A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Computer Aided Geometric Design
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Surfaces of R3 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. This 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.