Abstract
The computation of visible surfaces is usually formulated in a regularization framework based on thin-plate and membrane splines. When discretized, this formulation leads to large sparse linear systems. Most surface interpolation methods solve these sparse systems with iterative methods. Here we explore the use of direct methods. Through a careful analysis of the regularization operator, we derive direct methods that efficiently make use of all zeros in the sparse discretization of the operator. Experimental results show that, compared with iterative interpolation methods, the direct methods we present are competitive in general, and they provide significant speed-ups for problems involving discontinuities. In addition to their use in visible-surface interpolation, the presented methods also support very efficient time integration for deformable surfaces.
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