Monthly Archives: March 2009

Circle of Particles

By Zevan | March 17, 2009

Actionscript:

var canvas:BitmapData = new BitmapData(400,400, false, 0xFFFFFF);
addChild(new Bitmap(canvas));
var eraser:BitmapData = new BitmapData(400,400, true, 0x33FFFFFF);
 
var particles:Array = new Array();
for (var i:int = 0; i <1000; i++){
    particles.push(makeParticle());
}
 
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
    canvas.copyPixels(eraser, eraser.rect, new Point(0,0), null, null, true);
    for (var i:int = 0; i <particles.length; i++){
        particles[i]();
    }
}
 
function makeParticle():Function {
    var dx:Number, dy:Number;
    var x:Number = 200;
    var y:Number = 200;
    var vx:Number = Math.random() * 4 - 2;
    var vy:Number = Math.random() * 4 - 2;
    return function():void {
              x += vx;
              y += vy;
              dx = x - 200;
              dy= y - 200;
               if (Math.sqrt((dx * dx) + (dy * dy))> 100){
                 vx *= -1;
                 vy *= -1;
               }
               canvas.setPixel(x, y, 0x000000);
    }
}

This creates a circular area filled with moving particles/pixels. It makes use of yesterdays functional programming techniques.

Posted in BitmapData, functions, motion, setPixel | Tagged actionscript, flash | Leave a comment

Functional Pseudo-Objects

By Zevan | March 16, 2009

CLICK HERE TO COPY

Actionscript:

var moverNum:int = 40;
var movers:Array = new Array();
 
for (var i:int = 0; i<moverNum; i++){
    movers.push(makeMover());
}
 
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
    for (var i:int = 0; i<moverNum; i++){
        movers[i]();
    }
}
 
function makeMover():Function{
    // mover vars & setup
    var xVel:Number = Math.random() * 5 + 1;
    var right:Number = stage.stageWidth + 30;
    var s:Shape = Shape(addChild(new Shape()));
    with(s.graphics) beginFill(0xFF0000), drawCircle(0,0,5);
    s.x = Math.random() * stage.stageWidth;
    s.y = Math.random() * stage.stageHeight;
    // return a "run" function
    return function():void {
         s.x += xVel;
         if (s.x> right){
            s.x = -30; 
         }
    }
}

This snippet creates 40 shapes that move to the right at a random velocity. When they animate off the right hand side of the stage they return from the left.

The makeMover() function has a series of variable definitions related to the x velocity and position of a Shape. The makeMover() function then returns an anonymous function that contains some logic to move the Shape "s". The anonymous function has access to the makeMover() functions temporary variables...

On the main loop we run all of the anonymous functions - animating all the shapes by their random x velocities.

It would be interesting to write the same program using classes and test the for speed differences. My assumption is that anonymous functions are expensive, but it would still be interesting to see...

Posted in functions, motion | Tagged actionscript, flash | Leave a comment

Bezier Intersections (not a snippet)

By Zevan | March 15, 2009

CLICK HERE TO COPY

Actionscript:

var resolution:Number = .03;
var pointNum:int = Math.ceil(1 / resolution);
 
var bezA:Array = new Array();
populateArray(bezA);
var a:Sprite = dot(100, 200);
var b:Sprite = dot(200, 100);
var c:Sprite = dot(300, 200);
 
var bezB:Array = new Array();
populateArray(bezB);
var d:Sprite = dot(300, 100, 0xCCCC00);
var e:Sprite = dot(120, 130, 0xCCCC00);
var f:Sprite = dot(200, 300, 0xCCCC00);
 
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
      with(graphics){
          clear();
          lineStyle(0, 0x000000);
       
          // calc and draw bezier points
          drawBezier(bezA, a, b, c);
          drawBezier(bezB, d, e, f);
          
          // calc collisions
          var intersections:Array = calculateIntersection(bezA, bezB);
          
           // draw collisions
           beginFill(0xFF0000);
           if (intersections.length> 0){
                for (var i:int = 0; i<intersections.length; i++){
                    drawCircle(intersections[i].x, intersections[i].y, 3);
                }
           }
           endFill();
     }
}
 
function populateArray(a:Array):void {
    for (var i:int = 0; i<pointNum; i++){
        a.push(new Point());
    }
}
 
function drawBezier(bez:Array, a:Sprite, b:Sprite, c:Sprite):void{
     with(graphics){
         bezier(bez, a.x, a.y, b.x, b.y, c.x, c.y);
         var leng:Number = bez.length; 
         moveTo(bez[0].x, bez[0].y);
         for (var i:int = 1; i<leng; i++){
             lineTo(bez[i].x, bez[i].y);
         }
     }
}
 
function bezier(bez:Array, x1:Number, y1:Number, x2:Number, y2:Number, x3:Number, y3:Number):void {
            var b:Number, a2:Number, ab2:Number, b2:Number;
            var pnt:Point;
            var inc:int = 0;
            for (var a:Number = 0; a <=1; a+=resolution) {
                b= 1 - a;
                a2 = a * a;
                ab2 = a * b * 2;
                b2 = b * b;
                pnt = bez[inc];
                pnt.x = a2 * x1 + ab2 * x2  + b2 * x3;
                pnt.y = a2 * y1 + ab2 * y2 + b2 * y3;      
                inc++;
            }
}
 
function calculateIntersection(bezA:Array, bezB:Array):Array {
    var intersections:Array = new Array();
    var ip:Point;
    var aLength:int = bezA.length;
    var bLength:int = bezB.length;
    var p1:Point, p2:Point, p3:Point, p4:Point;
    
    // compare all line segments and check for 
    // intersections
    for (var i:int = 1; i<aLength; i++){
        p1 = bezA[i - 1];
        p2 = bezA[i];
        for (var j:int = 1; j<bLength; j++){
            p3 = bezB[j - 1];
            p4 = bezB[j];
            ip = intersection(p1, p2, p3, p4);
            if (ip){
                intersections.push(ip.clone());
            }
        }
    }
    return intersections;
}
 
var ip:Point = new Point();
 
function intersection(p1:Point, p2:Point, p3:Point, p4:Point):Point {
     
    var nx:Number, ny:Number, dn:Number;
    var x4_x3:Number = p4.x - p3.x;
    var pre2:Number = p4.y - p3.y;
    var pre3:Number = p2.x - p1.x;
    var pre4:Number = p2.y - p1.y;
    var pre5:Number = p1.y - p3.y;
    var pre6:Number = p1.x - p3.x;
    
    nx = x4_x3 * pre5 - pre2 * pre6;
    ny = pre3 * pre5 - pre4 * pre6;
    dn = pre2 * pre3 - x4_x3 * pre4;
    
    if (dn == 0){
        return null
    }
    nx /= dn;
    ny /= dn;
    // has intersection
    if(nx>= 0 && nx <= 1 && ny>= 0 && ny <= 1){
        ny = p1.y + nx * pre4;
        nx = p1.x + nx * pre3;
        ip.x = nx;
        ip.y = ny;
    }else{
         return null;
    }
    return ip
}
 
// draggable dot
function dot(xp:Number, yp:Number, col:uint = 0x507399, noDrag:Boolean = false):Sprite {
    var s:Sprite = Sprite(addChild(new Sprite));
    s.x = xp;
    s.y = yp;
    with(s.graphics) beginFill(col), drawCircle(0,0,5);
    if (!noDrag){
        s.buttonMode = true;
       s.addEventListener(MouseEvent.MOUSE_DOWN, onDrag);
    }
    return s;
}
function onDrag(evt:MouseEvent):void {
    evt.currentTarget.startDrag()
}
 
stage.addEventListener(MouseEvent.MOUSE_UP, onUp);
function onUp(evt:MouseEvent):void{
    stopDrag();
}

This is not a snippet, but it uses some functions that could be considered snippets on their own. Take a look at the swf here:

Bezier Intersection Demo

This demo show a brute force method for getting the coordinates of all intersections between two given quadtratic bezier curves. The approach is pretty simple, each bezier is actually made up of a series of line segments. The resolution variable determines how many line segments make up one bezier curve. By default I use a resolution of 0.03 (~34 lines)... the higher the resolution decimal value, the fewer the number of line segments. I then use a slight variation on yesterdays line segment intersection function to test all existing line segments for intersections.

This is a brute for approach with lots of room for improvement. But in the scenario that you only need to check a few bezier curves for intersection this approach works quite nicely. I don't recommend this approach if your trying to create a complex vector drawing tool with boolean vector operations etc...

It's easy to get an idea of the different approaches to this problem with a little googling. One example I found is from Graphics Gems:

http://tog.acm.org/GraphicsGems/gemsiv/curve_isect/

it's been awhile, but I believe this website also contains information related to this topic:

http://algorithmist.wordpress.com/

Posted in Math, bezier | Tagged actionscript, flash | Leave a comment

Line Intersection Part 2 (optimized)

By Zevan | March 14, 2009

CLICK HERE TO COPY

Actionscript:

// optimized line to line intersection test:
// from wikipedia: http://en.wikipedia.org/wiki/Line-line_intersection
// and http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
var ip:Point = new Point();
 
function intersection(p1:Sprite, p2:Sprite, p3:Sprite, p4:Sprite):Point {
    var nx:Number, ny:Number, dn:Number;
    var x4_x3:Number = p4.x - p3.x;
    var y4_y3:Number = p4.y - p3.y;
    var x2_x1:Number = p2.x - p1.x;
    var y2_y1:Number = p2.y - p1.y;
    var x1_x3:Number = p1.x - p3.x;
    var y1_y3:Number = p1.y - p3.y;
    
    nx = x4_x3 * y1_y3 - y4_y3 * x1_x3;
    ny = x2_x1 * y1_y3 - y2_y1 * x1_x3;
    dn = y4_y3 * x2_x1 - x4_x3 * y2_y1;
    
    nx /= dn;
    ny /= dn;
    
    // has intersection
    if(nx>= 0 && nx <= 1 && ny>= 0 && ny <= 1){
        ny = p1.y + nx * y2_y1;
        nx = p1.x + nx * x2_x1;
        ip.x = nx;
        ip.y = ny;
    }else{
        // no intersection
        ip.x = ip.y = -1000;
    }
    return ip
}
 
 
//
// test out the function:
//
 
stage.frameRate = 30;
var a:Sprite = dot();
a.x = a.y = 100;
 
var b:Sprite = dot();
b.x = b.y = 200;
 
var c:Sprite = dot();
c.x = 200
c.y = 100;
 
var d:Sprite = dot();
d.x = 100
d.y = 200;
 
var inter:Sprite = dot(0xFF0000,true);
 
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
    var p:Point = intersection(a, b, c, d);
    inter.x = p.x;
    inter.y = p.y
    
    with(graphics){
        clear();
        lineStyle(0,0x000000);
        moveTo(a.x, a.y);
        lineTo(b.x, b.y);
        moveTo(c.x, c.y);
        lineTo(d.x,d.y);
    }
}
 
// draggable dot
function dot(col:uint = 0x507399, noDrag:Boolean = false):Sprite {
    var s:Sprite = Sprite(addChild(new Sprite));
    with(s.graphics) beginFill(col), drawCircle(0,0,5);
    if (!noDrag){
        s.buttonMode = true;
       s.addEventListener(MouseEvent.MOUSE_DOWN, onDrag);
    }
    return s;
}
function onDrag(evt:MouseEvent):void {
    evt.currentTarget.startDrag()
}
 
stage.addEventListener(MouseEvent.MOUSE_UP, onUp);
function onUp(evt:MouseEvent):void{
    stopDrag();
}

This is a significantly optimized version of yesterdays post. The function intersection() takes four sprites as its arguments. The four arguments could be considered starting points and ending points for two line segments.

The bottleneck in yesterdays post looked something like this;

nx = (p1.x * p2.y - p1.y * p2.x) * (p3.x - p4.x) - (p1.x - p2.x) * (p3.x * p4.y - p3.y * p4.x);
dn = (p1.x - p2.x) * (p3.y - p4.y) - (p1.y - p2.y) * (p3.x - p4.x);
ny = (p1.x * p2.y - p1.y * p2.x) * (p3.y - p4.y) - (p1.y - p2.y) * (p3.x * p4.y - p3.y * p4.x);
return new Point(nx /dn, ny / dn);

nx and ny are the numerators for two fractions both with dn as their denominator.... after taking a look at this page:

http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/

We can simplify things a bit before we start wrapping repetitive math operations up in variables:

CLICK HERE TO COPY

Actionscript:

nx = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x);
// ny = (p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x);
dn = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y);
nx /= dn;
// ny /= dn
ny = p1.y + nx * (p2.y - p1.y);
nx = p1.x + nx * (p2.x - p1.x);
return new Point(nx, ny);

It's important to note here that if we didn't intend to calculate line segments we could exclude the initial calculation of ny.

At this point we're ready to get rid of duplicate math operations by wrapping them in variables. In this case this only includes subtraction:

CLICK HERE TO COPY

Actionscript:

var x4_x3:Number=p4.x-p3.x;
var y4_y3:Number=p4.y-p3.y;
var x2_x1:Number=p2.x-p1.x;
var y2_y1:Number=p2.y-p1.y;
var x1_x3:Number=p1.x-p3.x;
var y1_y3:Number=p1.y-p3.y;
 
nx=x4_x3*y1_y3-y4_y3*x1_x3;
ny=x2_x1*y1_y3-y2_y1*x1_x3;
dn=y4_y3*x2_x1-x4_x3*y2_y1;
 
nx/=dn;
ny/=dn;
 
ny=p1.y+nx*y2_y1;
nx=p1.x+nx*x2_x1;
 
return new Point(nx, ny);

After wrapping repetitive math into variables the only optimization left to be made is related to the instantiation of a new Point(). Instantiation of objects is an expensive process, so it's better to define the point once outside of the intersection() function definition.

In the end our function looks like this:

CLICK HERE TO COPY

Actionscript:

var ip:Point = new Point();
 
function intersection(p1:Sprite, p2:Sprite, p3:Sprite, p4:Sprite):Point {
    var nx:Number, ny:Number, dn:Number;
    var x4_x3:Number = p4.x - p3.x;
    var pre2:Number = p4.y - p3.y;
    var pre3:Number = p2.x - p1.x;
    var pre4:Number = p2.y - p1.y;
    var pre5:Number = p1.y - p3.y;
    var pre6:Number = p1.x - p3.x;
    nx = x4_x3 * pre5 - pre2 * pre6;
    ny = pre3 * pre5 - pre4 * pre6;
    dn = pre2 * pre3 - x4_x3 * pre4;
    nx /= dn;
    ny /= dn;
    // has intersection
    if(nx>= 0 && nx <= 1 && ny>= 0 && ny <= 1){
        ny = p1.y + nx * pre4;
        nx = p1.x + nx * pre3;
        ip.x = nx;
        ip.y = ny;
    }else{
        // no intersection
        ip.x = ip.y = -1000;
    }
    return ip
}

The final version contains a conditional that checks the end values of nx and ny, if they are between 0 and 1 then we know that there is an intersection between the segments.

Note: Optimized code usually breaks some best practices... as best practices are usually geared toward code flexibility and readability... and not speed.

Posted in Math, misc | Tagged actionscript, flash | Leave a comment

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Monthly Archives: March 2009

Circle of Particles

Functional Pseudo-Objects

Bezier Intersections (not a snippet)

Line Intersection Part 2 (optimized)

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