Algorithmes de partition pour la spécification et la vérification géométrique des produits

par Yifan Qie

Projet de thèse en Génie mécanique

Sous la direction de Nabil Anwer.

Thèses en préparation à université Paris-Saclay , dans le cadre de École doctorale Sciences Mécaniques et Energétiques, Matériaux et Géosciences , en partenariat avec Laboratoire Universitaire de Recherche en Production Automatisée (laboratoire) , Géométrie tridimensionnelle des pièces et des mécanismes (equipe de recherche) et de Ecole Normale Supérieure Paris-Saclay (référent) depuis le 28-02-2019 .

  • Titre traduit

    Partitioning Algorithms for Geometrical Product Specifications and Verilication

  • Résumé

    In ISO Geometrical Product Specifications and Verification Standards (GPS) [ISO11], Feature operations are used to obtain ideal and non-ideal features. The formalization of such operations enable to reduce ambiguity and uncertainty within the activities of design, manufacture and metrology of mechanical products, and their scientific investigation contribute to develop a sound mathematical framework and formalisms for the comprehension of engineering practices and the development of new standards. Among these operations Partition, Extraction, Filtration and Association have been particularly investigated. Partition is used to identify ideal or non-ideal features, Extraction enables to identify specific points from a non-ideal feature, Filtration is used to create a non-ideal feature from a non-ideal feature, and Association is used to fit ideal feature(s) to non-ideal feature(s) according to a criterion. Feature operations have been particularly researched in recent years by the research community from mathematical and computational point of view and some important results have been highlighted by new standardization efforts and the recent developments of geometry processing methods and tools in computational metrology. Partition is one of the fundamental operations used to specify the geometry of a product. Partition or Segmentation is also an important problem in geometry processing and is addressed by different topics and fields such as medical imaging, computer graphics, civil engineering and mechanical engineering in the context of reverse engineering. Here the object is decomposed into independent surface portions for further processing and analysis. The default partition, according to international standards, is that which divides the surface into maximal surface portions each of which belongs to one of the seven invariance classes of surfaces, (i.e. plane, sphere, cylinder, surface of revolution, prism, helix, and complex surface). Several classifications of partitioning methods and techniques have been proposed. In mechanical engineering applications [APP+07], two main families of methods have been exploited. The first seeks to identify contours from discontinuities and transitions in point clouds and meshes [ BV04] [XLX+11]. The second aggregates points and meshes into clusters to define regions with homogeneous geometric properties (region growing). Subsequently, edges and contours are obtained by the intersection of these regions [KCL09] [BJ88]. Hybrid methods have also been developed by exploiting the advantages of each method [LDB05] [RB03]. The default partition, according to international standards, is that which divides the surface into maximal surface portions each of which belongs to one of the seven invariance classes of surfaces, (i.e. plane, sphere, cylinder, surface of revolution, prism, helix, and complex surface). Few algorithms exist that can implement GPS partition, but they nearly all require assumptions and a-priori knowledge of the nominal model and its partitioning, and a high density of sampled points on the surface to ensure an accurate estimate of the surface normal. A new hybrid approach has been developed in the framework of Zhao's thesis [Zha10]. This hybrid partitioning method combines vertex clustering and region growing and is based on a new set of curvature-based shape descriptors (curvedness and shape index). This approach is proved to be efficient for segmentation and feature recognition but is not adapted to GPS partition since it requires a high density of surface points [ZAB13] [XAM+16] and doesn't consider invariance classes. The PhD research project will develop robust partitioning algorithms in the context of new ISO Geometrical Product Specifications and Verification Standards. In order to reinforce the actual work from the novel developments from computational geometry, vision and machine learning, a state-of-the-art survey of segmentation methods and techniques reported in the literature will be conducted. The research work will focus on the earlier works conducted by ISO/TC 213 experts related to slippage analysis (Stanford method [GG04]), probabilistic identification of invariance classes (Turin method [CD05]) and curvature-based shape segmentation (Cachan method [ZAB13]) to draw new type of classification and usage for partitioning to enrich the concepts and provide scientific basis for ISO 18183 series [ASS18]. Default partition and geometric specifications will be addressed considering invariance classes of surfaces. The work will also investigate new statistical approaches for vertex clustering, robust estimation of normal and curvature parameters, and the evaluation of partitioning results. [ASS18] Anwer, N., Scott, P. J., Srinivasan, V., 2018, Toward a Classification of Partitioning Operations for Standardization of Geometrical Product Specifications and Verification, 15th CIRP Conference on Computer Aided Tolerancing – CIRP CAT 2018, 11-13 June 2018, Milano, Italy. Procedia CIRP, Volume 75, 2018, Pages 325-330. [APP+07] Agathos, A., Pratikakis, I., Perantonis, S., Sapidis, N., Azariadis, P., 3D mesh segmentation methodologies for cad applications, Computer Aided Design and Applications, 4(6), 827–841, 2007 [BJ88] Besl, J., Jain R., Segmentation through variable order of surface fitting, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(2), 167-192, 1988 [BV04] Benko, P., Varady, T., Segmentation method for smooth point regions of conventional engineering objects, Computer-Aided Design, 36, 511-523, 2004 [CD05] Chiabert, P., De Maddis M., Statistical modelling of geometrical invariant sampled sets; In: Proceedings of 9th CIRP International Seminar on Computer Aided Tolerancing, Tempe-Arizona (USA), 2005 [GG04] Gelfand, N., Guibas, L. J., Shape segmentation using local slippage analysis. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 214–223, 2004 [ISO11] ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model for geometrical specification and verification. Geneva, International Organization for Standardization 2011. [KCL09] Kim, H.-S., Choi, H.-K., Lee K.-H., Feature detection of triangle meshes based on tensor voting theory, Computer-Aided Design, 41, 47-58, 2009 [LDB05] Lavoué, G., Dupont F., Baskurt, A., A new CAD mesh segmentation method based on curvature tensor analysis, Computer-Aided Design, 37, 975-987, 2005 [RB03] Razdan, A., Bae, M.S., A hybrid approach to feature segmentation of triangle meshes, Computer-Aided Design, 35, 783-789, 2003 [XAM+16] Xu, S., Anwer, N., Mehdi-Souzani, C., Harik, R., Qiao, L., STEP-NC based reverse engineering of in-process model of NC simulation, International Journal of Advanced Manufacturing Technology, 86(9):3267-3188, 2016 [XLX+11] Xiao, D., Lin H., Xian C., Gao S., CAD mesh segmentation by clustering, Computers & Graphics, 35, 685 691, 2011 [ZAB13] Zhao, H., Anwer, N., Bourdet, P., Curvature-based Registration and Segmentation for Multisensor Coordinate Metrology, Procedia CIRP, 10, 112-118, 2013 [Zha10] Zhao, H., Multisensor Integration and Discrete Geometry Processing for Coordinate Metrology. Thèse de Doctorat, École Normale Supérieure de Cachan, 2010