Advances in computer graphics, computer vision, virtual reality, and medical data acquisition have led to a proliferation of 3D shapes, posing a challenge to analyze and process geometric data. In this project, we focus on geometric algorithms working with boundary surface representations. In particular, we study the problem of extrinsic geometry analysis. The term “extrinsic” refers to the spatial embedding of a surface, that is, how curved and bent the surface is in relation to surrounding space, which is ignored by previous intrinsic methods. We study extrinsic geometry through the lens of spectral computations, shown to have profound connections to extrinsic geometry in mathematical theory. Our approach leads to a versatile algorithmic toolbox for extrinsic geometry processing, drawing on ideas from partial differential equations (PDEs), functional analysis and differential geometry from mathematics, and tools from numerical analysis and optimization from computer science.
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