Reconstruction of freeform surfaces for metrology

14th International Conference on Metrology and Properties of Engineering Surfaces

El-Hayek, N.^1,4 ; Nouira, H.^1 ; Anwer, N.^2 ; Damak, M.^3,4 ; Gibaru, O.^4

Laboratoire Commun de Métrologie (LNE-CNAM), Laboratoire National de Métrologie et d'Essais (LNE), 1 Rue Gaston Boissier, 75015 Paris, France^1

Ecole Normale Supérieure de Cachan, University Research Laboratory in Automated Production, 61 avenue du Président Wilson, 94235 Cachan, France^2

GEOMNIA: 3D Metrology Engineering and Software Solutions, EuraTechnologies, 165 Avenue de Bretagne, 59000 Lille, France^3

Arts et Métiers de Lille (ENSAM), Laboratory of Information Sciences and Systems (LSIS), 8 Boulevard Louis XIV, 59046 Lille, France^4

关键词: Comparative studies;    Free-form surface;    Functional specification;    Initial conditions;    Parametric surfaces;    Piecewise linear approximations;    Polynomial splines;    Surface modeling;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/483/1/012003/pdf
DOI  :  10.1088/1742-6596/483/1/012003

来源: IOP

【 摘 要 】

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.