Free-form shape design using triangulated surfaces

We present an approach to modeling with truly mutable yet completely controllable free-form surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patch-based approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patch-based and particle-based representations. Automatic refinement, mesh smoothing, and re-triangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time.

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