5.6 Differentiation and Integration
Given any number of control points, we can construct a smooth approximation to the shape of the control polygon using a single Bezier curve. But if there are a large number of control points, this Bezier curve will be a polynomial of high degree, leading to slow and numerically unstable computations. Rather than using a single polynomial of high degree, it would be better numerically to construct a sequence of low-degree curves that join together smoothly. Thus we need a way to ensure that two Bezier curves meet smoothly at their join.
Bezier curves interpolate their first and last control points. Thus it is easy to connect two Bezier curves; all we need to do is to make sure that the first control point ...
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