M.Sc Thesis | |

M.Sc Student | Sifri Oren |
---|---|

Subject | Surface Meshing Using Geodesic Distances |

Department | Department of Computer Science |

Supervisors | MRS Alla Sheffer |

PROF. Chaim Craig Gotsman |

Generation of surface meshes remains an active research problem despite
the many publications addressing this topic. Acquiring a 3D model is a tedious
and error-prone procedure. The process of simplifying highly detailed scanned
models does not emphasize the quality of their elements, and results in meshes
which usually cannot be used as-is. An intermediate step, known as *remeshing*,
is required to correct the basic mesh geometry and connectivity. High-quality
meshes are necessary for the engineering community, where the emphasis is on
numerical accuracy, as well as for the computer graphics and modeling
community. The latter focus on the tradeoff between the visual quality of the
result and the rendering speed, achieved by reducing the number of elements.

The main issues, which must be
treated by a good remeshing algorithm, are: element quality, sizing control,
approximation accuracy, robustness and efficiency. One reason surface meshing is
such a challenging problem is the fact that using the Euclidean metric to
measure distances between points on the surface can generate large
discrepancies between the original surface and the constructed mesh. We solve
this problem by using geodesic distances on the surface. The ability to
accurately and efficiently compute geodesic distances, and propagate them
across the mesh, permits us to generate quality surface meshes, which closely
approximate the input without resorting to costly parameterization techniques.