Advanced programming techniques applied to Cgal's arrangement package

Computational Geometry: Theory and Applications

Volumn 38, Issue 1-2, 2007, Pages 37-63

  Wein, Ron ^a   Fogel, Efi ^a   Zukerman, Baruch ^a   Halperin, Dan ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Arrangements; Cgal; Design patterns; Exact computation; Generic programming; Robustness

Indexed keywords

EID: 84867943800     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2006.11.007     Document Type: Article

References (48)

1. Cgal-3.2 User and Reference Manual http://www.cgal.org/Manual/3.2/doc- html/cgal-manual/index.html 2006
2. P.K. Agarwal, E. Flato, and D. Halperin Polygon decomposition for efficient construction of Minkowski sums Computational Geometry: Theory and Applications 21 2002 39 61
3. M.H. Austern Generic Programming and the Stl: Using and Extending the C++ Standard Template Library 1998 Addison-Wesley
4. U. Bartuschka, S. Näher, M. Seel, A generic plane sweep framework, 2000, unpublished manuscript
5. J.L. Bentley, and T. Ottmann Algorithms for reporting and counting geometric intersections IEEE Transactions on Computers 28 9 1979 643 647
6. E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, L. Kettner, K. Mehlhorn, J. Reichel, S. Schmitt, E. Schömer, and N. Wolpert Exacus: Efficient and exact algorithms for curves and surfaces Proc. 13th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 3669 2005 Springer Berlin 155 166
7. E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, K. Mehlhorn, and E. Schömer A computational basis for conic arcs and Boolean operations on conic polygons Proc. 10th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 2461 2002 Springer Berlin 174 186
8. E. Berberich, M. Hemmer, L. Kettner, E. Schömer, N. Wolpert, An exact, complete and efficient implementation for computing planar maps of quadric intersection curves, in: Proc. 21st Annu. ACM Sympos. Comput. Geom. (SCG), 2005, pp. 99-106
9. J.-D. Boissonnat, O. Devillers, M. Teillaud, M. Yvinec, Triangulations in CGAL, in: Proc. 16th Annu. ACM Sympos. Comput. Geom., 2000, pp. 11-18
10. H. Brönnimann, C. Burnikel, and S. Pion Interval arithmetic yields efficient dynamic filters for computational geometry Discrete Applied Mathematics 109 1-2 2001 25 47
11. D. Cohen-Or, S. Lev-Yehudi, A. Karol, and A. Tal Inner-cover of non-convex shapes International Journal on Shape Modeling 9 2 2003 223 238
12. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf Computational Geometry: Algorithms and Applications second ed. 2000 Springer Berlin
13. O. Devillers, A. Fronville, B. Mourrain, and M. Teillaud Algebraic methods and arithmetic filtering for exact predicates on circle arcs Computational Geometry: Theory and Applications 22 1-3 2002 119 142
14. D.A. Duc, N.D. Ha, and L.T. Hang Proposing a model to store and a method to edit spatial data in topological maps Technical report, Ho Chi Minh University of Natural Sciences, Ho Chi Minh City, Vietnam, 2001 http://www.cgal.org/UserWorkshop/2002/ndha-abstract.pdf
15. A. Eigenwillig, L. Kettner, E. Schömer, N. Wolpert, Complete, exact and efficient computations with cubic curves, in: Proc. 20th Annu. ACM Sympos. Comput. Geom. (SCG), 2004, pp. 409-418
16. I.Z. Emiris, A. Kakargias, S. Pion, M. Teillaud, E.P. Tsigaridas, Towards an open curved kernel, in: Proc. 20th Annu. ACM Sympos. Comput. Geom. (SCG), 2004, pp. 438-446
17. A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, and S. Schönherr On the design of Cgal, the Computational Geometry Algorithms Library Software - Practice and Experience 30 2000 1167 1202
18. E. Flato Robust and efficient construction of planar Minkowski sums M.Sc. thesis, School of Computer Science, Tel-Aviv University, 2000 http://www.cs.tau.ac.il/CGAL/Theses/flato/thesis/
19. E. Flato, D. Halperin, I. Hanniel, O. Nechushtan, and E. Ezra The design and implementation of planar maps in Cgal The ACM Journal of Experimental Algorithmics 5 2000 1 23
20. E. Fogel, D. Halperin, Exact and efficient construction of Minkowski sums of convex polyhedra with applications, in: Proc. 8th Workshop Alg. Eng. Exper. (Alenex'06), 2006, pp. 3-15
21. E. Fogel, R. Wein, and D. Halperin Code flexibility and program efficiency by genericity: Improving Cgal's arrangements Proc. 12th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 3221 2004 Springer Berlin 664 676
22. E. Gamma, R. Helm, R. Johnson, and J. Vlissides Design Patterns - Elements of Reusable Object-Oriented Software 1995 Addison-Wesley
23. D. Halperin Arrangements J.E. Goodman, J. O'Rourke, Handbook of Discrete and Computational Geometry second ed. 2004 Chapman & Hall/CRC 529 562 Chapter 24
24. I. Hanniel, The design and implementation of planar arrangements of curves in Cgal, MSc thesis, School of Computer Science, Tel Aviv University, 2000
25. I. Hanniel, and D. Halperin Two-dimensional arrangements in Cgal and adaptive point location for parametric curves Proc. 4th Internat. Workshop Alg. Eng. (WAE) Lecture Notes in Comput. Sci. vol. 1982 2000 Springer Berlin 171 182
26. I. Haran, D. Halperin, An experimental study of point location in general planar arrangements, in: Proc. 8th Workshop Alg. Eng. Exper. (Alenex'06), 2006, pp. 16-25
27. S. Hert, M. Hoffmann, L. Kettner, S. Pion, and M. Seel An adaptable and extensible geometry kernel Proc. 5th Internat. Workshop Alg. Eng. (WAE) Lecture Notes in Comput. Sci. vol. 2141 2001 Springer Berlin 79 90
28. S. Hirsch, and D. Halperin Hybrid motion planning: Coordinating two discs moving among polygonal obstacles in the plane J.-D. Boissonnat, J. Burdick, K. Goldberg, S. Hutchinson, Algorithmic Foundations of Robotics V 2003 Springer Berlin 239 255
29. V. Karamcheti, C. Li, I. Pechtchanski, C. Yap, A core library for robust numeric and geometric computation, in: Proc. 15th Annu. ACM Sympos. Comput. Geom. (SCG), 1999, pp. 351-359
30. L. Kettner Using generic programming for designing a data structure for polyhedral surfaces Computational Geometry: Theory and Applications 13 1 1999 65 90
31. L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, and C. Yap Classroom examples of robustness problems in geometric computations Proc. 12th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 3221 2004 Springer Berlin 702 713
32. J. Keyser, T. Culver, M. Foskey, S. Krishnan, and D. Manocha Esolid - a system for exact boundary evaluation Computer-Aided Design 36 2 2004 175 193
33. J. Keyser, T. Culver, D. Manocha, and S. Krishnan Efficient and exact manipulation of algebraic points and curves Computer-Aided Design 32 11 2000 649 662
34. K. Mehlhorn, and S. Näher Leda: A Platform for Combinatorial and Geometric Computing 2000 Cambridge University Press Cambridge, UK
35. M. Meyerovitch Robust, generic and efficient construction of envelopes of surfaces in three-dimensional space Proc. 14th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 4168 2006 Springer Berlin 792 803
36. K. Mulmuley A fast planar partition algorithm, I Journal of Symbolic Computation 10 3-4 1990 253 280
37. N. Myers, A new and useful template technique: "Traits", in: S.B. Lippman (Ed.), C++ Gems, SIGS Reference Library, vol. 5, 1997, pp. 451-458
38. A. Fabri, S. Pion, A generic lazy evaluation scheme for exact geometric computations, in: Proc. 2nd Workshop on Library-Centric Software Design (LCSD), 2006, http://sms.cs.chalmers.se/bibliography/proceedings/2006-LCSD.pdf
39. F.P. Preparata, and M.I. Shamos Computational Geometry: An Introduction 1985 Springer New York
40. V. Rogol, Maximizing the area of an axially-symmetric polygon inscribed by a simple polygon, MSc thesis, Technion, Haifa, Israel, 2003
41. S. Schirra Robustness and precision issues in geometric computation J.-R. Sack, J. Urrutia, Handbook of Computational Geometry 1999 Elsevier Science Publishers B.V., North-Holland Amsterdam 597 632
42. J.G. Siek, L.-Q. Lee, and A. Lumsdaine The Boost Graph Library, User Guide and Reference Manual 2002 Addison-Wesley
43. J. Snoeyink, J. Hershberger, Sweeping arrangements of curves, in: Proc. 5th Annu. ACM Sympos. Comput. Geom. (SCG), 1989, pp. 354-363
44. R. Wein High-level filtering for arrangements of conic arcs Proc. 10th Europ. Sympos. Alg. (ESA) Lecture Notes in Comput. Sci. vol. 2461 2002 Springer Berlin 884 895
45. R. Wein Efficient implementation of red-black trees with split and catenate operations Technical report, Tel-Aviv University, 2005 http://www.cs.tau.ac.il/~wein/publications/pdfs/rb-tree.pdf
46. R. Wein, and E. Fogel The new design of Cgal's arrangement package Technical report, Tel-Aviv University, 2005 http://www.cs.tau.ac.il/~wein/ publications/pdfs/Arr-new-design.pdf
47. R. Wein, J.P. van den Berg, and D. Halperin The visibility-Voronoi complex and its applications Computational Geometry: Theory and Applications 36 1 2007 66 87
48. C.K. Yap Robust geometric computation J.E. Goodman, J. O'Rourke, Handbook of Discrete and Computational Geometry second ed. 2004 Chapman & Hall/CRC 927 952 Chapter 41