3D Bezier Rails

If you'd like to have a 3D "rail" in your application you can use Bezier curves.

Rails are really useful for defining paths for objects to travel across.

Bay-Z-Ay curves can be really simple too for implementing rails. All you need are:

• A list of 3D points in the order of your path.
• A function to evaluate the position along this path from time 0 to 1.

Here is an example of a function one could use to get this bezier curve position (written in javascript but it doesn't really matter):

function atT( t: float,
     p0 : Vector3, p1 : Vector3, p2 : Vector3 ) : Vector3 {
        var t2 : float = t * t;
        
        var one_min_t : float = 1 - t;
        var one_min_t_2 : float = one_min_t * one_min_t;
        
        var x : float = one_min_t_2 * p0.x + 
         2 * one_min_t * t * p1.x +
         t2 * p2.x;
        var y : float = one_min_t_2 * p0.y + 
         2 * one_min_t * t * p1.y +
         t2 * p2.y;
        var z : float = one_min_t_2 * p0.z + 
         2 * one_min_t * t * p1.z +
         t2 * p2.z;
        
        return(Vector3(x,y,z));
    }

So given your list of points ( 0, 1, 2, 3, 4, 5, 6... ), you'd break them up into groups of 3 like ( [0,1,2], [2,3,4], [4,5,6]... ). Keep track of which group/segment your on and just interpolate from 0 to 1 to move along it. When you hit 1, increment to the next group/segment and restart at 0.