论文信息 - Approximating Curves via Alpha Shapes

Approximating Curves via Alpha Shapes

We present a method of approximating a nonsingular curve C in the plane or in space with the use of alpha shapes. The procedure is based on sampling the curve C with a finite set S and then construct the alpha shape, Sα, of S. Then, Sα is shown to be a piecewise linear curve that is ambiently homeomorphic to, and within a prescribed tolerance from, C.

Takis Sakkalis | Ch. Charitos

[1] Nicholas M. Patrikalakis,et al. Analysis and applications of pipe surfaces , 1998, Comput. Aided Geom. Des..

[2] Nicholas M. Patrikalakis,et al. Topologically reliable approximation of composite Bézier curves , 1996, Comput. Aided Geom. Des..

[3] Herbert Edelsbrunner,et al. Three-dimensional alpha shapes , 1994, ACM Trans. Graph..

[4] David Eppstein,et al. The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction , 1998, Graph. Model. Image Process..

[5] K. Brown,et al. Graduate Texts in Mathematics , 1982 .

[6] Tamal K. Dey,et al. A simple provable algorithm for curve reconstruction , 1999, SODA '99.

[7] Chandrajit L. Bajaj,et al. Sampling and reconstructing manifolds using alpha-shapes , 1997, CCCG.