Actionscript:
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var canvas:BitmapData=new BitmapData(400,400,false,0xCCCCCC);
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addChild(new Bitmap(canvas));
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var a:Number=-1.21;
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var r:Rectangle=new Rectangle(0,0,3,5);
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var halfWidth:Number=canvas.width/2;
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var halfHeight:Number=canvas.height/2;
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render();
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function render():void{
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for (var x:Number = -2; x<=2; x+=.05) {
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for (var y:Number = -2; y<=2; y+=.05) {
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// equation from : http://en.wikipedia.org/wiki/Bicuspid_curve
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//(x^2 - a^2) * (x - a)^2 + (y^2 - a^2) * (y^2 - a^2) = 0
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// unpoptimized:
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// var e:Number = (x*x - a*a) * (x-a)*(x-a) + (y*y-a*a) * (y*y-a*a);
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// optimized:
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var x_a:Number=x-a;
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// factoring: x^2 - a^2 = (x + a) * (x - a)
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var y2_a2:Number = (y + a) * (y - a);
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var e:Number = (x + a) * x_a * x_a * x_a + y2_a2 * y2_a2;
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// tolerance beetween .7 & -.1;
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if (e<.7&&e>-.1) {
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r.x=halfWidth+y*50;
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r.y=halfHeight-x*100;
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canvas.fillRect(r, 0x000000);
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}
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}
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}
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}
I've been looking for a single math equation to draw a tooth for sometime.... today I stumbled upon this... and realized it could probably be changed to look more like a tooth.
This snippet will draw this:
I'm using a graphing method here that allows me to use the Cartesian form of the equation and not the parameteric... I'll explain a bit more about this in a later post.
Also posted in BitmapData | Tagged actionscript, flash |
By Zevan | March 31, 2009
Actionscript:
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var canvas:BitmapData = new BitmapData(400,400,false, 0x000000);
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addChild(new Bitmap(canvas));
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var pnts:Array = new Array();
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// make control points
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for (var i:int = 0; i<5; i++){
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var t:Number = i * 72 * Math.PI /180;
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pnts.push(dot(200 + 100 * Math.cos(t),200 +100 * Math.sin(t)));
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}
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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canvas.lock();
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canvas.fillRect(canvas.rect, 0x000000);
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curve(pnts);
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canvas.unlock();
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}
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function tangent(pk1:Sprite, pk_1:Sprite){
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return new Point((pk1.x - pk_1.x) / 2, (pk1.y - pk_1.y) / 2);
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}
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// all math from http://en.wikipedia.org/wiki/Cubic_Hermite_spline
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function curve(p:Array, res:Number=.03):void{
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var px:Number = 0;
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var py:Number = 0;
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var pIter:int = p.length - 1;
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var m:Array = [];
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m[0] = tangent(p[1] , p[pIter]);
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for (var i:int = 1; i<pIter; i++){
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m[i] = tangent(p[i + 1], p[i - 1]);
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}
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m[pIter] = tangent(p[0],p[pIter-1]);
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for (var t:Number = 0; t <1; t+=res){
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var t_2:Number = t * t;
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var _1_t:Number = 1 - t;
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var _2t:Number = 2 * t;
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var h00:Number = (1 + _2t) * (_1_t) * (_1_t);
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var h10:Number = t * (_1_t) * (_1_t);
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var h01:Number = t_2 * (3 - _2t);
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var h11:Number = t_2 * (t - 1);
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for (var k:int = 0; k <pIter; k++){
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var k1:int = k + 1;
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var pk:Sprite = p[k];
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var pk1:Sprite = p[k1];
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var mk:Point = m[k];
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var mk1:Point = m[k1];
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px = h00 * pk.x + h10 * mk.x + h01 * pk1.x + h11 * mk1.x;
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py = h00 * pk.y + h10 * mk.y + h01 * pk1.y + h11 * mk1.y;
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canvas.setPixel(px, py, 0xFFFFFF);
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}
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pk = p[k];
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pk1 = p[0];
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mk = m[k];
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mk1= m[0];
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px = h00 * pk.x + h10 * mk.x + h01 * pk1.x + h11 * mk1.x;
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py = h00 * pk.y + h10 * mk.y + h01 * pk1.y + h11 * mk1.y;
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canvas.setPixel(px, py, 0xFFFFFF);
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}
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}
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// draggable dot
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function dot(xp:Number, yp:Number, col:uint = 0xFF0000, rad:Number=4):Sprite {
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var s:Sprite = Sprite(addChild(new Sprite));
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s.x = xp;
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s.y = yp;
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with(s.graphics) beginFill(col), drawCircle(0,0,rad);
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s.buttonMode = true;
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s.addEventListener(MouseEvent.MOUSE_DOWN, onDrag);
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return s;
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}
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function onDrag(evt:MouseEvent):void {
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evt.currentTarget.startDrag()
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}
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stage.addEventListener(MouseEvent.MOUSE_UP, onUp);
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function onUp(evt:MouseEvent):void{
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stopDrag();
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}
This a variation on a post from a few days ago. This shows how to create a closed Catmull Rom spline.
See the other Catmull-Rom related Posts
By Zevan | March 30, 2009
Actionscript:
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x=stage.stageWidth/2;
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y=stage.stageHeight/2;
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var xp:Number = 0, yp:Number = 0;
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var r:Number = 0, t:Number = 0;
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var speed:Number=.1;
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var range:Number=.2;
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var b:Number = 20;
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var a:Number = b * range;
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var orbit:Number = 2 * Math.PI + speed;
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graphics.lineStyle(0,0x000000);
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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var sin:Number=Math.sin(t);
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r = Math.sqrt(4 * b * (a - b * (sin * sin)));
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xp= r * Math.cos(t);
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yp= r * sin;
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if (t==0) {
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graphics.moveTo(xp, yp);
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} else {
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graphics.lineTo(xp, yp);
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}
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-
t += speed;
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-
if (t> orbit) {
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range += .5;
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a= b * range;
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t= 0;
-
}
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}
The above draws a Hippopede
Also posted in Graphics, motion | Tagged actionscript, flash |
By Zevan | March 29, 2009
Actionscript:
-
x = stage.stageWidth / 2;
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y = stage.stageHeight / 2;
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var xp:Number = 0, yp:Number = 0;
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var r:Number = 0, t:Number = 0;
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var speed:Number = .07;
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var scale:Number = 20;
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var plot0:Shape = Shape(addChild(new Shape()));
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var plot1:Shape = Shape(addChild(new Shape()));
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plot0.graphics.lineStyle(0,0x000000);
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plot1.graphics.lineStyle(0,0x000000);
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addEventListener(Event.ENTER_FRAME, onLoop);
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function onLoop(evt:Event):void {
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r = scale * Math.sqrt(t);
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xp = r * Math.cos(t);
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yp = r * Math.sin(t);
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t += speed;
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-
plot0.graphics.lineTo(xp, yp);
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plot1.graphics.lineTo(-xp, -yp);
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}
This snippet draws Fermat's Spiral.
Also posted in Graphics, motion | Tagged actionscript, flash |