【摘要】 点法向（PN）细分算法是线性细分算法的推广，利用控制顶点和控制法向调整细分曲线和细分曲面的形状，具有与其对应的线性细分算法相同的收敛性和连续阶。基于PN细分算法的保圆/保球面性质，给出了一种PN细分曲线和细分曲面局部拟插值的充分条件，并利用该条件提出了一种PN-B样条细分曲线和PN-CatmullClark细分曲面几何插值算法。PN-B样条细分曲线和PN-Catmull-Clark细分曲面的控制顶点和控制法向可由给定插值点的位置、法向和曲率直接计算得到，控制顶点和控制法向中的自由参数可通过建立和优化Dirichlet能量函数选取。数值实验验证了法向调整、曲率约束及局部点位置变化对曲线和曲面几何形态的调控作用。更多还原

【Abstract】 Point-normal(PN) subdivision algorithms are generalizations of linear subdivision algorithms. PN subdivision adjusts the shape of subdivided curves and surfaces using control vertices and control normals while maintaining the same convergence and continuity order as linear subdivision curves/surfaces. In this paper, a sufficient condition for local quasi-interpolation of PN subdivision curves/surfaces is proposed based on their circle-preserving/sphere-preserving properties. Then geometric interpolation algorithms for PN-B spline subdivision curves and PNCatmull-Clark subdivision surfaces are given. The control vertices and normals of the interpolating PN-B spline curves and PN-Catmull-Clark surfaces can be directly computed from given points, normals, and curvatures. The free parameters in the control vertices and normals are determined by establishing and optimizing a Dirichlet energy function. Numerical experiments demonstrate the effectiveness of the proposed method for curve and surface modeling.更多还原