Abstract
The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.
Highlights
Freeform surfaces have seen enlarged applications since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy [7]
The general course of the surface reconstruction algorithms hereafter starts with the 3D Delaunay triangulation of the point set and extracts a triangular surface mesh from it
In this paper, a comparison of surface reconstruction algorithms is presented and lead to the choice of Cocone which fits at best our application
Summary
Delaunay and Voronoi-based meshing techniques [1] as well as implicit techniques [2] have been developed within the computer graphics community These techniques relate to the problem of surface reconstruction where only the cloud of points is known and concern applications such as video games, arts and reverse engineering. The general course of the surface reconstruction algorithms hereafter starts with the 3D Delaunay triangulation of the point set and extracts a triangular surface mesh from it. Doi:10.1088/1742-6596/483/1/012003 triangles that approximate the underlying surface are selected in the output mesh These triangles constitute the set of restricted Delaunay simplices. 3. Expected mesh quality and algorithm requirements The mesh of the dataset is a linear interpolation of the points, and is based on the Delaunay structure. The common approach for 3D datasets is to build a 3D Delaunay triangulation and extract triangular facets that are a linear approximation of the underlying surface.
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