Fundamental Technology Research On Subdivision Surface Modeling Based On Geometric Constraints

The subdivision surface is gradually becoming a powerful geometric modeling tool because of its advantage of arbitrary topological adaptability. Geometric constraints are important means to improve the precision of complex surface modeling. Points and curves are the most effective ones among geometric constraints. In order to improve the modeling abilities of subdivision surfaces and make it applied in conceptual design of CAD more efficiently, this dissertation mainly studies subdivision modeling technologies based on constraints of vertices and arbitrary topological curve networks. The main research contents and creative achievements are as fellows:(1) After introducing the definition of curve networks, we present the constructing and editing methods of them. Based on these methods, the combined subdivision scheme is extended to have the ability of interpolating arbitrary topological curve networks.(2) Based on the analyses of the feature and the unfair reasons of combined subdivision surfaces, we propose the non-uniform combined subdivision scheme by improving subdivision rules. The improved one can produce interpolating limit surface of better fairness. The surface generated by the non-uniform combined subdivision scheme reaches at least G1 continuity.(3) Two shape modification methods of combined subdivision surfaces are put forward by editing curve networks and applying point constraints based on PDE optimum method. The former is suitable to be used at the initial stage of combined subdivision surfaces'modification, and can be used to modify the local and the global regions of combined subdivision surfaces. The latter can modify the region far away from interpolated curve, and has the advantages of high calculation efficiency and more uniform curvature distribution of modified surfaces. Two methods work on different regions of combined subdivision surfaces and at different stages of shape modification. They supplement for each other to modify combined subdivision surfaces.(4) Two methods of constructing feature based on interpolated curves are presented. The first one is implemented by adjusting second derivatives on cross curve according to the given feature angle during subdivision and generating sharp feature on interpolated curves. The second one is to separate the curves defining features from the curves defining base surfaces and build compound curve networks, and then combined subdivision surface with sharp feature is generated after subdividing compound curve networks with the improved rules. The shape of features can be adjusted by changing the sharp coefficients related with the curves. The former has advantages of operating easily and realizing conveniently, and the latter can be used to design surfaces freely and produce features of better effect.(5) Method of constructing subdivision surfaces under constraints of vertices and normal vectors is proposed. The control net of the interpolating surface is obtained by repeatly modifying the positions of vertices according to the optimum result after refining mesh of constrained vertices once. This method avoids solving global equations so it has the advantages of high calculation efficiency and better fairness of interpolating surface. The shape of interpolating surface can be adjusted flexibly, and more freedom is given to designer.