B-spline Curve And Surface Reconstruction Under Geometric Constraint

Reconstruction on CAD model is one of the main technology for reverse engineering, How to set up CAD model with efficient and speed is one of the most hot topic. As a part of reconstruction on CAD model, curve and surface reconstruction is significant technique to design, manufacture and check on complicated product, it is attached importance to represent free-from curve and surface, the emphases for this paper is CAD model reconstruction based on B-spline curve and B-spline surface.Within the practical application, especially concept design phase on product outline, designer only pay attention to effect of visual. To reconstruct curve and surface which can meet requirement, geometric constraint is necessary, the geometric constraint will affect the shape and fitting effect. Therefore, develop the CAD model reconstruction method for curve and surface with geometric constraint will be considerably beneficial to the application. The paper study the free-from curve and surface reconstruction based on energy optimization , after the systematically analysis of the theories and the research on geometric constraint, a new reconstruction method for B-spline curve and surface with geometric constraint is presented. The main work and conclusion in this paper are as below:1. Dissertate the theories and method on B-spline curve and B-spline surface, discuss the theory on reconstruction based on energy optimization method and set up the finite element method solution based on physics energy deformation.2. Put forward the reconstruction method of B-spline curve under geometric constraint , it can avoids the sampling andparameterization problems result from traditional interpolation and approximation, considering the traditional solution method is difficult for geometric constraint, a solution method based on degrees of freedom transform is presented, which can solve geometric constraint by the finite element method. The example results verified the practicability and validity of the method.3. Put forward the reconstruction method of B-spline surface with geometric constraint. Describe all sorts of geometric constraints and apply solution method based on degrees of freedom transform to B-spline surface. This method can solve the problem caused by geometric constraint on B-spline surface well.