Anisotropic Smoothing of Point Sets
Please always quote using this URN: urn:nbn:de:0297-zib-8508
- The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive a shape operator, principal curvature properties of a point set, and an anisotropic Laplacian of the surface. This anisotropic Laplacian reflects curvature properties which can be understood as the point set analogue of Taubin's curvature-tensor for polyhedral surfaces. We combine these discrete tools with techniques from geometric diffusion and image processing. Several applications demonstrate the efficiency and accuracy of our method.
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| Author: | Carsten Lange, Konrad Polthier |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | anisotropic Laplace; anisotropic mean curvature; anisotropic sampling; f; mean curvature flow; point sets; principal curvatures; shape operator |
| MSC-Classification: | 53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Axx Classical differential geometry / 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] |
| CCS-Classification: | I. Computing Methodologies / I.3 COMPUTER GRAPHICS / I.3.5 Computational Geometry and Object Modeling |
| Date of first Publication: | 2005/03/08 |
| Series (Serial Number): | ZIB-Report (05-16) |
| ZIB-Reportnumber: | 05-16 |
| Published in: | Appeared in: Computer Aided Geometric Design 22 (2005) 680-692. Special issue: Geometric Modelling and Differential Geometry |
