The Community for Technology Leaders
RSS Icon
Issue No.05 - May (1987 vol.7)
pp: 44-55
Ingrid Carlbom , Schlumberger-Doll Research
Geometric set operations play an integral role in systems for CAD/CAM, for robot planning, and for modeling objects such as underground formations from empirical data. Two major issues in the implementation of geometric set operations are efficiency in the search for geometric intersections and effectiveness in the treatment of singular intersection cases. This article presents an algorithm for geometric set operations on planar polyhedral nonmanifold objects that addresses both these issues. First, an efficient search for geometric intersections is obtained by localizing the search to small regions of object space through a cellular subdivision scheme using the polytree data structure. Second, an effective treatment of singular intersection cases is obtained by mapping each singular intersection occurring in a region into one of a small set of cases.
Ingrid Carlbom, "An Algorithm for Geometric Set Operations Using Cellular Subdivision Techniques", IEEE Computer Graphics and Applications, vol.7, no. 5, pp. 44-55, May 1987, doi:10.1109/MCG.1987.276987
1. G.M.Hunter, "Geometrees for Interactive Visualization of Geology: An Evaluation," , Schlumberger-Doll Research 1984 research note
2. D.J.Vanderschel, "Divided Leaf Octal Tfees," , Schlumberger-Doll Research 1984 research note
3. I.Carlbom, I.Chakravarty, and D.Vanderschel, "A Hierarchical Data Structure for Representing the Spatial Decomposition of 3D Objects," Proc. Computer Graphics Tokyo 84 Apt 1984 (also appeared in Frontiers in Computer Graphics, T.L. Kunii, ed., Springer-Verlag, Tokyo, 1985)
4. I.Carlbom, I.Chakravarty, and D.Vanderschel, IEEE CG&A , Apr. 1985pp. 24-31
5. D.Ayala, P.Brunet, R.Juan, and I.Navazo, "Object Representation by Means of Nonminimal Division of Quadtrees and Octrees,"pp. 41-59 Jan. 1985 ACM Trans. Graphics
6. P.Brunet and I.Navazo, "Geometric Modeling Using Exact Octree Representation for Polyhedral Objects," Proc. Eurographics 85 1985pp. 159-169
7. I.Navazo, D.Ayala, and P.Brunet, "A Geometric Modeler Based on the Exact Octree Representation of Polyhedra," Computer Graphics Forum Vol. 5, pp. 91-104 1986
8. T.L.Kunii, T.Satoh, and K.Yamaguchi, IEEE CG&A , Mar. 1985pp. 29-38
9. A.A.G.Requicha and R.B.Tilove, "Mathematical Foundations of Constructive Solid Geometry: General Topology and Closed Regular Sets," , Univ. of Rochester 1978 Tech. Memo TM-27a, Production Automation Project
10. R.B.Tilove and A.A.G.Requicha, "Closure of Boolean Operations on Geometric Entities,"pp. 219-220 Sept. 1980 Computer-Aided Design
11. W.R.Franklin, "A Linear Time Exact Hidden Surface Algorithm," Computer Graphics (Proc. SIGGRAPH 80) July 1980pp. 117-123
12. W.R.Franklin, "Efficient Polyhedron Intersection and Union,"pp. 73-80 May 1982 Graphics Interface 82
13. M.Mantyla and M.Tamminen, "Localized Set Operations for Solid Modeling," Computer Graphics (Proc. SIGGRAPH 83) July 1983pp. 279-288
14. M.Mantyla and R.Sulonen, IEEE CG&A , Sept. 1982pp. 17-31
15. R.B.Tilove, A.A.G.Requicha, and M.R.Hopkins, "Efficient Editing of Solid Models by Exploiting Structural and Spatial Locality," Computer Aided Geometric Design Vol. 1, pp. 227-239 1984
16. R.B.Tilove, IEEE Trans. Computers , Oct. 1980pp. 874-883
17. A.A.G.Requicha and H.B.Voelcker, "Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms," Proc. IEEE Jan. 1985pp. 30-44
18. M.Mantyla, "Boolean Operations on 2-Manifolds through Vertex Neighborhood Classification,"pp. 1-29 Jan. 1986 ACM Trans. Graphics
19. M.A.Wesley, J.Encarnacao, Computer Aided Design , Springer-Verlag 1980
20. G.Markowsky and M.A.Wesley, "Fleshing out Wire Frames," , IBM J. of Research and Development Sept. 1980pp. 582-597
21. J.R.Woodwark and K.M.Quinlan, "Reducing the Effect of Complexity on Volume Model Evaluation,"pp. 89-95 Mar. 1982 Computer-Aided Design
22. F.Yamaguchi and T.Tokieda, IEEE CG&A , June 1984pp. 24-37
23. A.A.G.Requicha, "Representations for Rigid Solids: Theory, Methods, and Systems,"pp. 437-464 Dec. 1980 Computing Surveys
24. A.A.G.Requicha and H.B.Voelcker, IEEE CG&A , Oct. 1983pp. 25-37
25. R.A.Conover, A First Course in Topology: An Introduction to Mathematical Thinking , Williams & Wilkins 1975
26. W.S.Massey, Algebraic Topology: An Introduction , Harcourt 1967 Brace & World
27. D.Meagher, "Geometric Modeling Using Octree Encoding,"pp. 129-147 June 1982 Computer Graphics and Image Processing
28. I.Carlbom, "Polytree-A Data Structure for Geometric Modeling," SIAM Conf. on Geometric Modeling and Robotics 1985 SIAM (abstract only)
22 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool