【摘要】 给出了Doo-Sabin细分曲面在奇异面的极限位置和法矢计算公式,定义了正则网格带的局部等参数线。通过建立局部坐标系对曲面上所有点进行局部参数化,把曲面上点的位置、法向量及局部等参数线等约束转化为所有待调整控制顶点的约束,得到线性系统,从而可以在满足上述多种不同类型的几何约束时修改曲面的形状。从控制网格扰动量最小和能量优化的角度给出两种修改算法,并利用广义逆矩阵求得显式解。约束的线性关系表明,两种方法都存在逆过程,修改的结果与过程无关,便于实际操作与控制。更多还原

【Abstract】 The constraints of points,normal vectors and local isoparametric curves on Doo-Sabin subdivision surfaces,which were converted into those on control vertices to be adjusted,were specified via setting up local coordinate systems.A linear system was obtained and the shape of Doo-Sabin subdivision surfaces can be modified with various geometric constraints.By minimizing the variation of control net and optimizing the membrane energy,two methods were presented,which can be solved explicitly with pseudo-inverse matrices.Both methods are invertible,commutative and associative,which facilitates practical manipulation and control.更多还原