Walking On Broken Mesh: Defect-Tolerant Geodesic Distances and Parameterizations

Efficient methods to compute intrinsic distances and geodesic paths have been presented for various types of surface representations, most importantly polygon meshes. These meshes are usually assumed to be well-structured and manifold. In practice, however, they often contain defects like holes, gaps, degeneracies, non-manifold configurations – or they might even be just a soup of polygons. The task of repairing these defects is computationally complex and in many cases exhibits various ambiguities demanding tedious manual efforts. We present a computational framework that enables the computation of meaningful approximate intrinsic distances and geodesic paths on raw meshes in a way which is tolerant to such defects. Holes and gaps are bridged up to a user-specified tolerance threshold such that distances can be computed plausibly even across multiple connected components of inconsistent meshes. Further, we show ways to locally parameterize a surface based on geodesic distance �...

• Type: Journal
• Year: 2011
• Where: CGF
• Authors: Marcel Campen, Leif Kobbelt
• Keywords: CGF 2011, Computational Framework, Computational Geometry, Surface Representations