Article

Solving spatial basic geometric constraint configurations with locus intersection

Authors:

Christoph M. Hoffmann,

Wei-Qiang YangAuthors Info & Claims

SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications

Pages 95 - 104

https://doi.org/10.1145/566282.566299

Published: 17 June 2002 Publication History

Abstract

A basic idea of geometric constraint solving is to decompose the constraint problem into smaller ones according to some basic configurations. In this paper, we find all spatial basic configurations involving points, lines, and planes containing up to six geometric primitives in an automated way. Many of these basic configurations still resist effective analytical solutions. We propose the locus intersection method for geometric constraint solving, which is used to solve all these basic configurations.

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Cited By

Zou QFeng H(2019)Variational B-rep Model Analysis for Direct Modeling using Geometric PerturbationJournal of Computational Design and Engineering10.1016/j.jcde.2019.03.002Online publication date: Mar-2019
https://doi.org/10.1016/j.jcde.2019.03.002
Schreck P(2019)On the Mechanization of Straightedge and Compass ConstructionsJournal of Systems Science and Complexity10.1007/s11424-019-8347-132:1(124-149)Online publication date: 14-Feb-2019
https://doi.org/10.1007/s11424-019-8347-1
Imbach RMathis PSchreck P(2017)A robust and efficient method for solving point distance problems by homotopyMathematical Programming: Series A and B10.1007/s10107-016-1058-7163:1-2(115-144)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s10107-016-1058-7
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Index Terms

Solving spatial basic geometric constraint configurations with locus intersection
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Conferences

SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications

June 2002

424 pages

ISBN:1581135068

DOI:10.1145/566282

Conference Chairs:
Hans-Peter Seidel
Max-Planck-Institut für Informatik, Saarbrücken, Germany
,
Vadim Shapiro
University of Wisconsin, Madison, U.S.A.
,
Program Chairs:
Kunwoo Lee
Seoul National University, Seoul, Korea
,
Nick Patrikalakis
Massachsetts Institute of Technology, Cambridge, U.S.A.

Copyright © 2002 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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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 June 2002

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SM02

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SM02: ACM Symposium on Solid Modeling and Applications 2002

June 17 - 21, 2002

Saarbrücken, Germany

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SMA '02 Paper Acceptance Rate 43 of 93 submissions, 46%;

Overall Acceptance Rate 86 of 173 submissions, 50%

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Cited By

Zou QFeng H(2019)Variational B-rep Model Analysis for Direct Modeling using Geometric PerturbationJournal of Computational Design and Engineering10.1016/j.jcde.2019.03.002Online publication date: Mar-2019
https://doi.org/10.1016/j.jcde.2019.03.002
Schreck P(2019)On the Mechanization of Straightedge and Compass ConstructionsJournal of Systems Science and Complexity10.1007/s11424-019-8347-132:1(124-149)Online publication date: 14-Feb-2019
https://doi.org/10.1007/s11424-019-8347-1
Imbach RMathis PSchreck P(2017)A robust and efficient method for solving point distance problems by homotopyMathematical Programming: Series A and B10.1007/s10107-016-1058-7163:1-2(115-144)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s10107-016-1058-7
Lee-St.John ASidman J(2013)Combinatorics and the rigidity of CAD systemsComputer-Aided Design10.1016/j.cad.2012.10.03045:2(473-482)Online publication date: Feb-2013
https://doi.org/10.1016/j.cad.2012.10.030
Mathis PSchreck PImbach ROssowski SLecca P(2012)Decomposition of geometrical constraint systems with reparameterizationProceedings of the 27th Annual ACM Symposium on Applied Computing10.1145/2245276.2245298(102-108)Online publication date: 26-Mar-2012
https://dl.acm.org/doi/10.1145/2245276.2245298
Zhu YGortler SThurston D(2011)Sensor network localization using sensor perturbationACM Transactions on Sensor Networks10.1145/1921621.19216307:4(1-23)Online publication date: 4-Feb-2011
https://dl.acm.org/doi/10.1145/1921621.1921630
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
Imbach RMathis PSchreck P(2011)Tracking Method for Reparametrized Geometrical Constraint SystemsProceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2011.26(31-38)Online publication date: 26-Sep-2011
https://dl.acm.org/doi/10.1109/SYNASC.2011.26
Mathis PThierry S(2010)A formalization of geometric constraint systems and their decompositionFormal Aspects of Computing10.1007/s00165-009-0117-822:2(129-151)Online publication date: 1-Mar-2010
https://dl.acm.org/doi/10.1007/s00165-009-0117-8
Färber MBrüderlin BShin SOssowski S(2009)Multivariate root finding with search space decomposition and randomisationProceedings of the 2009 ACM symposium on Applied Computing10.1145/1529282.1529535(1142-1143)Online publication date: 8-Mar-2009
https://dl.acm.org/doi/10.1145/1529282.1529535
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