Abstract
This paper presents an experiment that demonstrates the feasibility of successfully applying CASL to design 3D geometric modelling software. It presents an abstract specification of a 3D geometric model, its basic constructive primitives together with the definition of the rounding high-level operation. A novel methodology for abstractly specifying geometric operations is also highlighted. It allows one to faithfully specify the requirements of this specific area and reveals new mathematical definitions of geometric operations. The key point is to introduce an inclusion notion between geometric objects, in such a way that the result of an operation is defined as the smallest or largest object satisfying some pertinent criteria. This work has been made easier by using different useful CASL features, like first-order logic, free types or structured specifications. Some assets of this specification are to be abstract, readable by researchers in geometric modelling and to simplify the programming process.
This project is partially supported by a French national project (Plan Pluri Formation 1998-2001) between the universities of Poitiers, Strasbourg and Évry, and by the ESPRIT Working Group 29432 (CoFI WG).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Bertrand and J.-F. Dufourd. Algebraic specification of a 3D-modeller Based on Hypermaps. Computer vision, graphical model, and image processing, 56(1):29–60, 1994.
J.-F. Dufourd. Algebras and formal specifications in geometric modeling. The Visual Computer, 13:131–154, 1997. Springer-Verlag.
H. Elter. Etude de structures combinatoires pour la représentation de complexes cellulaires. PhD thesis, Université de Strasbourg, 1994.
L. Fuchs, D. Bechmann, Y. Bertrand, and J.-F. Dufourd. Formal specification for free-form curves and surfaces. In Spring Conference on Computer Graphics, Bratislava, 1996.
F. Ledoux and A. Arnould. Geospec: specification libraries for geometric modelling, sept. 2001. http://www.sic.sp2mi.univ-poitiers.fr/GL/GeoSpec.
F. Ledoux, A. Arnould, P. Le Gall, and Y. Bertrand. A High-Level Operation in 3D Modelling: a CASL Case Study. Technical Report 52, Université d’Évry, 2000. ftp://ftp.lami.univ-evry.fr/pub/publications/reports/index.html.
P. Lienhardt. Topological models for boundary representations: a comparison with n-dimensional generalized maps. Computer-Aided Design, 23(1):59–82, 1991.
P. Lienhardt. N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications, 1994.
F. Ledoux, J.-M. Mota, A. Arnould, C. Dubois, P. Le Gall, and Y. Bertrand. Formal specification for a mathematics-based application domain: geometric modelling. Technical Report 51, Université d’Évry, 2000. ftp://ftp.lami.univ-evry.fr/pub/publications/reports/index.html.
M. Mantyla. Computational topology: A study of topological manipulations and interrogations in computer graphics and geometric modeling. Acta Polytech. Scand. Math. and Comput. Sci. Ser., MA37:1–49, 1983.
T Mossakowski, Anne Haxthausen, and Bernd KriegBruckner. Subsorted partial higher-order logic as an extension of casl. In Christine Choppy, Didier Bert, and Peter Mosses (eds.): Recent Developments in Algebraic Development Techniques, Lecture Notes in Computer Science, volume 1827, pages 126–145, Chateau de Bonas, France, 2000. Springer-Verlag.
P. D. Mosses. CASL: A guided tour of its design. Lecture Notes in Computer Science, 1589:216–240, 1999.
Till Mossakowski, Markus Roggenbach, Lutz Schroder, and Pascal Schmidt). CASL tool set (CATS) version 0.73, sept. 2001. http://www.tzi.de/cofi/CASL/CATS/download.html.
Till Mossakowski, Markus Roggenbach, Lutz Schroder, and Pascal Schmidt). HOL-CASL system version 0.6, sept. 2001. http://www.tzi.de/cofi/CASL/.
CoFI (Common Framework Initiative) Task Group on Language Design. CASL case studies, 2000. http://www.pst.informatik.uni-muenchen.de/baumeist/CoFI/case.html.
CoFI (Common Framework Initiative) Task Group on Language Design. CASL the common algebraic specification language summary, June 2000. ftp://ftp.brics.dk/Projects/CoFI.
F. Puitg and J.-F. Dufourd. Formal specification and theorem proving breakthroughs in geometric modeling. In Proc. 11th International Theorem Proving in Higher Order Logics Conference, pages 401–422, 1998.
François Puitg and Jean-François Dufourd. Formalizing mathematics in higher-order logic: A case study in geometric modelling. Theoretical Computer Science, 234(1–2):1–57, 2000.
M. Roggenbach, T. Mossakowski, and L. Schroder. Basic datatypes in CASL. CoFI Note L-12-Version 0.4.1, http://www.brics.dk/Projects/CoFI/Notes/L-12/index.html, May 2000.
Tamás Várady, Ralph R. Martin, and Janos Vida. A survey of blending methods that use parametric surfaces. Computer-Aided Design, 26(5):341–365, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ledoux, F., Arnould, A., Le Gall, P., Bertrand, Y. (2002). Geometric Modelling with CASL. In: Cerioli, M., Reggio, G. (eds) Recent Trends in Algebraic Development Techniques. WADT 2001. Lecture Notes in Computer Science, vol 2267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45645-7_9
Download citation
DOI: https://doi.org/10.1007/3-540-45645-7_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43159-6
Online ISBN: 978-3-540-45645-2
eBook Packages: Springer Book Archive