Shape Modification of B-Spline Surfaces Based on Rigid Frame via Geometric Constraint Optimization

Space deformation is an important tool in the field of computer graphics and geometric modeling. In this paper, a new method based on rigid frame in FEM about shape modification of B-spline surface is presented. Firstly, rigid frame model of the surface is established according to its control mesh. Then, boundary conditions such as hinge and fix are imposed on selected nodes. Finally, after geometric constraints including point, normal vector and curve constraints are specified interactively, control vertices of original surface are computed via geometric constraint optimization so that the modified surface can meet some given geometric constraints. Two optimization objectives are proposed: One is based on minimizing external loads, and the other is based on minimizing displacement of nodes. The experimental results show that the proposed approach is simple, intuitive and applicable for CAD systems.