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Geometric Modeling and Processingmathscidoc:1608.16070

Computer Aided Design, 34, (2), 97-108 , 2002
Solving geometric constraint systems in 3-D is much more complicated than that in 2-D because the number of variables is larger and some of the results valid in 2-D cannot be extended for 3-D. In this paper, we propose a new DOF-based graph constructive method to geometric constraint systems solving that can efficiently handle well-, over- and under-constrained systems based on the dependence analysis. The basic idea is that the solutions of some geometric elements depend on some others because of the constraints between them. If some geometric elements depend on each other, they must be solved together. In our approach, we first identify all structurally redundant constraints, then we add some constraints to well constrain the system. And we prove that the order of a constraint system after processing under-constrained cases is not more than that of the original system multiplied by 5. After that, we apply a recursive searching process to identify all the clusters, which is shown to be capable of getting the minimum order-reduction result of a well-constrained system. We also briefly describe the constraint evaluation phase and show the implementation results of our method.
Geometric constraints, Dependence analysis, Basic clusters, Graph reduction
```@inproceedings{yan-tao2002a,
title={A Constructive Approach to Solving 3-D Geometric Constraint Systems Using Dependence Analysis},
author={Yan-Tao Li, Shi-Min Hu, and Sun Jiaguang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160825215759907449453},
booktitle={Computer Aided Design},
volume={34},
number={2},
pages={97-108 },
year={2002},
}
```
Yan-Tao Li, Shi-Min Hu, and Sun Jiaguang. A Constructive Approach to Solving 3-D Geometric Constraint Systems Using Dependence Analysis. 2002. Vol. 34. In Computer Aided Design. pp.97-108 . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160825215759907449453.