Article

Numerical decomposition of geometric constraints

Authors:

Dominique Michelucci,

Jean-Paul JurzakAuthors Info & Claims

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

Pages 143 - 151

https://doi.org/10.1145/1060244.1060261

Published: 13 June 2005 Publication History

Abstract

Geometric constraint solving is a key issue in CAD/CAM. Since Owen's seminal paper, solvers typically use graph based decomposition methods. However, these methods become difficult to implement in 3D and are misled by geometric theorems. We extend the Numerical Probabilistic Method (NPM), well known in rigidity theory, to more general kinds of constraints and show that NPM can also decompose a system into rigid subsystems. Classical NPM studies the structure of the Jacobian at a random (or generic) configuration. The variant we are proposing does not consider a random configuration, but a configuration similar to the unknown one. Similar means the configuration fulfills the same set of incidence constraints, such as collinearities and coplanarities. Jurzak's prover is used to find a similar configuration.

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Cited By

Hu HKleiner MPernot JZhang CHuang YZhao QYeung S(2021)Geometric Over-Constraints Detection: A SurveyArchives of Computational Methods in Engineering10.1007/s11831-020-09509-yOnline publication date: 11-May-2021
https://doi.org/10.1007/s11831-020-09509-y
Foufou SMichelucci D(2012)Interrogating witnesses for geometric constraint solvingInformation and Computation10.1016/j.ic.2011.09.006216(24-38)Online publication date: 1-Jul-2012
https://dl.acm.org/doi/10.1016/j.ic.2011.09.006
Bettig BM. Hoffmann C(2011)Geometric Constraint Solving in Parametric Computer-Aided DesignJournal of Computing and Information Science in Engineering10.1115/1.359340811:2(021001)Online publication date: 2011
https://doi.org/10.1115/1.3593408
Show More Cited By

Index Terms

Numerical decomposition of geometric constraints
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

June 2005

287 pages

ISBN:1595930159

DOI:10.1145/1060244

Program Chairs:
Leif Kobbelt
RWTH Aachen University, Germany
,
Vadim Shapiro
University of Wisconsin--Madison, USA

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 13 June 2005

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SPM05: 2005 ACM Symposium on Solid and Physical Modeling

June 13 - 15, 2005

Massachusetts, Cambridge

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Cited By

Hu HKleiner MPernot JZhang CHuang YZhao QYeung S(2021)Geometric Over-Constraints Detection: A SurveyArchives of Computational Methods in Engineering10.1007/s11831-020-09509-yOnline publication date: 11-May-2021
https://doi.org/10.1007/s11831-020-09509-y
Foufou SMichelucci D(2012)Interrogating witnesses for geometric constraint solvingInformation and Computation10.1016/j.ic.2011.09.006216(24-38)Online publication date: 1-Jul-2012
https://dl.acm.org/doi/10.1016/j.ic.2011.09.006
Bettig BM. Hoffmann C(2011)Geometric Constraint Solving in Parametric Computer-Aided DesignJournal of Computing and Information Science in Engineering10.1115/1.359340811:2(021001)Online publication date: 2011
https://doi.org/10.1115/1.3593408
Michelucci DSchreck PThierry SFünfzig CGénevaux JElber GFischer AKeyser JKim M(2010)Using the witness method to detect rigid subsystems of geometric constraints in CADProceedings of the 14th ACM Symposium on Solid and Physical Modeling10.1145/1839778.1839791(91-100)Online publication date: 1-Sep-2010
https://dl.acm.org/doi/10.1145/1839778.1839791
Ait-Aoudia SFoufou S(2010)A 2D geometric constraint solver using a graph reduction methodAdvances in Engineering Software10.1016/j.advengsoft.2010.07.00841:10-11(1187-1194)Online publication date: 1-Oct-2010
https://dl.acm.org/doi/10.1016/j.advengsoft.2010.07.008
Michelucci DFoufou SBronsvoort WGonsor DRegli WGrandine TVandenbrande JGravesen JKeyser J(2009)Interrogating witnesses for geometric constraint solving2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling10.1145/1629255.1629301(343-348)Online publication date: 5-Oct-2009
https://dl.acm.org/doi/10.1145/1629255.1629301
Ait-Aoudia SBahriz MSalhi L(2009)2D Geometric Constraint SolvingProceedings of the 2009 Second International Conference in Visualisation10.1109/VIZ.2009.29(201-206)Online publication date: 15-Jul-2009
https://dl.acm.org/doi/10.1109/VIZ.2009.29
Michelucci DMoreau JFoufou S(2008)Robustness and RandomnessReliable Implementation of Real Number Algorithms: Theory and Practice10.1007/978-3-540-85521-7_8(127-148)Online publication date: 1-Mar-2008
https://dl.acm.org/doi/10.1007/978-3-540-85521-7_8
Michelucci DFoufou SLamarque LSchreck PMartin RHu S(2006)Geometric constraints solvingProceedings of the 2006 ACM symposium on Solid and physical modeling10.1145/1128888.1128915(185-196)Online publication date: 6-Jun-2006
https://dl.acm.org/doi/10.1145/1128888.1128915
Michelucci DFoufou S(2006)Geometric constraint solvingComputer-Aided Design10.1016/j.cad.2006.01.00538:4(284-299)Online publication date: 1-Apr-2006
https://dl.acm.org/doi/10.1016/j.cad.2006.01.005

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