Abstract:

For the shape modification of surface connected by multi B-spline surfaces, a deformation algorithm was presented. A uniform rigid frame model was created through merger of control mesh among the surfaces to illustrate the position of control vertexes of surfaces. The minimizations of the external load and node displacements were described in a uniform objective function with the displacement of node. Smooth connection relationship among different surfaces and geometric constraints (point constraint, point and normal constraint) were extracted as constraint equations. The penalty function method was introduced to solve this problem. Experimental examples show that this algorithm is intuitive and accurate.

Key words: computer aided geometric design, B-spline surface, shape deformation, geometric constraint

摘要：

针对由多张B-spline曲面拼接构成的曲面形状修改问题,提出了一种多张B-spline曲面变形算法。通过将曲面片控制顶点网格进行“合并”来建立多张B-spline曲面的刚架模型；以刚架节点位移为未知量，建立节点载荷最小和节点位移最小的统一优化目标函数；将曲面片之间的光滑拼接条件抽象为节点相对位置约束，结合点约束、点和法矢约束共同组成约束方程组；采用罚函数法求解得到变形后曲面新的控制顶点。变形实例表明该算法是直观有效的。

关键词: 计算机辅助几何设计, B样条曲面, 形状修改, 几何约束