Let $\mathbf{P}(t)$ be a piecewise bezier curve of degree $p$, which defines a jordan curve in the plane such the interior region $D$ is convex.
Question: How can I find the external $C_e$ and internal $C_i$ circles by using $\mathbf{P}$ ?
As example, if $\mathbf{P}$ defines a triangle, then bellow we have the internal and external circles to this triangle respectively.
Note 1: $p = 1$ tells $D$ is a polygon shape
Note 2: The external circle is the circle with minimum area such
- $\mathbf{P}(t) \in \overline{D}_{e} \ \ \ \ \forall t$
Note 3: The internal circle is the circle with maximum area such
- $\mathbf{P}(t) \notin D_{i} \ \ \ \ \forall t$
- $D \cap D_{i} \ne \emptyset $
Note 4: $D$ is a open set