Superformula

The Superformula developed by Johan Gielis is a simple formula that can generate a vast diversity of natural shapes. It produces everything from simple triangles and pentagons, to stars, spirals and petals. More information on the Superformula: Paul Bourke.
Based on the first Flash implementations of Flashforum members, Especially based on e2e4 and i++ contributions.

I’ve put together a little example to draw SuperShapes, copy the code into frame 1 of a new flash movie.

function getSuperPoint (m:Number, n1:Number, n2:Number, n3:Number, phi:Number)
{
 var r:Number;
 var t1:Number;
 var t2:Number;
 var a:Number = 1;
 var b:Number = 1;
 var x:Number = 0;
 var y:Number = 0;
 t1 = (1 / a) * Math.cos ((m / 4) * phi);
 t1 = Math.abs (t1);
 t1 = Math.pow (t1, n2);
 t2 = (1 / b) * Math.sin ((m / 4) * phi);
 t2 = Math.abs (t2);
 t2 = Math.pow (t2, n3);
 r = Math.pow (t1 + t2, 1 / n1);
 if (r != 0)
 {

  r = 1 / r;
  x = r * Math.cos (phi);
  y = r * Math.sin (phi);
 }
 var p:Object = {x:x, y:y};
 return p;
}
function drawSuperShape (m, n1, n2, n3)
{
 var maxAngle:Number = 12 * Math.PI;
 var x = 300;
 var y = 200;
 _root.lineStyle (1, 0x0000AA);
 for (var i = 0; i < = maxAngle; i += 0.01)
 {
  var p:Object = getSuperPoint (m, n1, n2, n3, i);
  if (i == 0)
  {
   _root.moveTo (x + (p.x * 100), y + (p.y * 100));
  }
  else
  {
   _root.lineTo (x + (p.x * 100), y + (p.y * 100));
  }
 }
}

// Then create an animated runner...

var a = 70, b = 10;
var m:Number = a / b;
var n1:Number = .5;
var n2:Number = 3;
var n3:Number = .5;

_root.createEmptyMovieClip ("control", 100);
control.onEnterFrame = function ()
{
 b -= 3;
 a += 1.5;
 _root.m = a / b;
 _root.clear ();
 _root.beginFill (0x000000, 10);
 _root.drawSuperShape (_root.m, _root.n1, _root.n2, _root.n3);
 _root.endFill ();
};

can you Digg it? is it del.icio.us?

Category: General