New geometric constraint solving formulation: Application to the 3D pentahedron

Hichem Barki, Jean Marc Cane, Dominique Michelucci, Sebti Foufou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be specified in many ways and that some formulations are much better than others, because they are much smaller and they avoid spurious degenerate solutions. Several experimentations showing a considerable performance enhancement (x42) are reported in this paper to consolidate our theoretical findings.

Original languageEnglish (US)
Title of host publicationImage and Signal Processing - 6th International Conference, ICISP 2014, Proceedings
PublisherSpringer Verlag
Pages594-601
Number of pages8
ISBN (Print)9783319079974
DOIs
StatePublished - Jan 1 2014
Event6th International Conference on Image and Signal Processing, ICISP 2014 - Cherbourg, France
Duration: Jun 30 2014Jul 2 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8509 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Image and Signal Processing, ICISP 2014
CountryFrance
CityCherbourg
Period6/30/147/2/14

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Keywords

  • 3D Pentahedron
  • Geometric Constraint Solving Problems
  • Parametrization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Barki, H., Cane, J. M., Michelucci, D., & Foufou, S. (2014). New geometric constraint solving formulation: Application to the 3D pentahedron. In Image and Signal Processing - 6th International Conference, ICISP 2014, Proceedings (pp. 594-601). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8509 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-07998-1_68