Meshes are computational data structures used to model physical objects, beings or locations. Such meshes can be two- or three-dimensional or surfaces meshes, on which several animations or simulations can be carried out.

The mesh generation problem deals with the automatic generation of such meshes. In [1], the author classifies mesh generation techiniques in the following (non-exhaustive) categories:

  1. Tri/Tetrahedral meshing
    1. Octree
    2. Delaunay
      1. Point insertion
      2. Boundary constrained triangulation
    3. Advancing front
  2. Quad/Hexahedral meshing
    1. Mapped meshing
    2. Unstructured quad meshing
      1. Indirect methods
      2. Direct methods
        1. Quad meshing by decomposition
        2. Advancing front quad meshing
    3. Unstructured hex meshing
      1. Indirect methods
      2. Direct methods
        1. Grid-based
        2. Medial surface
        3. Plastering
        4. Whisker weaving
    4. Hex-dominant methods
  3. Surface meshing
    1. Parametric space
    2. Direct 3D

There are still techniques to enhance the quality of an automatically generated mesh:

  1. Mesh post-processing
    1. Smoothing
      1. Averaging methods
      2. Optimization-based methods
      3. Physically-based methods
      4. Mid-node placement
    2. Cleanup
      1. Shape improvement
      2. Topological improvement
    3. Refinement
      1. Triangle/Tetrahedral refinement
        1. Edge bisection
        2. Point insertion
        3. Templates
      2. Quad/Hex refinement

The CRAb group works in all these research fields of mesh generation. In particular, our current work is related to:

  1. Adaptive surface mesh generation
  2. Triangular and tetrahedral mesh generation
    1. Serial advancing front technique for models with cracks
    2. Parallel advancing front technique for models with cracks
  3. Quadrilateral and hexahedral mesh generation
  4. Optimization of simplex meshes

More information about mesh generation can be found in:

[1] "A Survey of Unstructured Mesh Generation Technology", Proceedings of the 7th International Meshing Roundtable, Sandia National Lab, pp.239-267, October 1998, http://www.imr.sandia.gov/papers/authors/owen.html.
[2] "Basic Structured Grid Generation - With an Introduction to Unstructured Grid Generation", M. Farrashkhalvat and J. P. Miles, Butterworth-Heinemann, 2003, http://www.sciencedirect.com/science/book/9780750650588.
[3] "Triangulation and Applications - Mathematics and Visualizations", O. Hjelle and M. Daelen, Springer, 2006, http://www.springer.com/mathematics/computational+science+%26+engineering/book/978-3-540-33260-2.
[4] "Mesh Generation", P. J. Frey and P. L. George, 2nd ed, ISTE Publishing and John Wiley & Sons, 2008, http://www.wiley.com/WileyCDA/WileyTitle/productCd-1848210299.html.