基于隐式T样条的曲面重构算法

提出隐式T样条曲面，将T网格从二维推广到三维情形，同时利用八叉树及其细分过程，从无结构散乱点数据集构造T网格，利用曲面拟合模型将曲面重构问题转化为最优化问题；然后基于隐式T样条曲面将最优化问题通过矩阵形式表述，依据最优化原理将该问题转化成线性方程组，通过求解线性方程组解决曲面重构问题；最后结合计算实例进行讨论．该方法能较好地解决曲面重构问题，与传统张量B样条函数相比，能效地减少未知控制系数与计算量．

A Surface Reconstruction Algorithm Based on Implicit T-Spline Surfaces

In this paper, we introduce the implicit T-spline surfaces, generalize the definition of T- meshes from 2D to 3D, and construct the T-meshes from the unorganized collection of sampling points based on the octrees and subdivision. By exploiting the surface fitting models, we transform the problem of surface reconstruction to an optimization problem. Then based on the implicit T-spline surfaces, we describe the optimization problem in the matrix forms, and convert it to a linear system by the theory of optimization. By solving the linear system, we get the unknown coefficients and the reconstructed surfaces. Finally, we conclude the paper with some illustrating examples and conclusion remarks. Our method can solve the surface reconstruction problems well; ad hoc it can effectively reduce the unknown coefficients compared with the implicit tensor product B-spline functions.