number = 1.5707963267948965; //PI / 2 OR 90 deg static PI_4: number = 0.7853981633974483; //PI / 4 OR 45 deg static PI_8: number = 0.39269908169872413; //PI / 8 OR 22.5 deg static PI_16: number = 0.19634954084936206; //PI / 16 OR 11.25 deg static TWO_PI: number = 6.283185307179586; //2 * PI OR 180 deg static THREE_PI_2: number = 4.7123889803846895; //3 * PI_2 OR 270 deg static E: number = 2.71828182845905; //number e static LN10: number = 2.302585092994046; //ln(10) static LN2: number = 0.6931471805599453; //ln(2) static LOG10E: number = 0.4342944819032518; //logB10(e) static LOG2E: number = 1.442695040888963387; //logB2(e) static SQRT1_2: number = 0.7071067811865476; //sqrt( 1 / 2 ) static SQRT2: number = 1.4142135623730951; //sqrt( 2 ) static DEG_TO_RAD: number = 0.017453292519943294444444444444444; //PI / 180; static RAD_TO_DEG: number = 57.295779513082325225835265587527; // 180.0 / PI; static B_16: number = 65536;//2^16 static B_31: number = 2147483648;//2^31 static B_32: number = 4294967296;//2^32 static B_48: number = 281474976710656;//2^48 static B_53: number = 9007199254740992;//2^53 !!NOTE!! largest accurate double floating point whole value static B_64: number = 18446744073709551616;//2^64 !!NOTE!! Not accurate see B_53 static ONE_THIRD: number = 0.333333333333333333333333333333333; // 1.0/3.0; static TWO_THIRDS: number = 0.666666666666666666666666666666666; // 2.0/3.0; static ONE_SIXTH: number = 0.166666666666666666666666666666666; // 1.0/6.0; static COS_PI_3: number = 0.86602540378443864676372317075294;//COS( PI / 3 ) static SIN_2PI_3: number = 0.03654595;// SIN( 2*PI/3 ) static CIRCLE_ALPHA: number = 0.5522847498307933984022516322796; //4*(Math.sqrt(2)-1)/3.0; static ON: bool = true; static OFF: bool = false; static SHORT_EPSILON: number = 0.1;//round integer epsilon static PERC_EPSILON: number = 0.001;//percentage epsilon static EPSILON: number = 0.0001;//single float average epsilon static LONG_EPSILON: number = 0.00000001;//arbitrary 8 digit epsilon public cosTable = []; public sinTable = []; 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 within 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 * @public */ 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 * @public */ 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 * @public */ 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 * @public */ public linear(p0, p1, t) { return (p1 - p0) * t + p0; } /** * @method Bernstein * @param {Any} n * @param {Any} i * @public */ 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 * @public */ 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); } /** * 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. */ 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); } /** * 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 */ public sinCosGenerator(length: number, sinAmplitude?: number = 1.0, cosAmplitude?: number = 1.0, frequency?: number = 1.0) { var sin: number = sinAmplitude; var cos: number = cosAmplitude; var frq: number = frequency * Math.PI / length; this.cosTable = []; this.sinTable = []; for (var c: number = 0; c < length; c++) { cos -= sin * frq; sin += cos * frq; this.cosTable[c] = cos; this.sinTable[c] = sin; } return this.sinTable; } /** * Shifts through the sin table data by one value and returns it. * This effectively moves the position of the data from the start to the end of the table. * @return The sin value. */ public shiftSinTable(): number { if (this.sinTable) { var s = this.sinTable.shift(); this.sinTable.push(s); return s; } } /** * Shifts through the cos table data by one value and returns it. * This effectively moves the position of the data from the start to the end of the table. * @return The cos value. */ public shiftCosTable(): number { if (this.cosTable) { var s = this.cosTable.shift(); this.cosTable.push(s); return s; } } /** * Shuffles the data in the given array into a new order * @param array The array to shuffle * @return The array */ public shuffleArray(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 from this Point object to the given Point object. * @method distanceFrom * @param {Point} target - The destination Point object. * @param {Boolean} round - Round the distance to the nearest integer (default false) * @return {Number} The distance between this Point object and the destination Point object. **/ public distanceBetween(x1: number, y1: number, x2: number, y2: number): number { var dx = x1 - x2; var dy = y1 - y2; return Math.sqrt(dx * dx + dy * dy); } /** * Finds the length of the given vector * * @param dx * @param dy * * @return */ public vectorLength(dx: number, dy: number): number { return Math.sqrt(dx * dx + dy * dy); } } }