[Talk] An Application of Lie theory to Computer Graphics

Shizuo Kaji

Applied Topology, Będlewo, Poland, 2013.7

In computer graphics, various mathematics is used such as the Navie-Stokes equations for generating clouds and fires, reproducing kernel Hilbert space for mixing different facial expressions, and piecewise linear map (PL-map, in short) for morphing shapes. I will discuss an algorithm to blend/deform shapes based on PL-map and an elementary Lie theory. A shape is represented by a polyhedron and its deformation by a PL-map. The idea is to find a suitable PL-map which minimizes a certain energy functional dened on the space of 3-dimensional PL-maps.

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