Freeform Shape Representations for Efficient Geometry Processing

• Authors: Leif Kobbelt;Mario Botsch
• Venue: SMI '03 Proceedings of the Shape Modeling International 2003
• Year: 2003

The most important concepts for the handling and storageof freeform shapes in geometry processing applicationsare parametric representation and volumetric representations.Both have their specific advantages and drawbacks.While the algebraic complexity of volumetric representationsS = {(x,y,z) | f(x,y,z) = 0} is independent fromthe shape complexity, the domain \Omega of a parametric representationf : \Omega \rightarrow S usually has to have the same structureas the surface S itself (which sometimes makes it necessaryto update the domain when the surface is modified.On theother hand, the topology of a parametrically defined surfacecan be controlled explicitly while in a volumetric representation,the surface topology can change accidentally during deformation.A volumetric representation reduces distancequeries or inside/outside tests to mere function evaluationsbut the geodesic neighborhood relation between surfacepoints is difficult to resolve.As a consequence, it seemspromising to combine parametric and volumetric representationsto effectively exploit both advantages.In this talk, a number of applications is presented anddiscussed where such a combination leads to efficient andnumerically stable algorithms for the solution of variousgeometry processing tasks.These applications include surfaceremeshing, mesh fairing, global error control for meshdecimation and smoothing, and topology control for level-set surfaces.