An Example: Beziér Curves
We can generate points on the curve by repeated linear interpolation.
Starting with the control polygon (in red), the edges are subdivided (as noted in blue). These points are then connected in order and the resulting edges subdivided. The recursion stops when only one edge remains. This allows us to approximate the curve at multiple resolutions.
A Beziér curve can be defined in terms of a set of control points denoted in red.
Consider, for example, a cubic, or curve of degree 3: