Interpolation greatly simplifies 3D object's animation. Unlike parametric curves, it is not necessary to define the position of the object as a function of time. When interpolation is used, we only need to define control points or knots. The set of control points describes the path that the object that we want to animate will follow. There are many interpolation methods in the literature; however, it is always a good idea to start from the basics.
This method requires that we define the starting and ending points for the location of our object and also the number of interpolating steps. The object will move on the line determined by the starting and ending points.
This method allows us to determine as many control points as we want. The object will move from the starting point to the ending point and it will go through each one of the control points in between.
When using polynomials, an increasing number of control points can produce undesired oscillations on the object's path described by this technique. This is known as the Runge's phenomenon. In the following figure, you can see the result of moving one of the control points of a polynomial described with 11 control points.
This method is similar to polynomial interpolation with the difference that the control points are outside from the object's path. In other words, the object does not go through the control points as it moves. This method is common in computer graphics in general because the knots allow a much smoother path generation than the polynomial equivalent at the same time that fewer knots are required. B-Splines also respond better to the Runge's phenomenon.
In the following Time for action section we are going to see in practice the three different interpolation techniques that have been introduced: linear, polynomial and b-splines interpolation.