메뉴 건너뛰기




Volumn 42, Issue 6-7, 2009, Pages 536-550

Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere

Author keywords

cgal; Constructions; Curved objects; Generic programming; Geometric kernels; Predicates; Robustness; Spheres

Indexed keywords


EID: 84867965956     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2008.10.003     Document Type: Article
Times cited : (13)

References (39)
  • 2
    • 38149085434 scopus 로고    scopus 로고
    • Computational and structural advantages of circular boundary representation
    • Lecture Notes Comput. Sci.
    • O. Aichholzer, F. Aurenhammer, T. Hackl, B. Jüttler, M. Oberneder, Z. Sir, Computational and structural advantages of circular boundary representation, in: Proc. 10th International Workshop on Algorithms and Data Structures, in: Lecture Notes Comput. Sci., vol. 4619, 2007, pp. 374-385
    • (2007) Proc. 10th International Workshop on Algorithms and Data Structures , vol.4619 , pp. 374-385
    • Aichholzer, O.1
  • 5
    • 30244456320 scopus 로고
    • Computing the volume of the union of spheres
    • D. Avis, B.K. Bhattacharya, and H. Imai Computing the volume of the union of spheres The Visual Computer 3 6 1988 323 328
    • (1988) The Visual Computer , vol.3 , Issue.6 , pp. 323-328
    • Avis, D.1    Bhattacharya, B.K.2    Imai, H.3
  • 6
    • 0018515704 scopus 로고
    • Algorithms for reporting and counting geometric intersections
    • J. Bentley, and T. Ottmann Algorithms for reporting and counting geometric intersections IEEE Transactions on Computers 28 9 1979 643 647
    • (1979) IEEE Transactions on Computers , vol.28 , Issue.9 , pp. 643-647
    • Bentley, J.1    Ottmann, T.2
  • 8
    • 27144486382 scopus 로고    scopus 로고
    • An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
    • 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 Annual Symposium on Computational Geometry, 2005, pp. 99-106
    • (2005) Proc. 21st Annual Symposium on Computational Geometry , pp. 99-106
    • Berberich, E.1
  • 9
    • 0041770126 scopus 로고
    • Comments on Algorithms for reporting and counting geometric intersections
    • K.Q. Brown Comments on Algorithms for reporting and counting geometric intersections IEEE Transactions on Computers 30 2 1981 147 148
    • (1981) IEEE Transactions on Computers , vol.30 , Issue.2 , pp. 147-148
    • Brown, K.Q.1
  • 12
    • 78149239182 scopus 로고    scopus 로고
    • Exact and efficient computations on circles in CGAL
    • Technische Universität Graz Austria Full version available as INRIA Research Report 6091, Exact and efficient computations on circles in CGAL and applications to VLSI design
    • P.M.M. de Castro, S. Pion, and M. Teillaud Exact and efficient computations on circles in CGAL Abstracts 23rd European Workshop on Computational Geometry 2007 Technische Universität Graz Austria 219 222 Full version available as INRIA Research Report 6091, Exact and efficient computations on circles in CGAL and applications to VLSI design https://hal.inria.fr/inria-00123259
    • (2007) Abstracts 23rd European Workshop on Computational Geometry , pp. 219-222
    • De Castro, P.M.M.1    Pion, S.2    Teillaud, M.3
  • 14
    • 84867973317 scopus 로고    scopus 로고
    • Computing the arrangement of circles on a sphere, with applications in structural biology
    • this issue
    • F. Cazals, and S. Loriot Computing the arrangement of circles on a sphere, with applications in structural biology Computational Geometry 42 6-7 2009 551 565 this issue
    • (2009) Computational Geometry , vol.42 , Issue.67 , pp. 551-565
    • Cazals, F.1    Loriot, S.2
  • 15
    • 84867994909 scopus 로고    scopus 로고
    • Cgal, Computational Geometry Algorithms Library
    • Cgal, Computational Geometry Algorithms Library http://www.cgal.org
  • 17
    • 0011924356 scopus 로고    scopus 로고
    • Molecular surfaces: A review
    • M.L. Connolly Molecular surfaces: A review Network Science 14 1996 http://www.netsci.org/Science/Compchem/feature14.html
    • (1996) Network Science , vol.14
    • Connolly, M.L.1
  • 18
    • 84867991131 scopus 로고    scopus 로고
    • Core Number Library
    • Core Number Library http://cs.nyu.edu/exact/core-pages
  • 19
    • 84867969343 scopus 로고    scopus 로고
    • Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs
    • R.S. Drysdale, G. Rote, and A. Sturm Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs Computational Geometry: Theory and Applications 41 2008 31 47
    • (2008) Computational Geometry: Theory and Applications , vol.41 , pp. 31-47
    • Drysdale, R.S.1    Rote, G.2    Sturm, A.3
  • 21
    • 84867982454 scopus 로고    scopus 로고
    • Exacus, Efficient and Exact Algorithms for Curves and Surfaces
    • Exacus, Efficient and Exact Algorithms for Curves and Surfaces http://www.mpi-inf.mpg.de/projects/EXACUS
  • 23
    • 57349188186 scopus 로고    scopus 로고
    • A generic lazy evaluation scheme for exact geometric computations
    • A. Fabri, S. Pion, A generic lazy evaluation scheme for exact geometric computations, in: Proc. 2nd Library-Centric Software Design, 2006, pp. 75-84
    • (2006) Proc. 2nd Library-Centric Software Design , pp. 75-84
    • Fabri, A.1    Pion, S.2
  • 24
    • 58349083460 scopus 로고    scopus 로고
    • Generic programming and the CGAL library
    • J.-D. Boissonnat, M. Teillaud, Mathematics and Visualization Springer-Verlag
    • E. Fogel, and M. Teillaud Generic programming and the CGAL library J.-D. Boissonnat, M. Teillaud, Effective Computational Geometry for Curves and Surfaces 2006 Mathematics and Visualization Springer-Verlag 313 320
    • (2006) Effective Computational Geometry for Curves and Surfaces , pp. 313-320
    • Fogel, E.1    Teillaud, M.2
  • 26
    • 84867994913 scopus 로고    scopus 로고
    • GMP, GNU Multiple Precision Arithmetic Library
    • GMP, GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp
  • 30
    • 84867991130 scopus 로고    scopus 로고
    • Leda, Library for Efficient Data Types and Algorithms
    • Leda, Library for Efficient Data Types and Algorithms http://www.algorithmic-solutions.com/enleda.htm
  • 31
    • 17644422204 scopus 로고    scopus 로고
    • Recent progress in exact geometric computation
    • Special issue on the practical development of exact real number computation
    • C. Li, S. Pion, and C.K. Yap Recent progress in exact geometric computation Journal of Logic and Algebraic Programming 64 1 2005 85 111 Special issue on the practical development of exact real number computation
    • (2005) Journal of Logic and Algebraic Programming , vol.64 , Issue.1 , pp. 85-111
    • Li, C.1    Pion, S.2    Yap, C.K.3
  • 33
    • 0036773411 scopus 로고    scopus 로고
    • Quantification of protein surfaces, volumes and atom-atom contacts using a constrained Voronoi procedure
    • B.J. McConkey, V. Sobolev, and M. Edelman Quantification of protein surfaces, volumes and atom-atom contacts using a constrained Voronoi procedure Bioinformatics 18 10 2002 1365 1373
    • (2002) Bioinformatics , vol.18 , Issue.10 , pp. 1365-1373
    • McConkey, B.J.1    Sobolev, V.2    Edelman, M.3
  • 34
    • 10044269575 scopus 로고    scopus 로고
    • On the computation of an arrangement of quadrics in 3d
    • Special issue, 19th European Workshop on Computational Geometry
    • B. Mourrain, J.-P. Técourt, and M. Teillaud On the computation of an arrangement of quadrics in 3d Computational Geometry: Theory and Applications 30 2005 145 164 Special issue, 19th European Workshop on Computational Geometry
    • (2005) Computational Geometry: Theory and Applications , vol.30 , pp. 145-164
    • Mourrain, B.1    Técourt, J.-P.2    Teillaud, M.3
  • 35
    • 84867993407 scopus 로고    scopus 로고
    • in: CGAL Editorial Board (Ed.), CGAL User and Reference Manual. 3.2 and 3.3 edition, 2006 and 2007
    • S. Pion, and M. Teillaud 2D circular kernel in: CGAL Editorial Board (Ed.), CGAL User and Reference Manual. 3.2 and 3.3 edition, 2006 and 2007 http://www.cgal.org/Manual/3.3/doc-html/cgal-manual/packages.html#Pkg: CircularKernel2
    • 2D Circular Kernel
    • Pion, S.1    Teillaud, M.2
  • 37
    • 67349217775 scopus 로고    scopus 로고
    • in: CGAL Editorial Board (Ed.), CGAL User and Reference Manual. 3.2 and 3.3 edition, 2006 and 2007
    • R. Wein, E. Fogel, B. Zukerman, and D. Halperin 2D arrangements in: CGAL Editorial Board (Ed.), CGAL User and Reference Manual. 3.2 and 3.3 edition, 2006 and 2007 http://www.cgal.org/Manual/3.3/doc-html/cgal-manual/packages.html#Pkg: Arrangement2
    • 2D Arrangements
    • Wein, R.1    Fogel, E.2    Zukerman, B.3    Halperin, D.4
  • 38
    • 84867994915 scopus 로고    scopus 로고
    • Worldwide Protein Data Bank
    • Worldwide Protein Data Bank http://www.wwpdb.org
  • 39
    • 0001119219 scopus 로고
    • The exact computation paradigm
    • D.-Z. Du, F.K. Hwang, second ed. Lecture Notes Series on Computing World Scientific Singapore
    • C.K. Yap, and T. Dubé The exact computation paradigm D.-Z. Du, F.K. Hwang, Computing in Euclidean Geometry second ed. Lecture Notes Series on Computing vol. 4 1995 World Scientific Singapore 452 492
    • (1995) Computing in Euclidean Geometry , vol.4 , pp. 452-492
    • Yap, C.K.1    Dubé, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.