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The spaces of geodesic triangulations on surfaces

Student-Run Research Seminar

Speaker: Yanwen Luo, UC Davis
Location: 3106 MSB
Start time: Thu, Dec 5 2019, 1:30PM

How to construct a straight-line embedding of any given planar graph is a fundamental problem in computational geometry. In 1963, Tutte provided a simple constructive method to produce a straight-line embedding of a 3-vertex-connected planar graph by solving a sparse linear system. In this talk, we will show that this idea can be applied to give a very short proof of the Bloch-Connelly-Henderson theorem, which states that the space of geodesic triangulations of a convex polygon with a fixed combinatorial type is a contractible space. We will also generalize this idea to the cases of star-shaped polygons and flat tori, and mention some applications in computer graphics.

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