Research On Methods Of Redundancy Analysis And Solution Of 2D/3D Geometric Constraint Problem

Development and application of Computer Aided Design(CAD)technology has become one of the important standards for measuring the level of modernization of science and technology and industry modernization.The geometry constraint solving technology also develops with the CAD,and becomes the hotspot of the research.The thesis combined graph theory with numerical method to solve the geometric constraints.Thinking of thesis to solve the problem of geometric constrain were:firstly carried out unified modeling for the geometric constraints of 2D and 3D;secondly used graph theory to analyze,judge and process the redundancy of geometric constraint;finally,transformed the constraint problem into optimization problem and used optimization algorithm to solve.Firstly,the first task of the geometric constraint system was to solve the problem of modeling,in order to realize the unified expression of geometric constraints,firstly realized the unified expression of geometric entities,introduced into transcendental function in view of the Euler angle and Cardan angle,thesis used geometric entities unified expression based on Euler parameters.In face of complex geometric entities and geometric constraints,could be decomposed into a number of basic geometric entities or basic geometric constraints of the combination to express.In this thesis,a model based on bipartite graph was used to describe the geometric constraint system,aiming at the traditional modeling method rough describing the relationship between entity and constraint,could only determine the defects in the relationship between under-and over-constraint structure of constraints system,the thesis improved the traditional method of modeling,model could be more accurate to describe the relationship between specific parameters of entity and the basic constraints,achieves to determine the geometric relationship between under and over constraint of constraints system.Secondly,the thesis used bipartite graph DM decomposition algorithm to determine under-,over-constrained of geometric constraints.For solution of maximum matching in bipartite graph,difficult understanding,realizing complexity,time complexity of traditional algorithm,the thesis was proposed node degree for priority of optimal selection algorithm,and reduced the time complexity of solving the maximum matching.In process of dealing with under-constrained geometric constraints,in order to improve the processing speed,set adding constraint priority,automatically chose to add constraints by system;in process of dealing with over-constrained geometric constraints,firstly determined the type of over-constraint,aiming at decision algorithm computation complexity,realizing complexity and slow solving speed of the traditional symbol,the thesis proposed using the improved artificial bee colony algorithm to determine the consistency and inconsistency of constraint,used different methods to handle different types of over-constrained problems.Finally,thesis proves feasibility of the under-,over-constrained decision algorithm and processing algorithm by examples.Finally,solving complete constraint of geometric constraint problem,transformed geometric constraint problem into a single objective optimization problem,used intelligent algorithm to solve,the thesis proposed to use artificial bee colony algorithm to solve the geometric constraint problems.For the existence "premature" defects of the traditional artificial bee colony algorithm and problems of the relative slow convergence speed,the thesis improved the traditional artificial bee colony algorithm,in the improved artificial bee colony algorithm,employment bee in search stage to multi-dimensional progressive search optimal value replaced random one-dimensional search of traditional artificial bee colony algorithm,and adopted a new adaptive method for following calculating the probability of non-employment bee,and dynamically adjusted the frequency of bees elimination.Through the example simulation test,contrasting experimental data of improved artificial bee colony algorithm,classical particle swarm optimization algorithm and traditional artificial bee colony algorithm showed that,the comprehensive performance of the improved artificial bee colony algorithm is significantly better than the latter two,and haves the advantages of fast convergence,high accuracy,high efficiency,more stabilization.