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Foundation of a computable solid modeling

Authors:

Abbas Edalat and

André LieutierAuthors Info & Claims

SMA '99: Proceedings of the fifth ACM symposium on Solid modeling and applications

June 1999

Pages 278 - 284

https://doi.org/10.1145/304012.304040

Published: 01 June 1999 Publication History

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References

[1]

S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3. Clarendon Press, 1994.

Digital Library

Google Scholar

[2]

R. M. Amadio and P.-L. Curien. Domains and Lambda- Calculi. Cambridge Tracts in Theoretical Computer Science, 1998.

Digital Library

Google Scholar

[3]

Sean Michael Barker. Toward a topology for computational geometry. Computer Aided Design, 27(4):311-318, 1995.

Crossref

Google Scholar

[4]

Vasko Brattka and Klaus Weihrauch. Computatbility on subsets of Euclidean space I: Closed and compact subsets. 1998.

Digital Library

Google Scholar

[5]

H. Bronimann, J. Emiris, V. Pan, and S.Pion. Computing exact geometric predicates using modular arithmetic with single precision. ACM Symposium on Computational Geomet~., 1997.

Digital Library

Google Scholar

[6]

N. J. Cutland. Computability: An Introduction to Recursive function theory. Cambridge University Press, 1980.

Crossref

Google Scholar

[7]

D.S.Bridges. Computability. Springer, 1994.

Google Scholar

[8]

A. Edalat. Domains for computation in mathemetics, physics and exact real arithmetic. Bulletin of Symbolic Logic, 3(4):401-452, 1997.

Crossref

Google Scholar

[9]

A. Edalat and P. J. Potts. A new representation for exact real numbers.In Proceedings of Mathematical Foundations of Programming Semantics 13, volume 6 of Electronic Notes in Theoretical Computer Science. Elsevier Science B. V., 1997. Available from URL: http ://www. elsevier, nl/Iocate/entcs/volu m e6. html.

Google Scholar

[10]

Y.L. Ershov. Computable functionals of finite types. Algebra and Logic, 11 (4):267-437, 1972.

Crossref

Google Scholar

[11]

M.H. Escard6 an6 T. Streicher. Induction and recursion on the partial real line via biquotients of bifree algebras. In Twelfth Annual IEEE Symposium on Logic in Computer Science. IEEE, 1997.

Digital Library

Google Scholar

[12]

EPreparata and M,. Shamos. Computational Geometry: an introduction. Springier Verlag, 1985.

Digital Library

Google Scholar

[13]

L.J. Guibas, D. Salesin, and J. Stolfi. Epsilon Geometry : Building robust algorithms from imprecise computations. ACM,Symposium on Computational Geometry, pages 208- 217, 1989.

Digital Library

Google Scholar

[14]

H.Desaulniers and N.F. Stewart. Robustness of numerical methods in geometric computation when problem data is uncertain. Computer Aided Design, special issue on uncertainties in geometrical design, 1993.

Google Scholar

[15]

Chun-Yi Hu. Towards Robust Interval Solid Modeling of Curved Objects. PhD thesis, MIT, May 1995.

Digital Library

Google Scholar

[16]

Chun-Yi Hu, Takashi Maekawa, Nicholas Patrika}~akis, and Evan Sherbrooke. Robust interval algorithm for curve intersections. Computer Aided Design, 28(6-7):495-506, 1996.

Crossref

Google Scholar

[17]

David J.Jackson. Boundary Representation Mode}ling with local Tolerances. ACM Conference on Solid Modelling, 1995.

Digital Library

Google Scholar

[18]

A. Lieutier. Repr6sentation b.rep et calculabilit6. LMC, IMAG, Universit6 Joseph Fourrier, BP 53X 38041 Grenoble Cedex, France, 1997. Journ6es modeleurs g6om6triques.

Google Scholar

[19]

A. Lieutier. Toward a data type for Solid Modeling based on Domain Theory. lnformatik Berichte 235, FernUniversitat Hagen, www.informatik.fernuni-hagen.de/cca/, I998. Workshop on Computability and Complexity in Analysis.

Google Scholar

[20]

T.J. Peters, D.R. Fe:rguson, N.E Stewart, and P.S. Fussell. Algorithmic tolerances and semantics in data exchange. ACM Symposium on Computational Geometry, 1997.

Digital Library

Google Scholar

[21]

P. J, Potts. Efficient on-line computation of real functions using exact floating point. Submitted for publication.available from: http://theory,doc.ic.ac.uk/~pip,1997.

Google Scholar

[22]

M. B. Pout-El and J. I. Richards. Computability in Analysis and Physics. Springer-Verlag, ! 988.

Google Scholar

[23]

A. Requicha and R. Tilove. Mathematical Foundations of Constructive Solid Geometry : General Topology of closed Regular Sets. In Automata, Languages and Programming, Production Automation Project, March 78, University of Rochester, Rochester, New York, 1978.

Google Scholar

[24]

Aristides A.G. Requicha. Representation for Rigid Solids : Theory, Methods, ~tnd Systems. Computer Surveys, 12(4), 1980.

Digital Library

Google Scholar

[25]

Aristides A.G. Requicha and Herbert B. Voelker. Boelean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms. Proceedings of the IEEE, 73(1), 1985.

Google Scholar

[26]

H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967.

Digital Library

Google Scholar

[27]

D. S. Scott. Outline of a mathematical theory of computation. In 4th Annual Princeton Conference on Information Sciences and Systems, pages 169-176, 1970.

Google Scholar

[28]

M. SegaI. Using tolerances to guarantee valid polyhedral modeling results. Computer Graphics, 24, 1990.

Digital Library

Google Scholar

[29]

V. Stoltenberg-Hansen, I. Lindstr6m, and E. R. Griffor. Mathematical Theol. of Domains, volume 22 of Cambridge Tract~ in Theoretical Computer Science. Cambridge University Press, 1994.

Digital Library

Google Scholar

[30]

K. Weihrauch. Computability, volume 9 of EATCS Mono. graphs on Theoretical Computaer Science. Springer-Verlag, 1987.

Digital Library

Google Scholar

Cited By

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Paoluzzi AShapiro VDiCarlo AScorzelli GOnofri E(2023)Finite Algebras for Solid Modeling using Julia’s Sparse ArraysComputer-Aided Design10.1016/j.cad.2022.103436155(103436)Online publication date: Feb-2023
https://doi.org/10.1016/j.cad.2022.103436
Davari MEdalat ALieutier ABouyer P(2019)The convex hull of finitely generable subsets and its predicate transformerProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470178(1-14)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470178
Davari MEdalat ALieutier A(2019)The convex hull of finitely generable subsets and its predicate transformer2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2019.8785680(1-14)Online publication date: Jun-2019
https://doi.org/10.1109/LICS.2019.8785680
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Foundation of a computable solid modeling

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SMA '99: Proceedings of the fifth ACM symposium on Solid modeling and applications

June 1999

327 pages

ISBN:1581130805

DOI:10.1145/304012

Chairmen:
Deba Dutta
Univ. of Michigan, Ann Arbor
,
Willem F. Bronsvoort
Delft Univ. of Technology, Delft, The Netherlands
,
David C. Anderson
Purdue Univ., Lafayette, IN

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 June 1999

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SM99: 5th Symposium on Solid Modeling and Applications, 1999

June 8 - 11, 1999

Michigan, Ann Arbor, USA

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Paoluzzi AShapiro VDiCarlo AScorzelli GOnofri E(2023)Finite Algebras for Solid Modeling using Julia’s Sparse ArraysComputer-Aided Design10.1016/j.cad.2022.103436155(103436)Online publication date: Feb-2023
https://doi.org/10.1016/j.cad.2022.103436
Davari MEdalat ALieutier ABouyer P(2019)The convex hull of finitely generable subsets and its predicate transformerProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470178(1-14)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.5555/3470152.3470178
Davari MEdalat ALieutier A(2019)The convex hull of finitely generable subsets and its predicate transformer2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2019.8785680(1-14)Online publication date: Jun-2019
https://doi.org/10.1109/LICS.2019.8785680
Lysenko MShapiro V(2016)Effective contact measuresComputer-Aided Design10.1016/j.cad.2015.06.01970:C(134-143)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cad.2015.06.019
Wilkie A(2014)2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08The Bulletin of Symbolic Logic10.2178/bsl/123108177215:1(95-139)Online publication date: 15-Jan-2014
https://doi.org/10.2178/bsl/1231081772
Johnson KTucker J(2013)The data type of spatial objectsFormal Aspects of Computing10.1007/s00165-011-0182-725:2(189-218)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1007/s00165-011-0182-7
Qi JShapiro V(2006)Geometric Interoperability With Epsilon SolidityJournal of Computing and Information Science in Engineering10.1115/1.22183676:3(213)Online publication date: 2006
https://doi.org/10.1115/1.2218367
Edalat AKhanban ALieutier A(2005)Computability in computational geometryProceedings of the First international conference on Computability in Europe: new Computational Paradigms10.1007/11494645_15(117-127)Online publication date: 8-Jun-2005
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Edalat ALieutier A(2002)Domain theory and differential calculus (functions of one variable)Proceedings 17th Annual IEEE Symposium on Logic in Computer Science10.1109/LICS.2002.1029836(277-286)Online publication date: 2002
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Khanban AEdalat ALieutier A(2002)Computability of Partial Delaunay Triangulation and Voronoi Diagram [Extended Abstract]Electronic Notes in Theoretical Computer Science10.1016/S1571-0661(04)80381-566:1(91-103)Online publication date: Jul-2002
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Global and local deformations of solid primitives

Global and local deformations of solid primitives

Skeleton based solid representation with topology preservation

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Skeleton based solid representation with topology preservation

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