v2: [modded] explicit meta-structure

by bradsedito 18 Aug 2011

• Forked from bradsedito's [modded] explicit meta-structure
• Diff: 1
• Related works: 1
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/**
 * Copyright bradsedito ( http://wonderfl.net/user/bradsedito )
 * MIT License ( http://www.opensource.org/licenses/mit-license.php )
 * Downloaded from: http://wonderfl.net/c/pwGq
 */

// forked from bradsedito's [modded] explicit meta-structure




package {
    import flash.display.Sprite;
    import flash.events.Event;
    import flash.utils.getTimer;
    
    [SWF(backgroundColor="#FFFFFF", frameRate="100")]

    public class CassiniTest extends Sprite {
        public const sW:Number = new Number(stage.stageWidth);
        public const sH:Number = new Number(stage.stageHeight);
        
        public var c1:Cassini = new Cassini;
        public var c2:CassiniMod = new CassiniMod;
        
        public function CassiniTest () {
            addEventListener (Event.ENTER_FRAME, loop);
            this.rotationZ = rotationZ++;
        }
        
        public function loop (e:Event):void {
            var a:Number = 1 + Math.sin (2e-3 * getTimer ());
            var c:Cassini = (c2); 
            var ranges:Vector.<Range> = c.ranges (a);

            graphics.clear ();
            graphics.lineStyle (40);
            var t:int, X:Number, Y:Number;
            for each (var range:Range in ranges) { 
//          //  positive
                X = range.x (0);
                graphics.moveTo((sW/2)+75*X, (sH/2));
                for (t = 1; t < 101; t++) {
                    X = range.x (t / 100);
                    Y = c.y (X, a);
                    graphics.lineTo((sW/2)+75*X, (sH/2) - 75 * Y);
                }
//          //  negative
                X = range.x (0);
                graphics.moveTo((sW/2)+75*X, (sH/2));
                for (t = 1; t < 101; t++) {
                    X = range.x (t / 100);
                    Y = c.y (X, a);
//          //  Changing the (- 75) to a (+ 75) here creates the same effect but with 2 half circles
//          //  Could be useful maybe?                   
                    graphics.lineTo((sW/2)+75*X, (sH/2) + 75 * Y);
                }
            }
        }
    }
}

class Range {
    public var a:Number;
    public var b:Number;
    public function Range (from:Number, to:Number) {
        a = from; b = to;
    }
    public function x (t:Number):Number {
        return a + (b - a) * t;
    }
}


/**
 * Cassini oval, a=0..2, b=1.
 * @see http://paulbourke.net/geometry/egg/
 */
class Cassini {
    public function y (x:Number, a:Number, b:Number = 1):Number {
        var a2:Number = a * a, x2:Number = x * x;
        var D:Number = Math.max (0, 4 * a2 * x2 + b * b);
        var D2:Number = Math.max (0, Math.sqrt (D) - a2 - x2);
        return Math.sqrt (D2);
    }

    /**
     * Assumes b=1.
     */
    public function ranges (a:Number):Vector.<Range> {
        var a2:Number = a * a;
        var D:Number = a2 - 1, D2:Number = a2 + 1;
        if (D > 0) {
            return new <Range> [
                new Range ( -Math.sqrt (D2), -Math.sqrt (D)),
                new Range ( +Math.sqrt (D), +Math.sqrt (D2))
            ];
        }
        return new <Range> [
            new Range ( -Math.sqrt (D2), +Math.sqrt (D2))
        ];
    }
}


//Modified Cassini oval.
class CassiniMod extends Cassini {
    override public function y (x:Number, a:Number, ignore:Number = 1):Number {
        return super.y (x, a, 1 + (a * a + a) / 4);
    }

    override public function ranges (a:Number):Vector.<Range> {
        var a2:Number = a * a;
        var D:Number = 3 * a2 - a - 4, D2:Number = 5 * a2 + a + 4;
        if (D > 0) {
            return new <Range> [
                new Range ( -0.5 * Math.sqrt (D2), -0.5 * Math.sqrt (D)),
                new Range ( +0.5 * Math.sqrt (D), +0.5 * Math.sqrt (D2))
            ];
        }
        return new <Range> [
            new Range ( -0.5 * Math.sqrt (D2), +0.5 * Math.sqrt (D2))
        ];
    }
}