Question

I am trying to translate an OpenGl object around in a helical pattern. I cannot figure this out. Problem is I know I need to increment the angle for the x, y, and z coordinates, but the translate function that I use only moves the object by a translate amount which is specific to the object. The Axis I am using is Y up, Z toward the screen and X to the right.

public override void Move(Figure fig)
{
   double angle = 0;
   double x = RADIUS * Math.Cos(angle);
   double y = (angle / RADIUS);
   double z = RADIUS * Math.Sin(angle);
   fig.Translate(x, y, z);
   angle += .5;
}
public void Translate(double fx, double fy, double fz)
{
   translateAmt[0] += fx;
   translateAmt[1] += fy;
   translateAmt[2] += fz;

}

Answer 1

Here are two ways you could approach this:

Procedurally

Check out the ProcessHelix function in NeHe Lesson 36. A little bit hard to read but you should be able to see the basic loop and calculations used to get the points along a helix.

2 Translations and a Rotation

If you perform these transformations in the proper order you can get the helical motion. This is the order you would imagine doing it in your head:

1. Translate the object away from the origin (e.g. +x) the radius of your helix
2. Rotate the object around the origin (y axis), creating circular motion
3. Translate the object along the y axis, creating helical motion.

So in OpenGL, you’d do those backwards, as the last matrix specified is the first one applied… translate in +y (time dependent), rotate around y (time dependent), and translate in x.