Abstract
This paper proposes a DOF-based graph reduction approach to geometric constraint solving. The proposed approach incrementally solves 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 the two solving procedures: algebraic method and numerical method, instead of solving it simultaneously using a numerical method. However, the use of the numerical method is restricted to solve only those parts that must be solved numerically. By combining the advantages of algebraic solving with the universality of numerical solving, the proposed method can maximize the efficiency, robustness, and extensibility of a geometric constraint solver.
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Lee, J.Y. (1999). A 2D Geometric Constraint Solver for Parametric Design Using Graph Analysis and Reduction. In: Automated Deduction in Geometry. ADG 1998. Lecture Notes in Computer Science(), vol 1669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47997-X_13
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DOI: https://doi.org/10.1007/3-540-47997-X_13
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