skip to main content
10.1145/800059.801159acmconferencesArticle/Chapter ViewAbstractPublication PagessiggraphConference Proceedingsconference-collections
Article
Free access

Localized set operations for solid modeling

Published: 01 July 1983 Publication History

Abstract

Set operation algorithms form an important component of solid modeling systems. Their efficiency can be enhanced by localizing the search for geometric intersections to the region of overlap using a spatial directory. We present an algorithm that employs a three-dimensional extendible cell (EXCELL) directory to the set operation problem, and demonstrate by practical experiments the efficiency and the local nature of the algorithm.

References

[1]
Baumgart, B.G., Geometric modeling for computer vision. Report No. AIM-249, STAN-CS-74-463, Stanford AI Lab., Stanford University, Oct. 1974
[2]
Bentley, J.L. and Friedman, J.H., A survey of algorithms and data structures for range searching. ACM Comp. Surv. 11(1979)4, p. 397-409.
[3]
Bentley, J.L. and Wood D. An optimal worst case algorithm for reporting intersections of rectangles. IEEE Trans. Comp. C-29(1980)7, p. 571-577.
[4]
Braid, I.C., Notes on a Geometric Modeller. CAD Group Document No. 101, Computer Laboratory, University of Cambridge, Cambridge, England, June, 1979
[5]
Eastman, C.M. and Weiler, K., Geometric Modeling Using the Euler Operators. Proc. First Ann. Conf. on Computer Graphics in CAD/CAM Systems, MIT, Apr,. 1979, p. 248-254
[6]
Fagin, R., Nievergelt, J., Pippenger, N. and Strong H.R., Extendible hashing, a fast access method for dynamic files. ACM TODS 4(1979)3, p. 315-344.
[7]
Franklin, W.R., A linear exact hidden surface algorithm. ACM Computer Graphics 14(1980)3, p. 117-123.
[8]
Griffiths, J.G., Eliminating hidden edges in line drawings. Comput. Aided Des. 11(1979)2, p. 71-78.
[9]
Kedem, G., The quad-CIF tree data structure for hierarchical on-line algorithms, Proc. ACM Nineteenth Design Automation Conference, 1982, Las Vegas.
[10]
Lomet, D.B., Digital B-trees. Proc. 7th Int. Conf. on Very Large Data Bases, Cannes 1981, p. 333-344.
[11]
Meagher, D., Geometric modeling using octree encoding. Computer Graphics and Image Processing 19(1982), p. 129-147.
[12]
Mäntylä, M. and Sulonen, R., GWB - A Solid Modeler With Euler Operators. IEEE Computer Graphics & Applications 2(1982)7, p. 17-31
[13]
Nievergelt, J. and Preparata, F.P., Plane-sweep algorithms for intersecting geometric figures. Comm. ACM 25(1982)10; p. 739-747.
[14]
Okino, N. et al., TIPS-1 '77 Version. Hokkaido University, 1977.
[15]
Quinlan, K.M. and Woodwark, J.R., A spatially-segmented solids datamase - justification and design, Proc. CAD 82 Conference, Brighton, England, 1982.
[16]
Requicha, A.A.G., Representations of rigid solids: theory, methods and systems. ACM Comp. Surv. 12(1980), p. 437-464.
[17]
Requicha, A.A.G. and Voelcker, H.B., Constructive Solid Geometry. Tech. Memo. No 25, Production Automation Project, University of Rochester, Rochester, N.Y., 1977.
[18]
Requicha, A.A.G. and Voelcker, H.B., Solid modeling: a historical summary and contemporary assessment. IEEE Computer Graphics and Applications 2(1982)6, p. 9-24.
[19]
Roth, S.D., Ray Casting for Modeling Solids. Computer Graphics and Image Processing 18(1982)2, p. 109-144
[20]
Shamos, M.I., Computational Geometry. PhD thesis, Yale University, 1978.
[21]
Six, H.W. and Wood, D., Counting and reporting intersections of d-ranges. IEEE trans. Comp. C-31(1982)3, p. 181-187.
[22]
Steinberg, H.A., Overlap and separation calculations using the SynthaVision three dimensional solid modeling system. Proc. Conf. On CAD/CAM Technology in Mechanical Engineering, Cambridge, Mass., March 24-26, 1982, p. 13-19.
[23]
Sutherland, I.E., Sproull, R.F. and Schumacher, R.A., A characterization of ten hidden-surface algorithms. ACM Comp. Surv. 6(1974)1, p. 1-55.
[24]
Tamminen, M., A note on extendible hashing with overflow. Info. Proc. Lett. 15(1982)5, p. 227-232.
[25]
Tamminen, M. and Sulonen, R., The EXCELL method for efficient geometric access to data. Proc. ACM Nineteenth Design Automation Conference, 1982, Las Vegas, p. 345-351.
[26]
Tikkanen, M., User's manual of Blk. Rep. HTKK-TKO-B36, CAD-Project, Laboratory of Information Processing Science, Helsinki University of Technology, Espoo, 1981
[27]
Tilove, R.B., Set membership classification: a unified approach to geometric intersection problems. IEEE Trans. Computers, C-29(1980)10, p. 874-883.
[28]
Tilove, R.B., Exploiting spatial and structural locality in geometric modeling. Tech. Memo. No 38, Production Automation Project, University of Rochester, 1981.
[29]
Voelcker, H.B. and Requicha, A.A.G., Geometric Modeling of Mechanical Parts and Processes. IEEE Computer 10(1977)2, p. 48-57

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SIGGRAPH '83: Proceedings of the 10th annual conference on Computer graphics and interactive techniques
July 1983
420 pages
ISBN:0897911091
DOI:10.1145/800059
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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1983

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Geometric directories
  2. Set operations
  3. Spatial search

Qualifiers

  • Article

Conference

SIGGRAPH '83
Sponsor:
SIGGRAPH '83: Computer graphics and interactive techniques
July 25 - 29, 1983
Michigan, Detroit, USA

Acceptance Rates

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)61
  • Downloads (Last 6 weeks)19
Reflects downloads up to 14 Sep 2024

Other Metrics

Citations

Cited By

View all

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media