关键词: B样条曲面, 能量优化, 形状修改

Abstract: For the shape modification of B-spline surface, it is difficult to select freely the deformable zone and calculate accurately the modified distance. Moreover, the modifying process is inefficient. Therefore, a method for shape modification of B-spline surface is proposed based on the idea of energy optimization. A method of segmenting B-spline surface into small surface patches by the knot vectors is given. By using an analogy between B-spline surface patches and the thin-plate elements of the finite element method, the external loads applied on the patches are replaced with a bilinear interpolation of the forces applied at the fours ends. The internal energy functional equation of B-spline surface and the energy functional equation of the external loads are constructed respectively. The change of external load results in the change of internal energy of B-spline rariation, the variation of the surface control points after modification can be obtained by solving an optimization problem that minimizes the variation of internal energy of B-spline. In addition, a method of calculating the modified distance accurately is provided to improve the accuracy and efficiency of shape modification B-spline surface. Examples verify the effectiveness and practicability of the proposed shape modification for the surface.

Key words: B-spline surfaces, Energy optimization, Shape modification