Article

Free access

Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation

Authors:

M. Benouamer,

D. Michelucci,

B. PerocheAuthors Info & Claims

SMA '93: Proceedings on the second ACM symposium on Solid modeling and applications

Pages 115 - 126

https://doi.org/10.1145/164360.164403

Published: 01 June 1993 Publication History

PDF eReader

References

[1]

B. G. Baumgart, A polyhedron Representation for Computer Vision. National Computer Conference, pp. 589-596, 1975.

Google Scholar

[2]

M.O. Benouamer, P. Jaillon, D. Michelucci, J.M. Moreau, A Lazy Exact Arithmetic Library. To be published in the l lth. IEEE Symposium on Computer Arithmetic, Canada, 1993.

Google Scholar

[3]

H. Edclsbrunner and E. P. Mtlcke, Simulation of Simplicity: A technique to Cope with Degenerate Cases in Geometric Algorithms. Proc. of the 4th ACM Symposium on Computational Geometry, pp. 118-1330 1988.

Digital Library

Google Scholar

[4]

M. Gangnet, J.M. Van Thong, Robust Boolean Operations on 2D paths, COMPUGRAPHICS'91 Proceeding, vol 2, Harold P. Santo ed., pp. 434-443~ Sesimbra, Portugal, 1991.

Google Scholar

[5]

M. Gangnet, J.C. Herv~, T. Pudet, J.M. Van Thong, Incremental Computation of Planar Maps, SIGGRAPH'89 Proceeding, Addison Wesley, Reading, 1989.

Digital Library

Google Scholar

[6]

L. Guibas, D. Salesin, and J. Stolfi, Epsilon Geometry: Building Robust Algorithms From Imprecise Computations. Proc. of the 5th ACM Symposium on Computational Geometry, pp. 208-217, 1989.

Digital Library

Google Scholar

[7]

C. M. Hoffmann, J. E. Hopcroft, and M. S. Karasick, Towards implementing Robust Geometric Computations. Proc. 4th ACM Symposium on Computational Geometry, pp. 106-118, 1988.

Digital Library

Google Scholar

[8]

C. M. Hoffmann, J. E. Hopcroft, and M. S. Karasick, Robust Set Operations on Polyhedral Solids. IEEE CG&A, Vol. 9, No. 6, pp. 50-59, Nov, 1989.

Digital Library

Google Scholar

[9]

M. Karasick, D. Lieber, and L. R. Nakman, Efficient Delaunay Triangulation Using Rational Arithmetic. IBM Research Report RC-14455, #64722, 3/8/89.

Google Scholar

[10]

U.W. Kulisch, W.L. Milanker, Computer arithmetic in Theory and Practice, Academic Press, New York, 1981. See also by the same authors, A New Approach to Scientific Computation. Academic Press. New York, 1982.

Digital Library

Google Scholar

[11]

D.H. Laidlaw, W.B. Trumbore, and J.F. Hugues, Constructive Solid Geometry for Polyhedral Objects. Computer Graphics (Proc. SIC_~RAPH'86), Vol. 20, No. 4, pp. 161-180, Aug. 1986.

Digital Library

Google Scholar

[12]

M. Mlntyllt and R. Sulonen, GWB: A Solid Modeler with Euler Operators. IEEE CG&A, Vol. 2, No. 7, pp. 18-31, Sept. 1982.

Google Scholar

[13]

M. MIntyli and M. Tammimen, Localised Set Operations for Solid Modeling. Computer Graphics, Vol. 18, No. 3, pp. 279-288, 1983.

Digital Library

Google Scholar

[14]

K. Mehlhorn, Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry. Springer-Verlag, Berlin, 1984.

Digital Library

Google Scholar

[15]

D. Michelucci, Les representations par les fronti~res: quelque.r constructions; di~ultds rencontrdes. ~ de Doctorat, Ecole des Mines de Saint-Etienne, France, 1987.

Google Scholar

[16]

V.J. Milenkovic, Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic. Ph.D. Dissertation, CMU-CS-168, Carnegie- Mellon, 1988.

Digital Library

Google Scholar

[17]

J. M. Moreau, Hic~rarchisation et facetisation de la representation par segments d'un graphe planaire dans le cadre d'une aritlmuftique mixte. Th~se de Doctorat en Informatique, Ecole des Mines de saint-Etienne, France, 1990.

Google Scholar

[18]

A. A. G. Requicha, Representation for Rigid Solids: Theory, Methods and Systems. ACM Computing surveys Vol. 12, No. 4, pp. 437-464, Dec. 1980.

Digital Library

Google Scholar

[19]

A. A. G. Requicha and H. B. Voelcker, Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms. Proc. IEEE, Vol. 73, No. l, pp. 30-44, Jan. 1985.

Crossref

Google Scholar

[20]

M. Segal and C.H. Sequin, Consistent Calculations for Solid Modeling. Proc. First ACM Symposium on Computational Geometry, pp. 29-38, 1985.

Digital Library

Google Scholar

[21]

M. Segal and C.H. Sequin, Partitioning Polyhedral Objects into Non Intersecting Parts. IEEE CG&A, Vol. 8, No. I, pp. 53-67, 1988.

Digital Library

Google Scholar

[22]

M. Segal, Using Tolerances to Guarantee Valid Polyhedral Modeling Results. Computer Graphics, Vol. 24, No. 4, pp. 105-114, 1990.

Digital Library

Google Scholar

[23]

K. Sugihara, and M. Iri, A Solid Modelling System Free From Topological Inconsistency. Research Memorandum RMI 89-03, Dept. of Math. Engr. and Information Physics, Tokyo Univenity, Tokyo, Japan, 1989.

Google Scholar

[24]

R. B. Tilove, Setmembership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Trans. on Computers, Vol. C-29, No. 10, pp. 874-883, Oct. 1980.

Google Scholar

Cited By

View all

Sugihara K(2011)Robust geometric computation based on the principle of independenceNonlinear Theory and Its Applications, IEICE10.1587/nolta.2.322:1(32-42)Online publication date: 2011
https://doi.org/10.1587/nolta.2.32
Bernstein GFussell DPolthier KAlexa MKazhdan M(2009)Fast, exact, linear BooleansProceedings of the Symposium on Geometry Processing10.5555/1735603.1735606(1269-1278)Online publication date: 15-Jul-2009
https://dl.acm.org/doi/10.5555/1735603.1735606
Shirayanagi KSekigawa HSasaki TShirayanagi KKotsireas I(2009)Reducing exact computations to obtain exact results based on stabilization techniquesProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577219(191-198)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577219
Show More Cited By

Index Terms

Recommendations

Reliable Floating-Point Arithmetic Algorithms for Error-Coded Operands

Reliable floating-point arithmetic is vital for dependable computing systems. It is also important for future high-density VLSI realizations that are vulnerable to soft-errors. However, the direct checking of floating-point arithmetic is still an open ...
Finite Precision Rational Arithmetic: An Arithmetic Unit

The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including ...
Error Correction in Residue Arithmetic

It is shown how single-error correction in a residue arithmetic system can be accomplished in an efficient and fast manner. Two redundant moduli are necessary. This construction is extended to multiple errors. Another method of error detection or ...

Comments

Information & Contributors

Information

Published In

SMA '93: Proceedings on the second ACM symposium on Solid modeling and applications

June 1993

498 pages

ISBN:0897915844

DOI:10.1145/164360

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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1993

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

SMF93

Sponsor:

SIGGRAPH

SMF93: ACM Symposium in Solid Modeling Foundations and CAD/CAM Applications

May 19 - 21, 1993

Quebec, Montreal, Canada

Acceptance Rates

Overall Acceptance Rate 86 of 173 submissions, 50%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
327
Total Downloads

Downloads (Last 12 months)56
Downloads (Last 6 weeks)22

Reflects downloads up to 12 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Sugihara K(2011)Robust geometric computation based on the principle of independenceNonlinear Theory and Its Applications, IEICE10.1587/nolta.2.322:1(32-42)Online publication date: 2011
https://doi.org/10.1587/nolta.2.32
Bernstein GFussell DPolthier KAlexa MKazhdan M(2009)Fast, exact, linear BooleansProceedings of the Symposium on Geometry Processing10.5555/1735603.1735606(1269-1278)Online publication date: 15-Jul-2009
https://dl.acm.org/doi/10.5555/1735603.1735606
Shirayanagi KSekigawa HSasaki TShirayanagi KKotsireas I(2009)Reducing exact computations to obtain exact results based on stabilization techniquesProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577219(191-198)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577219
Bernstein GFussell D(2009)Fast, Exact, Linear BooleansComputer Graphics Forum10.1111/j.1467-8659.2009.01504.x28:5(1269-1278)Online publication date: 31-Aug-2009
https://doi.org/10.1111/j.1467-8659.2009.01504.x
Minakawa TSugihara K(2005)Topology oriented vs. exact arithmetic — Experience in implementing the three-dimensional convex hull algorithmAlgorithms and Computation10.1007/3-540-63890-3_30(273-282)Online publication date: 29-Jul-2005
https://doi.org/10.1007/3-540-63890-3_30
Edalat AHeckmann R(2002)Computing with Real NumbersApplied Semantics10.1007/3-540-45699-6_5(193-267)Online publication date: 20-Sep-2002
https://doi.org/10.1007/3-540-45699-6_5
Higashi MNakano HNakamura AHosaka M(2001)Use of topological constraints in construction and processing of robust solid modelsProceedings of the sixth ACM symposium on Solid modeling and applications10.1145/376957.376960(18-29)Online publication date: 1-May-2001
https://dl.acm.org/doi/10.1145/376957.376960
Higashi MNakano HNakamura AHosaka M(2001)Use of Topological Constraints in Construction and Processing of Robust Solid ModelsJournal of Computing and Information Science in Engineering10.1115/1.14315481:4(330)Online publication date: 2001
https://doi.org/10.1115/1.1431548
Sugihara K(2001)Degeneracy and Instability in Geometric ComputationGeometric Modelling10.1007/978-0-387-35490-3_1(3-16)Online publication date: 2001
https://doi.org/10.1007/978-0-387-35490-3_1
Sugihara K(2001)Robust Geometric Computation Based on Topological ConsistencyComputational Science — ICCS 200110.1007/3-540-45545-0_10(12-26)Online publication date: 17-Jul-2001
https://doi.org/10.1007/3-540-45545-0_10
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Reliable Floating-Point Arithmetic Algorithms for Error-Coded Operands

Finite Precision Rational Arithmetic: An Arithmetic Unit

Error Correction in Residue Arithmetic

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

PDF

eReader

Login options

Full Access

References

Cited By

Index Terms

Recommendations

Reliable Floating-Point Arithmetic Algorithms for Error-Coded Operands

Finite Precision Rational Arithmetic: An Arithmetic Unit

Error Correction in Residue Arithmetic

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations