基于代数张量积B样条的隐式曲面重构

Implicit surface reconstruction based on algebraic tensor-product B-spline

提出一种以代数张量积B-样条曲面作为几何表示形式的方式,采用Sampson距离来度量数据点与曲面之间的误差,它不仅是几何距离的很好近似且具有齐性和刚体不变的良好性质。建立了近似几何误差和薄板能量极小化的最优化隐式曲面重构模型。同时结合最优化理论中的信赖域思想和拟牛顿法,给出自适应的迭代求解算法及其实现。理论上由信赖域法的收敛性分析,迭代算法具有总体收敛性。最后基于散乱点数据集,给出曲面重构的实例,并作简单的讨论。

An implicit surface reconstruction method is proposed which represents the surface with an algebraic tensor-product B-spline, and minimizes the tension of the B-spline and based on the Sampson error, which is a different approximation of geometric distance from the point set to the surface. The method is dynamic and self-adaptive based on trust-region algorithm and quasi-Newton method in optimization theory. According to the convergence analysis of the trust region algorithms, the iteration algorithm could reach global convergence. Some examples are given and conclusion remarks are concluded.