Research On The Key Issues Of Geometric Constraint Solving

Geometry constraint solving is the most central technology in the Parameter design methods on the basis of constraint satisfaction. It is the key of the quality of the parameterization design system to weigh to whether the geometric constraint technology is mature or not. In the present paper several issues concerning the geometry constraint solving are addressed as follows.(1) A novel under-constrained solving algorithm based on the constraint directed graph is proposed to advance the efficiency of under-constrained solving. For the constraint directed graph, the solving method of every geometric element is defined and the number of geometry elements is reduced by way of analysis. This method is highly effective to minimize the volume of solving work and to satisfy the design intention in great degree.(2) For the multi-solutions problem in the process of geometric constraint solving, a process method is proposed with adding additional constraints. The location constraint and structure constraint are introduced to confine the topology shape of every geometric element, and a solution satisfying the user'intention was got.(3) Chaotic particle swarm algorithm is proposed for solving the geometric constraint problems. Based on the basic PSO algorithm, the chaotic search is carried out in the whole solution space to avoid sticking at local optima effectively. The chaotic particle swarm algorithm is applied when the Newton-Raphson iterative algorithm is failure for some geometric constraint problems.(4) A new PSO algorithm based on simulated anealing and mutation was proposed to solve the extremum problem. First, use mutation strategy to produce a new feasible solution. Then, in the operation of simulated annealing, determine if the generated feasible solution can be further optimized and adjusted. A great number of experiments indicate that new algorithm has greater convergence speed and accuracy than basic PSO.(5) In parametric CAD systems, unreasonable parameter values in a parametric model often result in improper shape of the geometric object. To resolve this problem, we proposed an algebraic algorithm for determining the valid range of parameter values in 2-dimensional parametric CAD models. The result shows that all values within the valid range provided by the algorithm can ensure that topological shape of geometric object not change after reconstruction, and so the algorithm to some extent can improve the designing efficiency of parametric CAD software and intellectual level of human-computer interaction.In conclusion, the achievements of this dissertation make the applied research on the geometric constraint solving theory progress. It has a certain theory significance and application importance. It provides effective methods and means for the research on the geometric constraint solving.