Abstract
Some aspects of geometric design programming using a functional language and a dimension-independent approach to geometric data structureare discussed in this paper. In particular it is shown that such an environment allows for a very easy implementation of geometric transformations, hierarchical assemblies and parametric curves, surfaces and solids. Since geometric shapes are associated to generating functions, and geometric expressions can be passed to functions as actual parameters, this approach allows for a very powerful programming approach to variational geometry. The paper also aims to show that this language can accommodate both the description of methods for generating geometric shapes (see e.g. the definition of either the Coons surfaces or the Bezier curves) as well as the use of such methods to generate specific shape instances. Finally, the language allows for both bottom-up and top-down development of the designed shape, as it is shown in the appendix, where the generation of the model of a parametric umbrella by successive refinements is discussed.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
Backus, J. Can Programming Be Liberated from the Von Neumanns Style? A Functional Style and its Algebra of Programs. Communications of the ACM, 21(8):613–641, (ACM Turing Award Lecture). 1978.
Backus, J., Williams, J.H. and Wimmers, E.L. An Introduction to the Programming Language FL. In Research Topics in Functional Programming, D.A. Turner (Ed.), Addison-Wesley, Reading, MA, 1990.
Backus, J., Williams, J.H., Wimmers, E.L., Lucas, P., and Aiken, A. Fl Language Manual, Parts 1 and 2. IBM Research Report RJ 7100 (67163), 1989.
Coons, S.A. Surfaces for Computer Aided Design of Space Forms. Report MACTR-41, Project MAC, MIT, 1967.
Gurtin, G. An Introduction to Continuum Mechanics. Academic Press, Boston, MA, 1981.
Gregory, J.A. (Ed.) The mathematics of surfaces. The Institute of Mathematics, Oxford University Press, New York, NY, 1986.
Paoluzzi, A., and Sansoni, C. Programming language for solid variational geometry. Computer Aided Design 24, 7 (1992), 349–366.
Paoluzzi, A., Pascucci, V., and Vicentino, M. Geometric programming: A programming approach to geometric design. ACM Transactions on Graphics 14, 4 (Oct. 1995).
Bernardini, F., Ferrucci, V., Paoluzzi, A. and Pascucci, V. Product operator on cell complexes. In Proc. of the Second ACM/IEEE Symp. on Solid Modeling and Application, Montreal, Canada, ACM Press, (May 1993), 43–52.
Pascucci, V., Ferrucci, V., and Paoluzzi, A. Dimension-independent convex-cell based HPC: Skeletons and Product. Int. Journal of Shape Modeling 2, 1 (1996), 37–67.
Paoluzzi, A., Bernardini, F., Cattani, C., and Ferrucci, V. Dimensionin-dependent modeling with simplicial complexes. ACM Transactions on Graphics 12, 1 (Jan. 1993), 56–102.
Takala, T. Geometric Boundary Modelling Without Topological Data Structures. In Eurographics '86 (Amsterdam, 1986), A.A.G. Rquicha, Editor, North-Holland.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paoluzzi, A. (1996). Generative geometric modeling in a functional environment. In: Calmet, J., Limongelli, C. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1996. Lecture Notes in Computer Science, vol 1128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61697-7_9
Download citation
DOI: https://doi.org/10.1007/3-540-61697-7_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61697-9
Online ISBN: 978-3-540-70635-9
eBook Packages: Springer Book Archive