Datasheet

Part 1: Getting Started

The parametric equations for a torus are:

x=(c+a*cos(v))cos(u)

y=(c+a*cos(v))sin(u)

z=a*sin(v)

where c is the donut radius, and a is the tube radius. And u is the parameter that takes you around the

larger radius (the donut) and v around the smaller tube radius as shown in Figure 1.7.

tube

radius

donut radius

Figure 1-7

You now use these equations to create a parametric path on your torus. What you want to do is have

your graphical element spiral around the torus. You can accomplish this by iterating the parameters u

and v simultaneously adjusting v to get to the desired spiral velocity. The parametric path is extremely

easy to execute. Just take the code from the 3D Flash 10 Engine in 13 lines and substitute your parametric

equations for ball.x, ball.y, and ball.z as shown below:

import flash.display.Sprite;//imports sprite class

var myAngle:Number =0;//Angle of ball

var ball:Sprite = new Sprite();//instantiates ball sprite

ball.graphics.beginFill(0xFF0000);//Assign a ball color

ball.graphics.drawCircle(0, 0, 10);//draws your ball at 0,0

ball.graphics.endFill();//ends the fill

addChild(ball);//adds the ball to the stage

addEventListener(Event.ENTER_FRAME, myonEnterFrame);//loops equations

function myonEnterFrame(event:Event):void{

myAngle=myAngle+.1;//iterates angle

//ball parametric orbit x

ball.x = (100+50*Math.cos(2*myAngle))*Math.cos(myAngle/4)+200;

//ball parametric orbit y

ball.y = (100+50*Math.cos(2*myAngle))*Math.sin(myAngle/4)+200;

//ball parametric orbit z

ball.z = 50*Math.sin(2*myAngle);}

It works flawlessly, but a single ball isn ’ t very exciting. Now add a few more balls to your

parametric path.

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