By Zevan | April 10, 2009
Actionscript:
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var xn:Number = 1;
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var xn1:Number = 0
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var square:Number =39;
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trace("find the sqrt of ", square);
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trace("Math.sqrt: ", Math.sqrt(square))
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// no starting approximation, just try up to 35 iterations
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for(var i:int = 0; i<35; i++){
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xn1 = .5 * (xn + square / xn);
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if (xn1== xn){
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trace("other sqrt: ", xn1);
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break;
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}
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xn = xn1;
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}
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/*outputs
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find the sqrt of 39
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Math.sqrt: 6.244997998398398
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other sqrt: 6.244997998398398
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*/
I was reading about calculating square roots - not for speed optimization purposes, just to see some of the different ways to go about it. The above snippet uses the Babylonian method to find the square root of a number. I left out the first step of guessing at the square root... so this snippet is by no means efficient...
Posted in Math | Also tagged actionscript |
Actionscript:
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// Superformula (equations from):
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// http://www.geniaal.be/downloads/AMJBOT.pdf
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// http://en.wikipedia.org/wiki/Superformula
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const TWO_PI:Number = Math.PI * 2;
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function superShape(a:Number, b:Number, m:Number, n1:Number, n2:Number, n3:Number, pnt:Point, scale:Number):void{
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var r:Number = 0
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var p:Number = 0;
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var xp:Number = 0, yp:Number = 0;
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while(p <= TWO_PI){
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var ang:Number = m * p / 4;
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with(Math){
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r = pow(pow(abs(cos(ang) / a), n2) + pow(abs(sin(ang) / b), n3),-1/n1);
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xp = r * cos(p);
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yp = r * sin(p);
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}
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p += .01;
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canvas.setPixel(pnt.x + xp *scale, pnt.y + yp * scale, 0xFFFFFF);
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}
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}
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// test it out:
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var canvas:BitmapData = new BitmapData(700,600,false, 0x000000);
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addChild(new Bitmap(canvas, "auto", true));
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superShape(1, 1, 5, 23, 23, 23, new Point(100,80), 30);
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superShape(1, 1, 5, 13, 13, 3, new Point(200,80), 30);
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superShape(1, 1, 8, 3, 13, 3, new Point(300,80), 30);
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superShape(10,8, 16, 30, 13, 3, new Point(450,80), 30);
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superShape(1,1, 1, .5, .5, .5, new Point(100,190), 100);
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for (var i:int = 0; i <150; i++){
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superShape(1,1, 2, 1+i/800, 4, 8-i * .1, new Point(550,350), 50);
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}
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for (i = 0; i <20; i++){
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superShape(1.1,1.2, 6, 2 + i , 4, 9 - i, new Point(200,350), 50);
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}
The above snippet demos a function that will draw Supershapes using the Superformula...
From wikipedia:
The Superformula appeared in a work by Johan Gielis. It was obtained by generalizing the superellipse, named and popularized by Piet Hein...
Here is the result of the above code:
You can read more about the Superformula here in the original paper by Gielis.
wikipedia entry...
3d Supershapes by Paul Bourke
Actionscript:
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var target:Number = 1024;
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var slices:Array = [target];
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var leng:int = 11;
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for (var i:int = 0; i<leng-1; i++){
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var index:int = int(Math.random()*slices.length);
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var val:Number = slices[index];
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var rand:Number = Math.random() * val/2;
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slices[index] = val - rand;
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slices.push(rand);
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}
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trace(slices);
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// test that they all add up
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var sum:Number = 0;
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for (i = 0; i<slices.length; i++){
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sum += slices[i];
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}
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trace("test that they all add up: ", sum);
The above snippet creates an array of a specified length whose elements all add up to the variable target. Here is some example output:
165.31133050055192,322.23456030456015,
257.47582363389245,26.9984893942173,1.96283924962002,
5.466277873168191,21.362282634705164,62.68168197512457,
76.63028224500404,36.27274381401516,12.558309228795265,35.04537914634583
test that they all add up: 1024
Posted in arrays, misc | Also tagged actionscript |
Actionscript:
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var target:Number = 360;
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var steps:Array = new Array();
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for (var step:Number = 0; step <target; step += int(Math.random() * 36 + 36)){
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steps.push(Math.min(target,step));
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}
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steps.push(target);
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trace(steps);
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/* outputs something similar to:
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0,46,99,144,189,259,330,360
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*/
This is something I've had to do a few times recently.... it randomly steps a number toward a given target...
Posted in arrays, misc | Also tagged actionscript |