DocumentCode :
3063198
Title :
Certified meshing of families of isosurfaces
Author :
Plantinga, Simon ; Vegter, Gert
Author_Institution :
Univ. of Groningen, Groningen
fYear :
2007
fDate :
13-15 June 2007
Firstpage :
261
Lastpage :
270
Abstract :
Level sets are isosurfaces of an implicit function F: R3 rarr R K, that is the set of points satisfying F(x, y, z) = 0.In this paper we introduce an algorithm to move at interactive speed through the different level sets. Furthermore the meshes of the level sets are isotopic to the isosurface itself, as long as the surface stays away from singularities. When the surface moves close to singularities, the algorithm indicates arbitrarily small boxes where the topology is not certified. In this case, the user can decide to decrease the size of the boxes by further refinement. For special classes of functions, such as algebraic surfaces, other methods could be used to determine the topology inside the singular boxes.
Keywords :
computational geometry; mesh generation; set theory; surface fitting; topology; algebraic surfaces; certified meshing; isosurface families; level sets; topology; Arithmetic; Clustering algorithms; Density functional theory; Displays; Isosurfaces; Level set; Surface reconstruction; Testing; Topology; Visualization;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Shape Modeling and Applications, 2007. SMI '07. IEEE International Conference on
Conference_Location :
Lyon
Print_ISBN :
0-7695-2815-5
Type :
conf
DOI :
10.1109/SMI.2007.11
Filename :
4273390
Link To Document :
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