Solving dynamic geometric constraints involving inequalities

Authors:
Hoon Hong;Liyun Li;Tielin Liang;Dongming Wang
Affiliations:
Department of Mathematics, North Carolina State University, Raleigh, NC;LMIB – School of Science, Beihang University, Beijing, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China;LMIB – School of Science, Beihang University, Beijing, China
Venue:
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Year:
2006

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Abstract

This paper presents a specialized method for solving dynamic geometric constraints involving equalities and inequalities. The method works by decomposing the system of constraints into finitely many explicit solution representations in terms of parameters with radicals using triangular decomposition and real quantifier elimination. For any given values of the parameters, if they verify some set of computed relations, the values of the dependent variables may be easily computed by direct evaluation of the corresponding explicit expressions. The effectiveness of our method and its experimental implementation is illustrated by some examples of diagram generation.