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Geometric constraint solving with conics and linkages
Authors:Xiao-Shan GaoAuthor Vitae  Kun JiangAuthor VitaeChang-Cai ZhuAuthor Vitae
Affiliation:Institute of Systems Science, AMSS, Academia Sinica, Beijing 100080, China
Abstract:Most geometric construction methods of geometric constraint solving systems use line and circle (rule and compass) as basic drawing tools. In this paper, by introducing conics and linkages, we provide a set of complete drawing tools for the construction approach of geometric constraint solving. Using these tools, we may enlarge the drawing scope of the construction approach and still keep the elegant style of geometric solutions to geometric constraint solving. As applications, we obtain pure geometric solutions to three sets of well-known constraint problems: the 10 Apollonian drawing problems, the 13 cases of a smallest tri-connected constraint graph, and constraint problems with distance constraints only.
Keywords:Geometric constraint solving  Parametric CAD  Construction methods  Conics  Linkages  Apollonian drawing problems  Tri-connected constraint graph
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