A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes

When using triangle meshes in numerical simulations or other sophisticated downstream applications, we have to guarantee that no degenerate faces are present since they have, e.g., no well defined normal vectors. In this paper we present a simple but effective algorithm to remove such artifacts from a given triangle mesh. The central problem is to make this algorithm numerically robust because degenerate triangles are usually the source for all kinds of numerical instabilities. Our algorithm is based on a slicing technique that cuts a set of planes through the given polygonal model. The mesh slicing operator only uses numerically stable predicates and therefore is able to split faces in a controlled manner. In combination with a custom tailored mesh decimation scheme we are able to remove the degenerate faces from meshes like those typically generated by tesselation units in CAD systems.

[1]  David P. Dobkin,et al.  MAPS: multiresolution adaptive parameterization of surfaces , 1998, SIGGRAPH.

[2]  Paolo Cignoni,et al.  A comparison of mesh simplification algorithms , 1998, Comput. Graph..

[3]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[4]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[5]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[6]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[7]  Mario Botsch,et al.  Feature sensitive surface extraction from volume data , 2001, SIGGRAPH.

[8]  Marc Levoy,et al.  Zippered polygon meshes from range images , 1994, SIGGRAPH.

[9]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[10]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[11]  Hans-Peter Seidel,et al.  A General Framework for Mesh Decimation , 1998, Graphics Interface.

[12]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[13]  David E. Breen,et al.  Semi-regular mesh extraction from volumes , 2000 .

[14]  Hans-Peter Seidel,et al.  A Shrink Wrapping Approach to Remeshing Polygonal Surfaces , 1999, Comput. Graph. Forum.

[15]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[16]  Hans-Peter Seidel,et al.  Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity , 2000, Comput. Graph. Forum.

[17]  Jindong Chen,et al.  Automatic Reconstruction of 3D CAD Models from Digital Scans , 1999, Int. J. Comput. Geom. Appl..

[18]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.