Mesh Processing

This is the webpage of the mesh processing tutorial at ECCV 2008 (Sunday October 12th - Morning : 9-12.30), see also this link: ECCV tutorials

Speaker: Bruno LÚvy

Book

Polygon Mesh Processing, Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez and Bruno Levy, AK Peters / CRC press. More information

Abstract

Polygon Mesh is a widely used representation for 3D geometry. The reasons for its success is first the ease of representation. A mesh can be stored in a file as an array of vertices and an array of polygons. The other reason is the versatility, a mesh can be used for both designed objects and acquired objects, it works for both manufactured objects and natural shapes. However, manipulating this type of representation (i.e. geometry processing with meshes) requires special data structures and special mathematics.

Syllabus and references

1) Efficiently navigating in a mesh with the halfedge data structure

  • Designing a data structure for polyhedral surfaces, Lutz Kettner, SOCG 1998
  • N-dimensional generalized combinatorial maps and cellular quasi-manifolds, Lienhardt P, International Journal on Computational Geometry and Applications, Vol. 4, n░ 3, pp. 275-324 - 1994
  • Implementations: see CGAL, OpenMesh, Graphite links below
  • Slides

2) Differential geometry for non-differentiable geometry

  • A Signal Processing Approach to Fair Surface Design, Gabriel Taubin, SIGGRAPH 1995
  • Discrete Fairing of Curves and Surfaces based on Linear Curvature Distribution, Schneider and Kobbelt, Curves and Surfaces, 1999
  • Using Partial Differential Equations to Generate Free-form Surfaces (1990), M.I.G. Bloor and M.J. Wilson, Computer Aided Design, 1990
  • Graphite software tutorial: MeshRepair

3) Bridging the gap between parametric representations (Splines) and Meshes: mesh parameterization

4) Computing on a mesh: Finite Elements Modeling and Discrete Exterior Calculus

5) Local to global: Spectral geometry processing

6) The engine behind the scene: numerical optimization

Slides

Links, further reading

Software

  • Graphite An experimental 3D modeler with geometry processing algorithms
  • CGAL The "computational geometry algortihms library", robust and efficient implementations of Delaunay triangulations + other functionalities
  • OpenMesh Data structures + algorithms for geometry processing
  • Meshlab (complete mesh manipulation package)
  • VCG (triangle and tetrahedral meshes)

Data (publically available meshes)

Yellow pages