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Computer-Aided Design
Volume 30, Issue 11, 15 September 1998, Pages 883-896
 
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doi:10.1016/S0010-4485(98)00045-1    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1998 Elsevier Science Ltd. All rights reserved

A 2-D geometric constraint solver using DOF-based graph reduction

Jae Yeol Leea and Kwangsoo Kimb, *

a Systems Integration Division, Computer Software Technology Lab., Electronics and Telecommunications Research Institute (ETRI), Taejon 305-333, South Korea b Department of Industrial Engineering, Pohang University of Science and Technology, Pohang 790-784 South Korea

Received 14 November 1997;
revised 12 June 1998;
accepted 18 June 1998.
Available online 25 November 1998.

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Abstract

In this paper, we propose a new DOF-based graph reduction approach to geometric constraint solving. In the proposed approach, we incrementally solve a geometric constraint problem that is not ruler-and-compass constructible by incrementally identifying a set of constrained geometric entities with 3 DOF (degree of freedom) as a rigid body and determining the geometric entities in the rigid body using one of two solving procedures: algebraic procedure and numerical procedure, instead of solving it simultaneously using a numerical method. By solving a complex geometric constraint problem incrementally, the proposed method can maximize the efficiency and robustness of a geometric constraint solver.

Author Keywords: parametric design; variational design; rigid body; graph reduction; constraint solving

Index Terms: Computer aided design; Problem solving; Graph theory; Computational geometry; Constraint theory; Algebra; Numerical methods; Variational techniques; Degrees of freedom (mechanics); Graph reduction; Parametric design; Constructive method

Article Outline

1. Introduction
2. Geometric constraint solving: overview
3. Plan generation
3.1. Preprocessing the constraint graph
3.2. Cluster forming
4. Plan execution
4.1. Solving the RCC configurations
4.2. Solving the ERCC configurations
4.3. Solving the RCNC configurations
4.4. Obtaining the intended solution
5. Implementation
6. Discussions
Acknowledgements
Appendix A: The correctness proof of the solver
A.1. Definition 1
A.2. Definition 2
A.3. Lemma 1
A.4. Proof
A.5. Theorem 1
A.6. Proof
A.7. Lemma 2
A.8. Proof
A.9. Theorem 2
A.10. Proof
A.11. Theorem 3
A.12. Proof
References
Vitae
Vitae
















Computer-Aided Design
Volume 30, Issue 11, 15 September 1998, Pages 883-896
 
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