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SMA
2006
ACM

Identifying flat and tubular regions of a shape by unstable manifolds

14 years 4 months ago
Identifying flat and tubular regions of a shape by unstable manifolds
We present an algorithm to identify the flat and tubular regions of a three dimensional shape from its point sample. We consider the distance function to the input point cloud and the Morse structure induced by it on R3. Specifically we focus on the index 1 and index 2 saddle points and their unstable manifolds. The unstable manifolds of index 2 saddles are one dimensional whereas those of index 1 saddles are two dimensional. Mapping these unstable manifolds back onto the surface, we get the tubular and flat regions. The computations are carried out on the Voronoi diagram of the input points by approximating the unstable manifolds with Voronoi faces. We demonstrate the performance of our algorithm on several point sampled objects. CR Categories: F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations; I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid and object representations
Samrat Goswami, Tamal K. Dey, Chandrajit L. Bajaj
Added 14 Jun 2010
Updated 14 Jun 2010
Type Conference
Year 2006
Where SMA
Authors Samrat Goswami, Tamal K. Dey, Chandrajit L. Bajaj
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