• Title/Summary/Keyword: constructible set

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A Study on the Geometric Constraint Solving with Graph Analysis and Reduction (그래프의 분석과 병합을 이용한 기하학적제약조건 해결에 관한 연구)

  • 권오환;이규열;이재열
    • Korean Journal of Computational Design and Engineering
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    • v.6 no.2
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    • pp.78-88
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    • 2001
  • In order to adopt feature-based parametric modeling, CAD/CAM applications must have a geometric constraint solver that can handle a large set of geometric configurations efficiently and robustly. In this paper, we describe a graph constructive approach to solving geometric constraint problems. Usually, a graph constructive approach is efficient, however it has its limitation in scope; it cannot handle ruler-and-compass non-constructible configurations and under-constrained problems. To overcome these limitations. we propose an algorithm that isolates ruler-and-compass non-constructible configurations from ruler-and-compass constructible configurations and applies numerical calculation methods to solve them separately. This separation can maximize the efficiency and robustness of a geometric constraint solver. Moreover, the solver can handle under-constrained problems by classifying under-constrained subgraphs to simplified cases by applying classification rules. Then, it decides the calculating sequence of geometric entities in each classified case and calculates geometric entities by adding appropriate assumptions or constraints. By extending the clustering types and defining several rules, the proposed approach can overcome limitations of previous graph constructive approaches which makes it possible to develop an efficient and robust geometric constraint solver.

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A Geometric Constraint Solver for Parametric Modeling

  • Jae Yeol Lee;Kwangsoo Kim
    • Korean Journal of Computational Design and Engineering
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    • v.3 no.4
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    • pp.211-222
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    • 1998
  • Parametric design is an important modeling paradigm in CAD/CAM applications, enabling efficient design modifications and variations. One of the major issues in parametric design is to develop a geometric constraint solver that can handle a large set of geometric configurations efficiently and robustly. In this appear, we propose a new approach to geometric constraint solving that employs a graph-based method to solve the ruler-and-compass constructible configurations and a numerical method to solve the ruler-and-compass non-constructible configurations, in a way that combines the advantages of both methods. The geometric constraint solving process consists of two phases: 1) planning phase and 2) execution phase. In the planning phase, a sequence of construction steps is generated by clustering the constrained geometric entities and reducing the constraint graph in sequence. in the execution phase, each construction step is evaluated to determine the geometric entities, using both approaches. By combining the advantages of the graph-based constructive approach with the universality of the numerical approach, the proposed approach can maximize the efficiency, robustness, and extensibility of geometric constraint solver.

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