Abstract
In Computer Aided Geometric Design (CAGD) the automated fitting of surfaces to massive series of data points presents several difficulties: (i) even the formal definition of the problem is ambiguous because the mathematical characteristics (continuity, for example) of the surface fit are dependent on non-geometric considerations, (ii) the data has an stochastic sampling component that cannot be taken as literal, and, (iii) digitization characteristics, such as sampling interval and directions are not constant, etc. In response, this investigation presents a set of computational tools to reduce, organize and re-sample the data set to fit the surface. The routines have been implemented to be portable across modeling or CAD servers. A case study is presented from the footwear industry, successfully allowing the preparation of a foreign, neutral laser digitization of a last for fitting a B-spline surface to it. Such a result was in the past attainable only by using proprietary software, produced by the same maker of the digitizing hardware.
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References
ANSIY14.5.1M-Draft (1993) Mathematical Definition of Dimensioning and Tolerancig Principles, American Society of Mechanical Engineers. New York.
Carr, K. (1995) Modeling and verification methods for the inspection of geometric tolerances using point data , Ph.D. Dissertation, University of Illinois at Urbana-Champaign.
Edelsbrunner, H., Mücke, E. (1994) Three Dimensional Alpha Shapes. ACM Transactions on Graphics, Vol. 13, No. 1, pp. 43–72.
Farin, G. (1990) Curves and Surfaces for Computer Aided Geometric Design. A Practical Guide. Academic Press. Boston.
Guo, B. (1997) Surface Reconstruction: from Points to Splines. Computer Aided Design. Vol. 29, No. 4, pp. 269–277.
Mortenson, M. (1985) Geometric Modeling, John Wiley and Sons. New York.
Posada, J. (1997) An Implementation of the AIS Interface on Micro Station, B.Sc. Thesis, EAFIT University Medellin, Colombia.
Preparata, F., Shamos, M. I. (1985) Computational Geometry. An Introduction, Springer Verlag. New York.
Ranyak, P. (1994) Application Interface Specification (AIS) Version 2.1. Consortium for Advanced Manufacturing International (CAM-I). Integrity Systems, USA.
Ruiz, O., Marin, R. and Ferreira, P. (1994) A Geometric Reasoning Server with Applications to Geometric Constraint Satisfaction and Reconfigurable Feature Extraction. Proceedings, 3rd Luso-German Workshop on Graphics and Modeling in Science and Technology, Coimbra, Portugal.
Ruiz, O. (1995) Geometric Reasoning in Computer Aided Design, Manufacturing and Process Planning, Ph.D. Dissertation, University of Illinois at Urbana-Champaign.
Saldarriaga, J. and Isaza D. (1997) An Implementation of the AIS Interface on Auto CAD, B.Sc. Thesis, EAFIT University Medellin, Colombia.
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© 1999 Springer Science+Business Media Dordrecht
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Ruiz, O.E., Posada, J.L. (1999). Computational Geometry in the Preprocessing of Point Clouds for Surface Modeling. In: Batoz, JL., Chedmail, P., Cognet, G., Fortin, C. (eds) Integrated Design and Manufacturing in Mechanical Engineering ’98. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9198-0_23
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DOI: https://doi.org/10.1007/978-94-015-9198-0_23
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