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1255 lines (1009 loc) · 34.8 KB
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/**
* @author Richard Davey <rich@photonstorm.com>
* @copyright 2016 Photon Storm Ltd.
* @license {@link https://github.com/photonstorm/phaser/blob/master/license.txt|MIT License}
*/
/**
* A collection of useful mathematical functions.
*
* These are normally accessed through `game.math`.
*
* @class Phaser.Math
* @static
* @see {@link Phaser.Utils}
* @see {@link Phaser.ArrayUtils}
*/
Phaser.Math = {
/**
* Twice PI.
* @property {number} Phaser.Math#PI2
* @default ~6.283
*/
PI2: Math.PI * 2,
/**
* Returns a random float in the range `[min, max)`. If these parameters are not in order than they will be put in order.
* Default is 0 for `min` and 1 for `max`.
*
* @method Phaser.Math#random
* @param {number} min - The minimum value. Must be a Number.
* @param {number} max - The maximum value. Must be a Number.
* @return {number} A floating point number between min (inclusive) and max (exclusive).
*/
random: function (min, max) {
if (min === undefined) { min = 0; }
if (max === undefined) { max = 1; }
if (min === max)
{
return min;
}
if (min < max)
{
var temp = min;
min = max;
max = temp;
}
return (Math.random() * (max - min) + min);
},
/**
* Returns a random integer in the range `[min, max]`. If these parameters are not in order than they will be put in order.
* Default is 0 for `min` and 1 for `max`.
*
* @method Phaser.Math#between
* @param {number} min - The minimum value. Must be a Number.
* @param {number} max - The maximum value. Must be a Number.
* @return {number} An integer between min (inclusive) and max (inclusive).
*/
between: function (min, max) {
if (min === undefined) { min = 0; }
if (max === undefined) { max = 1; }
if (min === max)
{
return min;
}
if (min < max)
{
var temp = min;
min = max;
max = temp;
}
min = Math.ceil(min);
max = Math.floor(max);
return Math.floor(Math.random() * (max - min + 1)) + min;
},
/**
* Two number are fuzzyEqual if their difference is less than epsilon.
*
* @method Phaser.Math#fuzzyEqual
* @param {number} a - The first number to compare.
* @param {number} b - The second number to compare.
* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
* @return {boolean} True if |a-b|<epsilon
*/
fuzzyEqual: function (a, b, epsilon) {
if (epsilon === undefined) { epsilon = 0.0001; }
return Math.abs(a - b) < epsilon;
},
/**
* `a` is fuzzyLessThan `b` if it is less than b + epsilon.
*
* @method Phaser.Math#fuzzyLessThan
* @param {number} a - The first number to compare.
* @param {number} b - The second number to compare.
* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
* @return {boolean} True if a<b+epsilon
*/
fuzzyLessThan: function (a, b, epsilon) {
if (epsilon === undefined) { epsilon = 0.0001; }
return a < b + epsilon;
},
/**
* `a` is fuzzyGreaterThan `b` if it is more than b - epsilon.
*
* @method Phaser.Math#fuzzyGreaterThan
* @param {number} a - The first number to compare.
* @param {number} b - The second number to compare.
* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
* @return {boolean} True if a>b+epsilon
*/
fuzzyGreaterThan: function (a, b, epsilon) {
if (epsilon === undefined) { epsilon = 0.0001; }
return a > b - epsilon;
},
/**
* Applies a fuzzy ceil to the given value.
*
* @method Phaser.Math#fuzzyCeil
* @param {number} val - The value to ceil.
* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
* @return {number} ceiling(val-epsilon)
*/
fuzzyCeil: function (val, epsilon) {
if (epsilon === undefined) { epsilon = 0.0001; }
return Math.ceil(val - epsilon);
},
/**
* Applies a fuzzy floor to the given value.
*
* @method Phaser.Math#fuzzyFloor
* @param {number} val - The value to floor.
* @param {number} [epsilon=0.0001] - The epsilon (a small value used in the calculation)
* @return {number} floor(val+epsilon)
*/
fuzzyFloor: function (val, epsilon) {
if (epsilon === undefined) { epsilon = 0.0001; }
return Math.floor(val + epsilon);
},
/**
* Averages all values passed to the function and returns the result.
*
* @method Phaser.Math#average
* @params {...number} The numbers to average
* @return {number} The average of all given values.
*/
average: function () {
var sum = 0;
var len = arguments.length;
for (var i = 0; i < len; i++)
{
sum += (+arguments[i]);
}
return sum / len;
},
/**
* @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=0] - Optional starting offset for gap.
* @return {number} The snapped value.
*/
snapTo: function (input, gap, start) {
if (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=0] - Optional starting offset for gap.
* @return {number} The snapped value.
*/
snapToFloor: function (input, gap, start) {
if (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=0] - Optional starting offset for gap.
* @return {number} The snapped value.
*/
snapToCeil: function (input, gap, start)
1021A
{
if (start === undefined) { start = 0; }
if (gap === 0) {
return input;
}
input -= start;
input = gap * Math.ceil(input / gap);
return start + input;
},
/**
* Round to some place comparative to a `base`, default is 10 for decimal place.
* The `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=0] - The place to round to.
* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
* @return {number} The rounded value.
*/
roundTo: function (value, place, base) {
if (place === undefined) { place = 0; }
if (base === undefined) { base = 10; }
var p = Math.pow(base, -place);
return Math.round(value * p) / p;
},
/**
* Floors to some place comparative to a `base`, default is 10 for decimal place.
* The `place` is represented by the power applied to `base` to get that place.
*
* @method Phaser.Math#floorTo
* @param {number} value - The value to round.
* @param {number} [place=0] - The place to round to.
* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
* @return {number} The rounded value.
*/
floorTo: function (value, place, base) {
if (place === undefined) { place = 0; }
if (base === undefined) { base = 10; }
var p = Math.pow(base, -place);
return Math.floor(value * p) / p;
},
/**
* Ceils to some place comparative to a `base`, default is 10 for decimal place.
* The `place` is represented by the power applied to `base` to get that place.
*
* @method Phaser.Math#ceilTo
* @param {number} value - The value to round.
* @param {number} [place=0] - The place to round to.
* @param {number} [base=10] - The base to round in. Default is 10 for decimal.
* @return {number} The rounded value.
*/
ceilTo: function (value, place, base) {
if (place === undefined) { place = 0; }
if (base === undefined) { base = 10; }
var p = Math.pow(base, -place);
return Math.ceil(value * p) / p;
},
/**
* Rotates currentAngle towards targetAngle, taking the shortest rotation distance.
* The lerp argument is the amount to rotate by in this call.
*
* @method Phaser.Math#rotateToAngle
* @param {number} currentAngle - The current angle, in radians.
* @param {number} targetAngle - The target angle to rotate to, in radians.
* @param {number} [lerp=0.05] - The lerp value to add to the current angle.
* @return {number} The adjusted angle.
*/
rotateToAngle: function (currentAngle, targetAngle, lerp) {
if (lerp === undefined) { lerp = 0.05; }
if (currentAngle === targetAngle)
{
return currentAngle;
}
if (Math.abs(targetAngle - currentAngle) <= lerp || Math.abs(targetAngle - currentAngle) >= (Phaser.Math.PI2 - lerp))
{
currentAngle = targetAngle;
}
else
{
if (Math.abs(targetAngle - currentAngle) > Math.PI)
{
if (targetAngle < currentAngle)
{
targetAngle += Phaser.Math.PI2;
}
else
{
targetAngle -= Phaser.Math.PI2;
}
}
if (targetAngle > currentAngle)
{
currentAngle += lerp;
}
else if (targetAngle < currentAngle)
{
currentAngle -= lerp;
}
}
return currentAngle;
},
/**
* Gets the shortest angle between `angle1` and `angle2`.
* Both angles must be in the range -180 to 180, which is the same clamped
* range that `sprite.angle` uses, so you can pass in two sprite angles to
* this method, and get the shortest angle back between the two of them.
*
* The angle returned will be in the same range. If the returned angle is
* greater than 0 then it's a counter-clockwise rotation, if < 0 then it's
* a clockwise rotation.
*
* @method Phaser.Math#getShortestAngle
* @param {number} angle1 - The first angle. In the range -180 to 180.
* @param {number} angle2 - The second angle. In the range -180 to 180.
* @return {number} The shortest angle, in degrees. If greater than zero it's a counter-clockwise rotation.
*/
getShortestAngle: function (angle1, angle2) {
var difference = angle2 - angle1;
if (difference === 0)
{
return 0;
}
var times = Math.floor((difference - (-180)) / 360);
return difference - (times * 360);
},
/**
* Find the angle of a segment from (x1, y1) -> (x2, y2).
*
* @method Phaser.Math#angleBetween
* @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.
*/
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;