“This tutorial covers the basic principles of stepping motors and stepping motor control systems, including both the physics of steppers, the electronics of the basic control systems, and software architectures appropriate for motor control.”

www.cs.uiowa.edu/~jones/step/

danthompsonsblog.blogspot.com/2009/02/smoothstep-interpolation-with-arduino.html
sol.gfxile.net/interpolation/index.html

For example, X ranges between points A and B in N steps.

With linear interpolation:

 for (i = 0; i < N; i++)
 {
   v = i / N;
   X = (A * v) + (B * (1 – v));
 } 

With smoothing:

#define SMOOTHSTEP(x) ((x) * (x) * (3 – 2 * (x)))
for (i = 0; i < N; i++)
 {
   v = i / N;
   v = SMOOTHSTEP(v);
   X = (A * v) + (B * (1 – v));
 }