This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems wi...This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.展开更多
This paper applies genetic simulated annealing algorithm (SAGA) to solving geometric constraint problems. This method makes full use of the advantages of SAGA and can handle under-/over- constraint problems naturally....This paper applies genetic simulated annealing algorithm (SAGA) to solving geometric constraint problems. This method makes full use of the advantages of SAGA and can handle under-/over- constraint problems naturally. It has advantages (due to its not being sensitive to the initial values) over the Newton-Raphson method, and its yielding of multiple solutions, is an advantage over other optimal methods for multi-solution constraint system. Our experiments have proved the robustness and efficiency of this method.展开更多
This paper proposes a constructive approach to solving geometric constraint systems.The approach incorporates graph-based and rule-based approaches, and achieves interactive speed.The paper presents a graph representa...This paper proposes a constructive approach to solving geometric constraint systems.The approach incorporates graph-based and rule-based approaches, and achieves interactive speed.The paper presents a graph representation of geometric conStraint syStems, and discusses in detailthe algorithm of geometric reasoning based on poinl-cluster reduction. An example is made forillustration.展开更多
To solve the problem that in parametric drawing systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, this paper proposes a novel algebraic algorithm for...To solve the problem that in parametric drawing systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, this paper proposes a novel algebraic algorithm for determining the valid range of parameter values in certain 2-dimensional parametric drawing systems. This algorithm can solve valid range of parameters such as radius and coordinate of centre points of parametric models with only linear segments and circles. The result of the study shows that all values within the valid range provided by this algorithm can ensure that the topological shape of a geometric object does not change after reconstruction, and to some extent, this algorithm can significantly promote the efficiency of parametric drawing system design and the intel- lectual level of human-computer interaction. The analysis shows that complexity of this algorithm is O（n2）.展开更多
基金973" Project ( No. G19980306) by the National Natural Science Foundation of China under an outstanding youth grant ( Grant No. 69725002) .
文摘This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.
文摘This paper applies genetic simulated annealing algorithm (SAGA) to solving geometric constraint problems. This method makes full use of the advantages of SAGA and can handle under-/over- constraint problems naturally. It has advantages (due to its not being sensitive to the initial values) over the Newton-Raphson method, and its yielding of multiple solutions, is an advantage over other optimal methods for multi-solution constraint system. Our experiments have proved the robustness and efficiency of this method.
文摘This paper proposes a constructive approach to solving geometric constraint systems.The approach incorporates graph-based and rule-based approaches, and achieves interactive speed.The paper presents a graph representation of geometric conStraint syStems, and discusses in detailthe algorithm of geometric reasoning based on poinl-cluster reduction. An example is made forillustration.
文摘To solve the problem that in parametric drawing systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, this paper proposes a novel algebraic algorithm for determining the valid range of parameter values in certain 2-dimensional parametric drawing systems. This algorithm can solve valid range of parameters such as radius and coordinate of centre points of parametric models with only linear segments and circles. The result of the study shows that all values within the valid range provided by this algorithm can ensure that the topological shape of a geometric object does not change after reconstruction, and to some extent, this algorithm can significantly promote the efficiency of parametric drawing system design and the intel- lectual level of human-computer interaction. The analysis shows that complexity of this algorithm is O（n2）.
