Vincent Ma
Real-time perspective-correct silhouette edge generation.
In this tech talk I will discuss the theory behind an algorithm that determines, in real time, the perspective-correct silhouette edge set of a simple non-convex polytope with respect to a particular viewpoint. I will also cover implementation issues that arose during my implementation of this algorithm, and future work that will improve the algorithm.
Tutte associates a skew--symmetric matrix $T$, having indeterminate entries, with a graph. The rank of Tutte's matrix is exactly twice the size of a maximum cardinality matching in the graph. This observation led Tutte toward a proof of his famous matching theorem. We consider the problem of determining the rank of $T+K$, where $K$ is a skew--symmetric matrix with rational entries. This modest generalization of the matching problem contains the linear matroid matching problem. We revisit Tutte's techniques, from half a century ago, to prove a min--max formula for this more general problem.