Useful mathematical formulas in ActionScript 3

We have listed 12 very simple,basic but useful function source in Flex in the previous article. The mathematical calculation will be used regularly in our Flash applications, we can easily find the open source libraries like 30+ useful as3 open source projects, but it’s superfluous when we only need calculate the distance between two points, or only want to get the circle area. Here is the list of 18 useful AS3 arithmetic & formulas. Have any proudly and recommendable? Leave your comments to share please.

1. Distance Between Two Points

dx = x2 – x1;
  dy = y2 – y1;
  dist = Math.sqrt(dx*dx + dy*dy);

2. Inching Formulas

sprite.x += (targetX – sprite.x) * easing;//easing: inching coefficient
  sprite.y += (targetY – sprite.y) * easing;

3. Elastic Formulas

vx += (targetX – sprite.x) * spring; //spring: elastic coefficient
  vy += (targetY – sprite.y) * spring;
  sprite.x += (vx *= friction); //friction: friction force
  sprite.y += (vy *= friction);

4. Flexible Partial Shifts Formulas

var dx:Number = sprite.x – fixedX;
  var dy:Number = sprite.y – fixedY;
  var angle:Number = Math.atan2(dy, dx);
  var targetX:Number = fixedX + Math.cos(angle) * springLength;
  var targetY:Number = fixedX + Math.sin(angle) * springLength;

5. Rotation With Mouse Formulas

dx = mouseX – sprite.x;
  dy = mouseY – sprite.y;
  sprite.rotation = Math.atan2(dy, dx) * 180 / Math.PI;

6. Waveform Formulas

public function onEnterFrame1(event:Event):void {
   ball.y=centerScale+Math.sin(angle)*range;
   angle+=speed;
  }

7. Heartthrob Formulas

public function onEnterFrame1(event:Event):void {
   ball.scaleX=centerScale+Math.sin(angle)*range;
   ball.scaleY=centerScale+Math.sin(angle)*range;
   angle+=speed;
  }

8. Circle Rotation Formulas

public function onEnterFrame(event:Event):void {
   ball.x=centerX+Math.cos(angle)*radius;
   ball.y=centerY+Math.sin(angle)*radius;
   angle+=speed;
  }

9. Get Circle Area

public function getArea():Number
  {
   // The formula is Pi times the radius squared.
   return Math.PI * Math.pow((width / 2), 2);
  }

10. Get Circumference Ratio

public function getCircumference():Number
  {
   // The formula is Pi times the diameter.
   return Math.PI * width;
  }

11. Elliptic Rotation Formulas

public function onEnterFrame(event:Event):void {
   ball.x=centerX+Math.cos(angle)*radiusX;
   ball.y=centerY+Math.sin(angle)*radiusY;
   angle+=speed;
  }

12. Color operations

var t:uint=0×77ff8877
  var s:uint=0xff000000
  var h:uint=t&s
  var m:uint=h>>>24
  trace(m);

13. Hex to Decimal

trace(hexValue);

14. Decimal to Hex

decimalValue.toString(16);

15. Pick Up Color

red = color24 >> 16;
  green = color24 >> 8 & 0xFF;
  blue = color24 & 0xFF;
  alpha = color32 >> 24;
  red = color32 >> 16 & 0xFF;
  green = color32 >> 8 & 0xFF;
  blue = color232 & 0xFF;

16. Color Bit Arithmetic

color24 = red << 16 | green << 8 | blue;
  color32 = alpha << 24 | red << 16 | green << 8 | blue;

17. Percent of a Number

/**
   * Comparing the present with a series of numbers, provided the per cent over the range of those
   * @param start
   * @param end
   * @param current
   * @return percent of the number 0 - 100 if the start
   */
  public static function coPercent(c:Number, s:Number = 0, e:Number = 100):Number {
   return (((e - s) - (e - c))/(e - s)) * 100;
  }
  //50 -> 400 ~ 100%
  //50 -> 200 ~ ? % 
  // cal: 42.8%
  //percent = NumberUtilities.coPercent(200, 50, 400);
  //trace(percent); // 42.857142857142854

18. Number of a percent

/**
   * Percentage change from the current number
   * @param percent
   * @param start
   * @param end
   * @return
   */
  public static function dePercent(p:Number, s:Number = 0, e:Number = 100):Number {
   return (e - ((e - s) - ((p/100) * (e - s))));
  }
  //100% ~ 50 - 400
  //42.8%~ 50 - ?
  // cal: 200
  //number = NumberUtilities.dePercent(42.8, 50, 400);
  //trace(number); // ~200

For demo 17 - 18:

19. Number of factorial

/**
   * The term n! (pronounced n factorial) means multiply together all the whole numbers from 1 to n
   * @param n, remember 0! = 1
   * @return n!
   */
  public function factorial(n:Number):Number{
   var k:Number=1;
   for (var i:int = 1; i <= n; i++) k = k * i;
   return k;
  } 
//5! = 1 x 2 x 3 x 4 x 5 = 120

20. Number of factorial

/**
   * The number of ways of selecting r objects from a total of n is written as
   * @param n
   * @param r
   * @return
   */
  public function combinatorics(n:Number, r:Number):Number {
   return factorial(n) / (factorial(r) * factorial(n - r));
  }
//5C0 = 1
//5C1 = 5
//5C2 = 10
//5C3 = 10
//5C4 = 5
//5C5 = 1

21. Pascal's Triangle

/**
   * Pascal's Triangle
   * @param n
   * @param r
   * @return
   */
  public function pascal(n:Number, r:Number):Number{ 
   if (n > 1 && r > 0 && r < n) {
    var a:Number = pascal(n - 1, r - 1);
    var b:Number = pascal(n - 1, r);
    var c:Number = a + b;
    return c;
   }
   return 1;
  }
//(1 + x)3 = 3C0 + 3C1x + 3C2x2 + 3C3x3

	0	1	2	3	4	5	6
0	1	1	1	1	1	1	1
1	1	2	3	4	5	6
2	1	3	6	10	15
3	1	4	10	20
4	1	5	15
5	1	6
6	1