Implement Composite Bezier Curves
Although the book didn't talk about the actual implementation of composite bezier curves one could argue that their base implementation is trivial enough and that by describing their existence and difficulties one could include them as a topic.
As we all know from numerical analysis a composite bezier curve is implemented as
s(t) :=
\begin{cases}
\sum_{k=0}^n \beta_k^0 b_k^n(t) & t \in [0,1]\\
\sum_{k=0}^n \beta_k^1 b_k^n(t-1) & t \in [1,2]
\end{cases}
where \beta_k^i
describes the k
-th polygon point of the i
-th bezier curve.
Therefore it seems trivial to allow 2 curves of n-1
points to be composited by generating the \beta_n^0 = \beta_0^1
ourself in order to enforce the curve to be differentiable.
Or we just allow undifferentiable curves as well, which would result in not enforcing \beta_n^0 - \beta_{n-1}^0 = \beta_1^1 - \beta_0^1
TO BE DISCUSSED