Recently I was using ActionScript Physics Engine to create a simple 2-D arcade-style game. I looked into building an elliptical spring constraint in APE to serve as the boundaries of the game. In the end I decided not to use the elliptical boundaries, but they are easy enough to code up. Here’s a quick demo, and the ActionScript source code:
package
{
import flash.display.Sprite;
import flash.events.Event;
import org.cove.ape.*;
public class Main extends Sprite
{
public var defaultGroup:Group;
var car:SpringConstraint;
var ellipsePoints:Array; // points that define the outer ellipse
var wheel1:WheelParticle;
public function Main()
{
stage.frameRate = 30;
APEngine.init(1/4);
// set the default diplay container
APEngine.container = this;
defaultGroup = new Group();
defaultGroup.collideInternal = true;
init();
APEngine.addGroup(defaultGroup);
stage.addEventListener(Event.ENTER_FRAME, run);
}
public function init():void
{
ellipsePoints = new Array();
ellipsePoints = drawEllipse(calculateEllipse(380, 80, 60, 36, -24, 32));
addBall();
}
public function addBall():void
{
var circle = new CircleParticle(
160, // x
210, // y
40, // radius
false, // fixed
10, // mass
1.0, // elasticty
0 // friction
);
circle.setStyle(0, 0, 0, Math.random() * 0xffffff);
defaultGroup.addParticle(circle);
circle.velocity = (new Vector(20, 1));
}
/*
* This functions returns an array containing the points to draw an
* ellipse.
*
* @param x {double} X coordinate
* @param y {double} Y coordinate
* @param a {double} Semimajor axis
* @param b {double} Semiminor axis
* @param angle {double} Angle of the ellipse
*/
private function calculateEllipse(x, y, a, b, angle, steps)
{
if (steps == null)
steps = 36;
var points:Array = new Array();
// Angle is given by Degree Value
var beta = -angle * (Math.PI / 180); //(Math.PI/180) converts Degree Value into Radians
var sinbeta = Math.sin(beta);
var cosbeta = Math.cos(beta);
for (var i = 0; i < 360; i += 360 / steps)
{
var alpha = i * (Math.PI / 180) ;
var sinalpha = Math.sin(alpha);
var cosalpha = Math.cos(alpha);
var x = x + (a * cosalpha * cosbeta - b * sinalpha * sinbeta);
var y = y + (a * cosalpha * sinbeta + b * sinalpha * cosbeta);
var o:Object = new Object();
o.x = x;
o.y = y;
points.push(o);
}
return points;
}
private function drawEllipse(points:Array):Array
{
var circles:Array = new Array();
var i:Number;
for( i= 0; i < points.length; i++)
{
// CircleParticle(x, y, radius, fixed, mass, elasticity, friction)
var c:CircleParticle = new CircleParticle(points[i].x, points[i].y, 0, true, 0.4, 0, 0);
defaultGroup.addParticle(c);
circles.push(c);
if(i > 0)
{
var s:SpringConstraint = new SpringConstraint(circles[i-1], circles[i], 1, true, 1, 1, true);
defaultGroup.addConstraint(s);
}
}
// create the final constraint to close the ellipse:
var t:SpringConstraint = new SpringConstraint(circles[i-1], circles[0], 1, true, 1, 1, true);
defaultGroup.addConstraint(t);
return circles;
}
private function run(e:Event):void
{
APEngine.step();
APEngine.paint();
}
}
}
Anatomy of an Ellipse:
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