Friday April 18th, 2008
TITLE: What makes a good Steiner point?
Toyota Technological Institute at Chicago
The mesh refinement problem is to take an input geometry (defined by a set of points, curves, and surfaces), and output a set of points that both “respects” the geometry and has good “quality.” What it means for a tetrahedral mesh to respect curved surfaces is already interesting and will take some explaining. Even knowing what the goal is, mesh refinement algorithms typically are of the form: until the output is good enough, add points. But where should we add these additional Steiner points? And how do we know that the algorithm will stop? Most prior work is very specific about where to add points, and thus needs its own very specific proof that the algorithm ends.
In this talk, I will give a set of rules for choosing Steiner points. Any algorithm that follows my rules — as most previous algorithms do — will terminate. After hearing me out, you will know how to represent curved surfaces with linear elements, and you will be able to design your very own meshing algorithm with confidence.