CSCI 480/580 Lecture
29 - In-Class Problems
- Derive the Control matrix \(C\) (as
in \(\mathbf{\vec{p}} = C
\mathbf{\vec{a}}\) for a Hermite Spline, where
the four control points are the two end points and the two derivatives
at the endpoints. Recall that a Hermite Spline is a cubic polynomial
segment, which means it has the form \(\mathbf{f}(u) = a_0 + a_1u + a_2 u^2 + a_3
u^3\) \[
\begin{align*}
\mathbf{p}_0 &= \mathbf{f}(0)\\
\mathbf{p}_0 &= \mathbf{f'}(0)\\
\mathbf{p}_0 &= \mathbf{f}(1)\\
\mathbf{p}_0 &= \mathbf{f'}(1)
\end{align*}
\]