By Zevan | November 29, 2009
Actionscript:
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// print some floats as fractions
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printFraction(0.5);
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printFraction(0.75);
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printFraction(0.48);
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// try something a little more complex
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var float:Number = 0.98765432;
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trace("\na more complex example:");
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printFraction(float);
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var frac:Array = asFraction(float);
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trace("double check it:");
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trace(frac[0] + "/" + frac[1] +" = " + frac[0] / frac[1]);
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/* outputs:
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0.5 = 1/2
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0.75 = 3/4
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0.48 = 12/25
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-
a more complex example:
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0.98765432 = 12345679/12500000
-
double check it:
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12345679/12500000 = 0.98765432
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*/
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-
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function printFraction(n:Number):void{
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var frac:Array = asFraction(n);
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trace(n + " = " + frac[0] + "/" + frac[1]);
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}
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// takes any value less than one and returns an array
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// with the numerator at index 0 and the denominator at index 1
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function asFraction(num:Number):Array{
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var decimalPlaces:int = num.toString().split(".")[1].length;
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var denom:Number = Math.pow(10, decimalPlaces);
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return reduceFraction(num * denom, denom);
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}
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// divide the numerator and denominator by the GCF
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function reduceFraction(numerator:int, denominator:Number):Array{
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// divide by the greatest common factor
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var divisor:int = gcf(numerator, denominator);
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if (divisor){
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numerator /= divisor;
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denominator /= divisor;
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}
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return [numerator, denominator];
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}
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// get the greatest common factor of two integers
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function gcf(a:int, b:int):int{
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var remainder:int;
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var factor:Number = 0;
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var maxIter:int = 100;
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var i:int = 0;
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while (1){
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if (b> a){
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var swap:int = a;
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a = b;
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b = swap;
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}
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remainder = a % b;
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a = b;
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b = remainder
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if (remainder == 0){
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factor = a;
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break;
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}else if (remainder==1){
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break;
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}else if (i> maxIter){
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trace("failed to calculate gcf");
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break;
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}
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i++;
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}
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return factor;
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}
This snippet contains a few functions for calculating fractions based on float values. Writing this brought back some memories from grade school math.
Posted in Math, misc | Also tagged actionscript, as3 |
By Zevan | November 28, 2009
Actionscript:
-
trace(gcf(75,145));
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// outputs 5
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function gcf(a:int, b:int):int{
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var remainder:int;
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var factor:Number = 0;
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while (1){
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if (b> a){
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var swap:int = a;
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a = b;
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b = swap;
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}
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remainder = a % b;
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a = b;
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b = remainder
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if (remainder == 0){
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factor = a;
-
break;
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}else if (remainder==1){
-
-
break;
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}
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}
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return factor;
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}
I was messing around with Egyptian Fractions and found myself in need of some interesting functions. The first function I realized I would be needing was for a greatest common factor (GCF or GCD).
The above snippet is a quick implementation of Euclid's algorithm. It will return 0 if no GCF is found...
I wrote a few helper functions while working with Egyptian fractions... will post them over the next few days.
Posted in Math | Also tagged actionscript, as3 |
By Zevan | November 27, 2009
Actionscript:
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egyptianMultiply(12, 99);
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// trace(12 * 99) // test to make sure it works
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/* outputs:
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/64 768
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/32 384
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16 192
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8 96
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4 48
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/2 24
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/1 12
-
---
-
1188
-
*/
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-
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function egyptianMultiply(valueA:Number, valueB:Number):void {
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var left:Array = [];
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var right:Array = []
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// swap if valueB is smaller than value A
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if (valueB <valueA){
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var swap:int = valueB;
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valueB = valueA;
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valueA = swap;
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}
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// create left and right columns
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var currentLeft:int = 1;
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var currentRight:int = valueA;
-
-
while (currentLeft <valueB){
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left.push(currentLeft);
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right.push(currentRight);
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currentRight += currentRight;
-
currentLeft += currentLeft;
-
}
-
-
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// add up the right column based on the left
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currentLeft = 0;
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var rightSum:int;
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var leftSum:int;
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var i:int = left.length - 1;
-
-
while (currentLeft != valueB){
-
-
leftSum = currentLeft + left[i];
-
// if the next number causes the sum
-
// to go above valueB, skip it
-
if (leftSum <= valueB){
-
currentLeft = leftSum;
-
rightSum += right[i];
-
trace("/" + left[i] + " " + right[i]);
-
} else {
-
trace(" " + left[i] + " " + right[i]);
-
}
-
i--;
-
}
-
trace("---");
-
trace(rightSum);
-
}
Someone mentioned egyptian multiplication to me yesterday... So read a little about it here and whipped up this example. For some reason I decided to do it in processing ... once it worked I ported it to ActionScript.
The above link describing the technique I used is from http://www.jimloy.com/... I haven't spent much time digging around the site, but it appears to have some pretty nice stuff on it...
If you're curious, here is the original processing version:
JAVA:
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-
-
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int valueA = 10;
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int valueB = 8;
-
-
if (valueB <valueA){
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int swap = valueB;
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valueB = valueA;
-
valueA = swap;
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}
-
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int currentLeft = 1;
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int currentRight = valueA;
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while (currentLeft <valueB){
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left.add(currentLeft);
-
right.add(currentRight);
-
currentRight += currentRight;
-
currentLeft += currentLeft;
-
}
-
-
currentLeft = 0;
-
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int result = 0;
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int i = left.size() - 1;
-
while (currentLeft != valueB){
-
-
int temp
= currentLeft
+ (Integer) left.
get(i
);
-
if (temp <= valueB){
-
-
currentLeft = temp;
-
-
println("/" + left.get(i) + " " + right.get(i));
-
} else {
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println(" " + left.get(i) + " " + right.get(i));
-
}
-
-
i--;
-
}
-
println("---");
-
println(result);
After writing, this I took a look at the wikipedia entry... I also found myself on this short page about a scribe called Ahmes. (I recommend reading this if you are interested in PI)
Posted in Math, misc | Also tagged actionscript, as3, processing |
By Zevan | November 25, 2009
Actionscript:
-
var container:Sprite = new Sprite();
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container.x = stage.stageWidth / 2;
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container.y = stage.stageHeight / 2;
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addChild(container);
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-
var redBox:Sprite = new Sprite();
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redBox.graphics.beginFill(0xFF0000);
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redBox.graphics.drawRect(-50,-250,100,500);
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redBox.rotationZ = 10;
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container.addChild(redBox);
-
-
var logos:Array = []
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var elements:Array = [];
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elements.push({element:redBox, z:0});
-
-
// add the logos
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for (var i:int = 0; i<6; i++){
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var logoContainer:MovieClip = new MovieClip();
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var logoText:TextField = new TextField();
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logoText.defaultTextFormat = new TextFormat("_sans", 50);
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logoText.text = "LOGO";
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logoText.autoSize = "left";
-
logoText.selectable= false;
-
-
logoText.x = -logoText.width / 2;
-
logoText.y = -logoText.height / 2;
-
logoContainer.addChild(logoText);
-
logoText.backgroundColor = 0xFFFFFF;
-
-
container.addChild(logoContainer);
-
logos.push(logoContainer);
-
elements.push({element:logoContainer, z:0});
-
}
-
-
var ang:Number = -Math.PI / 2;
-
var rotationSpeed:Number = 0.05;
-
addEventListener(Event.ENTER_FRAME, onLoop);
-
function onLoop(evt:Event):void {
-
-
var dx:Number = (mouseY - stage.stageHeight / 2) / 10;
-
var dy:Number = (mouseX - stage.stageWidth / 2) / 10;
-
container.rotationX += (dx - container.rotationX) / 4;
-
container.rotationY += (dy - container.rotationY) / 4;
-
-
ang += rotationSpeed;
-
for (var i:int = 0; i<logos.length; i++){
-
var logo:Sprite = logos[i];
-
logo.x = 150 * Math.cos(ang + i);
-
logo.z = 150 * Math.sin(ang + i);
-
logo.alpha = 1 - logo.z / 200;
-
logo.rotationY = -Math.atan2(logo.z, logo.x) / Math.PI * 180 - 90;
-
}
-
-
// z-sort
-
for (i = 0; i<elements.length; i++){
-
elements[i].z = elements[i].element.transform.getRelativeMatrix3D(this).position.z;
-
}
-
-
elements.sortOn("z", Array.NUMERIC | Array.DESCENDING);
-
for (i = 0; i<elements.length; i++) {
-
container.addChild(elements[i].element);
-
}
-
}
A student of mine was having trouble creating a 3D logo for a client. I created this snippet to help explain how some of the fp10 3D stuff works.... z-sorting etc... The code could be optimized a bit... but it works nicely...
Have a look at the swf...
Posted in 3D, misc, motion | Also tagged actionscript, as3, fp10 |