隐式T样条实现封闭曲面重建

Closed Surface Reconstruction Based on Implicit T-Splines

为了简化法向偏差约束条件和优化光滑能量项,提出一种隐式T样条曲面重建算法.首先利用八叉树及其细分过程从采样点集构造三维T网格,以确定每个控制系数对应的混合函数;然后基于隐式T样条曲面建立目标函数,利用偏移曲面点集控制法向,采用广义交叉检验(GCV)方法估计最优光滑项系数,并依据最优化原理将该问题转化为线性方程组求解得到控制系数,从而实现三角网格曲面到光滑曲面的重建.在误差较大的区域插入控制系数进行T网格局部修正,使得重建曲面达到指定精度.该算法使重建曲面C1连续条件得到松弛,同时给出最优的光顺项系数估计,较好地解决了封闭曲面的重建问题.实例结果表明,文中算法逼近精度高,运算速度快,仿真结果逼真.

To simplify the normal deviation constraint and optimize the smooth energy parameter of objective function, an implicit T-splines surface reconstruction algorithm is proposed. First, three dimensional T-meshes are constructed from the sample point set by using the octrees and subdivision process. And the corresponding blending function of each control coefficient is determined from the topology of three dimensional T-meshes. Then the objective function is established based on the implicit T-spline surfaces. The normal direction of the surface is controlled by adding off-surface points. The generalized cross validation （GCV） method is adopted to estimate the optimal smoothing parameter. By using least square approximation the surface reconstruction problem is transformed into solving a system of quations to get control coefficients. With the local refinement of T-splines, the approximation error can achieve the prescribed error tolerance, thus a triangular mesh model is automaticlly converted into a smooth T-spline surface. When compared with the existing algorithm, the algorithm can solve the surface reconstruction problem well, for the Ca continuous condition is relaxed and the optimal smoothing parameter is chosen. Some examples show that it has the high accuracy approximation, fast operation speed, realistic simulation results as well.