Certified meshing of families of isosurfaces

Simon Plantinga; Gert Vegter

Certified meshing of families of isosurfaces

Simon Plantinga^*
, Gert Vegter

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Level sets are isosurfaces of an implicit function F : R3 → R, that is the set of points satisfying F(x, y, z) = θ. 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.

Original language	English
Title of host publication	IEEE International Conference on Shape Modeling and Applications 2007, Proceedings
Place of Publication	LOS ALAMITOS
Publisher	IEEE (The Institute of Electrical and Electronics Engineers)
Pages	261-268
Number of pages	8
ISBN (Print)	978-0-7695-2815-1
Publication status	Published - 2007
Event	9th International Conference on Shape Modeling and Applications - , France Duration: 13-Jun-2007 → 15-Jun-2007

Other

Other	9th International Conference on Shape Modeling and Applications
Country/Territory	France
Period	13/06/2007 → 15/06/2007

Keywords

SURFACES

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@inproceedings{339bd6cb7b4f4f6092034619592faf10,

title = "Certified meshing of families of isosurfaces",

abstract = "Level sets are isosurfaces of an implicit function F : R3 → R, that is the set of points satisfying F(x, y, z) = θ. 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 = "SURFACES",

author = "Simon Plantinga and Gert Vegter",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI); 9th International Conference on Shape Modeling and Applications ; Conference date: 13-06-2007 Through 15-06-2007",

year = "2007",

language = "English",

isbn = "978-0-7695-2815-1",

pages = "261--268",

booktitle = "IEEE International Conference on Shape Modeling and Applications 2007, Proceedings",

publisher = "IEEE (The Institute of Electrical and Electronics Engineers)",

}

Certified meshing of families of isosurfaces. / Plantinga, Simon; Vegter, Gert.
IEEE International Conference on Shape Modeling and Applications 2007, Proceedings. LOS ALAMITOS: IEEE (The Institute of Electrical and Electronics Engineers), 2007. p. 261-268.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Certified meshing of families of isosurfaces

AU - Plantinga, Simon

AU - Vegter, Gert

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 2007

Y1 - 2007

N2 - Level sets are isosurfaces of an implicit function F : R3 → R, that is the set of points satisfying F(x, y, z) = θ. 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.

AB - Level sets are isosurfaces of an implicit function F : R3 → R, that is the set of points satisfying F(x, y, z) = θ. 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.

KW - SURFACES

M3 - Conference contribution

SN - 978-0-7695-2815-1

SP - 261

EP - 268

BT - IEEE International Conference on Shape Modeling and Applications 2007, Proceedings

PB - IEEE (The Institute of Electrical and Electronics Engineers)

CY - LOS ALAMITOS

T2 - 9th International Conference on Shape Modeling and Applications

Y2 - 13 June 2007 through 15 June 2007

ER -

Certified meshing of families of isosurfaces

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