Bounds on the k-neighborhood for locally uniform sampled surfaces

Affordable Access

Bounds on the k-neighborhood for locally uniform sampled surfaces

Eurographics Association


Eurographics Symposium on Point-Based Graphics (2004) M. Alexa, S. Rusinkiewicz (Editors) Bounds on the k-Neighborhood for Locally Uniformly Sampled Surfaces Mattias Andersson1 Joachim Giesen2† Mark Pauly3 Bettina Speckmann4 1 Department of Computer Science, Lund Institute of Technology, S-22100 Lund, Sweden 2 Department of Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland 3 Computer Science Department, Stanford University, Stanford CA 94305, USA 4 Department of Mathematics and Computer Science, TU Eindhoven, 5600 MB Eindhoven, The Netherlands Abstract Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, sur- face, solid, and object representations 1. Introduction Point primitives have recently become popular as a means of surface representation in computer graphics and geometric modeling. With an abundance of 3D acquisition and sampling methods that create point samples from surfaces, numerous algorithms for di- rect processing and rendering of these data sets have been proposed. These methods typically exploit the structural simplicity of point clouds for compact stor- age [KV03], fast re-sampling [PGK02], and efficient rendering [RL00, BWK02]. In the most general case, 3D acquisition or sam- pling methods create a finite set of points that only sample the 3D position of the underlying surface. However, subsequent processing or rendering algo- rithms [ZPvG01, KV01, PKKG03] require additional geometric information on the surface, such as surface normals or local curvatures, which have to be

There are no comments yet on this publication. Be the first to share your thoughts.


Seen <100 times