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Algorithm 889: Jet_fitting_3:-A Generic C++ Package for Estimating the Differential Properties on Sampled Surfaces via Polynomial Fitting

机译:算法889:Jet_fitting_3:-用于通过多项式拟合估算采样表面上的微分特性的通用C ++程序包

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摘要

Surfaces of R~3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in computer graphics, computer aided design, computational geometry, and computer vision. One strategy to perform such an estimation consists of resorting to polynomial fitting, either interpolation or approximation, but this route is difficult for several reasons: choice of the coordinate system, numerical handling of the fitting problem, and extraction of the differential properties.rnThis article presents a generic C++ software package solving these problems. On the theoretical side and as established in a companion paper, the interpolation and approximation methods provided achieve the best asymptotic error bounds known to date. On the implementation side and following state-of-the-art coding rules in computational geometry, genericity of the package is achieved thanks to four template classes accounting for, (a) the type of the input points, (b) the internal geometric computations, (c) a conversion mechanism between these two geometries, and (d) the linear algebra operations. An instantiation within the Computational Geometry Algorithms Library (CGAL, version 3.3) and using LAPACK is also provided.
机译:R〜3的表面在科学和工程学中无处不在,估计离散为点云或三角形网格的表面的局部微分特性是计算机图形学,计算机辅助设计,计算几何和计算机视觉的核心组成部分。执行这种估计的一种策略是求助于多项式拟合,无论是插值法还是逼近法,但是这种方法很困难,原因有几个:坐标系统的选择,拟合问题的数值处理以及微分性质的提取。提供了解决这些问题的通用C ++软件包。从理论上讲,并在随附的论文中确定,所提供的插值和逼近方法可实现迄今为止已知的最佳渐近误差范围。在实现方面,并遵循计算几何学中的最新编码规则,该软件包的通用性得益于四个模板类,这些类考虑了(a)输入点的类型,(b)内部几何学计算,(c)这两个几何之间的转换机制,以及(d)线性代数运算。还提供了计算几何算法库(CGAL,版本3.3)中的实例化并使用LAPACK。

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