Drawing Planar Graphs on Points Inside a Polygon
In this paper, we study the problem of drawing a given planar graph such that vertices are at pre-specified points and the entire drawing is inside a given polygon. We give a method that shows that for an $n$-vertex graph and a $k$-sided polygon, $\Theta(kn^2)$ bends are always sufficient. We also give an example of a graph where $\Theta(kn^2)$ bends is necessary for such a drawing.