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Presentation

Repulsive Surfaces
Event Type
Technical Papers
Hybrid Formats
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TimeThursday, December 161:33pm - 1:44pm JST
LocationHall B5 (1) (5F, B Block) & Virtual Platform
DescriptionGeometric functionals that penalize bending or stretching of a surface play a key role in geometric modeling and digital geometry processing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves. This paper develops a numerical framework for optimization of surface geometry while avoiding (self-)collision. The starting point is the tangent-point energy, which effectively pushes apart pairs of points that are close in space but distant along the surface. We develop a discretization of this energy for triangle meshes, and introduce a novel acceleration scheme based on a fractional Sobolev inner product. In contrast to similar schemes developed for curves, we avoid the complexity of building a multiresolution mesh hierarchy by decomposing our preconditioner into two ordinary Poisson equations, plus forward application of a fractional derivative. We further accelerate this scheme via hierarchical approximation, and describe how to incorporate a variety of constraints (area, volume, etc.). Finally, we explore how this machinery might be applied to applications in mathematical visualization and geometry processing.