메뉴 건너뛰기




Volumn 28, Issue 2, 2009, Pages

A BSP-based algorithm for dimensionally nonhomogeneous planar implicit curves with topological guarantees

Author keywords

Binary space partitioning; Geometric computing; Implicit curves; Numerical algorithms

Indexed keywords

ALGEBRAIC CURVES; BINARY SPACE PARTITIONING; EXTREMAL; GEOMETRIC COMPUTING; IMPLICIT CURVES; LINE SEGMENT; LOCAL MINIMUMS; MATHEMATICA; NON-HOMOGENEOUS; NUMERICAL ALGORITHMS; POLYNOMIAL FUNCTIONS; RECTANGULAR REGIONS; SELF-INTERSECTIONS; SIGN VARIATIONS;

EID: 70349684856     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1516522.1516528     Document Type: Article
Times cited : (5)

References (48)
  • 1
    • 38049058756 scopus 로고    scopus 로고
    • Regularity criteria for the topology of algebraic curves and surfaces
    • Mathematics of Surfaces XII, R. Martin et al., Eds. Springer-Verlag
    • ALBERTI, L. ANDMOURRAIN, B. 2007a. Regularity criteria for the topology of algebraic curves and surfaces. In Mathematics of Surfaces XII, R. Martin et al., Eds. Lecture Notes in Computer Science, vol.4647. Springer-Verlag, 1-28.
    • (2007) Lecture Notes in Computer Science , vol.4647 , pp. 1-28
    • Alberti, L.1    Andmourrain, B.2
  • 4
    • 0026240956 scopus 로고
    • Simplicial pivoting for mesh generation of implicitly defined surfaces
    • ALLGOWER, E. AND GNUTZMANN, S. 1991. Simplicial pivoting for mesh generation of implicitly defined surfaces. Comput. Aided Geom. Des. 8, 305-325.
    • (1991) Comput. Aided Geom. Des. , vol.8 , pp. 305-325
    • Allgower, E.1    Gnutzmann, S.2
  • 5
    • 84971748944 scopus 로고
    • Algebraic decomposition of regular curves
    • ARNBORG, S. AND FENG, H. 1988. Algebraic decomposition of regular curves. J. Symbol. Comput. 5, 1-2, 131-140.
    • (1988) J. Symbol. Comput. , vol.5 , Issue.1-2 , pp. 131-140
    • Arnborg, S.1    Feng, H.2
  • 6
    • 84971721358 scopus 로고
    • A polynomial time algorithm for the topological type of a real algebraic curve
    • ARNON, D. ANDMCCALLUM, S. 1988. A polynomial time algorithm for the topological type of a real algebraic curve. J. Symbol. Comput. 5, 1- 213-236.
    • (1988) J. Symbol. Comput. , vol.5 , Issue.1 , pp. 213-236
    • Arnon, D.1    McCallum, S.2
  • 7
    • 0030736122 scopus 로고    scopus 로고
    • Piecewise rational approximations of real algebraic curves
    • BAJAJ, C. AND XU, G. 1997. Piecewise rational approximations of real algebraic curves. J. Comput. Math. 15, 1, 55-71. (Pubitemid 127756159)
    • (1997) Journal of Computational Mathematics , vol.15 , Issue.1 , pp. 55-71
    • Bajaj, C.L.1    Xu, G.L.2
  • 8
    • 0016557674 scopus 로고
    • Multidimensional binary search trees used for associative searching
    • BENTLEY, J. 1975. Multidimensional binary search trees used for associative searching. Commun. ACM 18, 9, 509-517.
    • (1975) Commun. ACM , vol.18 , Issue.9 , pp. 509-517
    • Bentley, J.1
  • 9
    • 74349114123 scopus 로고
    • A generalization of algebraic surface drawing
    • BLINN, J. 1982. A generalization of algebraic surface drawing. ACM Trans. Graphics 1, 3, 235-256.
    • (1982) ACM Trans. Graphics , vol.1 , Issue.3 , pp. 235-256
    • Blinn, J.1
  • 10
    • 0024104710 scopus 로고
    • Poligonization of implicit surfaces
    • BLOOMENTHAL, J. 1988. Poligonization of implicit surfaces. Comput. Aided Geom. Design 5, 4, 341-355.
    • (1988) Comput. Aided Geom. Design , vol.5 , Issue.4 , pp. 341-355
    • Bloomenthal, J.1
  • 11
    • 0001287167 scopus 로고
    • An implicit surface polygonizer
    • Academic Press
    • BLOOMENTHAL, J. 1994. An implicit surface polygonizer. In Graphics Gems. Vol.4. Academic Press.
    • (1994) Graphics Gems , vol.4
    • Bloomenthal, J.1
  • 12
    • 0003234162 scopus 로고    scopus 로고
    • A computer program for the resolution of singularities
    • H. Hauser et al. Eds. Progress in Mathematics. Birkḧauser
    • BODŃAR, G. AND SCHICHO, J. 2000. A computer program for the resolution of singularities. In Resolution of Singularities, A Research Textbook in Tribute to Oscar Zariski, H. Hauser et al. Eds. Progress in Mathematics, vol.181. Birkḧauser, 231-238.
    • (2000) Resolution of Singularities, A Research Textbook in Tribute to Oscar Zariski , vol.181 , pp. 231-238
    • Bodńar, G.1    Schicho, J.2
  • 13
    • 0023983514 scopus 로고
    • A tracking algorithm for implicitly defined curves
    • CHANDLER, R. 1988. A tracking algorithm for implicitly defined curves. IEEE Comput. Graphics Appl. 8, 2, 83-89.
    • (1988) IEEE Comput. Graphics Appl. , vol.8 , Issue.2 , pp. 83-89
    • Chandler, R.1
  • 18
    • 0019033556 scopus 로고
    • On visible surface generation by a priori tree structures
    • FUCHS, H., KEDEM, Z., AND NAYLOR, B. 1980. On visible surface generation by a priori tree structures. Comput. Graphics 14, 3, 124-133.
    • (1980) Comput. Graphics , vol.14 , Issue.3 , pp. 124-133
    • Fuchs, H.1    Kedem, Z.2    Naylor, B.3
  • 22
    • 0036895253 scopus 로고    scopus 로고
    • Efficient topology determination of implicitly defined algebraic plane curves
    • GONZALEZ-VEGA, L. AND NECULA, I. 2002. Efficient topology determination of implicitly defined algebraic plane curves. Comput. Aided Geom. Des. 19, 9, 719-743.
    • (2002) Comput. Aided Geom. Des. , vol.19 , Issue.9 , pp. 719-743
    • Gonzalez-Vega, L.1    Necula, I.2
  • 23
    • 0015143013 scopus 로고
    • Integer arithmetic algorithms for polynomial real zero determination
    • HEINDEL, L. 1971. Integer arithmetic algorithms for polynomial real zero determination. J. ACM 18, 4, 533-548.
    • (1971) J. ACM , vol.18 , Issue.4 , pp. 533-548
    • Heindel, L.1
  • 24
    • 0032164109 scopus 로고    scopus 로고
    • Algorithms for trigonometric curves (simplification, implicitization, parameterization)
    • HONG, H. AND SCHICHO, J. 1998. Algorithms for trigonometric curves (simplification, implicitization, parameterization). J. Symbol. Comput. 26, 3, 279-300.
    • (1998) J. Symbol. Comput. , vol.26 , Issue.3 , pp. 279-300
    • Hong, H.1    Schicho, J.2
  • 26
    • 29644432370 scopus 로고    scopus 로고
    • New bounds for the Descartes' method
    • KRANDICK, W. AND MEHLHORN, K. 2006. New bounds for the Descartes' method. J. Symbol. Comput. 41, 1, 49-66.
    • (2006) J. Symbol. Comput. , vol.41 , Issue.1 , pp. 49-66
    • Krandick, W.1    Mehlhorn, K.2
  • 28
    • 0019668976 scopus 로고
    • Bounds on a polynomial
    • LANE, J. AND RIESENFELD, R. 1981. Bounds on a polynomial. BIT Numer. Math. 21, 1, 112-117.
    • (1981) BIT Numer. Math. , vol.21 , Issue.1 , pp. 112-117
    • Lane, J.1    Riesenfeld, R.2
  • 30
    • 0023381475 scopus 로고
    • Marching cubes: A high resolution 3D surface construction algorithm
    • LORENSEN,W. AND CLINE,W. 1987. Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graphics 21, 4, 163-169.
    • (1987) Comput. Graphics , vol.21 , Issue.4 , pp. 163-169
    • Lorensen, W.1    Cline, W.2
  • 32
    • 70349677863 scopus 로고    scopus 로고
    • Ageneralized false position method for finding zeros and extrema of a real function
    • MORGADO, J. ANDGOMES,A. 2005. Ageneralized false position method for finding zeros and extrema of a real function. In Lecture Series on Computer and Computational Sciences 4, 425-428.
    • (2005) Lecture Series on Computer and Computational Sciences , vol.4 , pp. 425-428
    • Morgado, J.1    Andgomes, A.2
  • 33
    • 33748062712 scopus 로고    scopus 로고
    • Subdivision methods for solving polynomial equations
    • Institut National de Recherche en Informatique et en Automatique (INRIA). August
    • MOURRAIN, B. AND PAVONE, J.-P. 2005. Subdivision methods for solving polynomial equations. Tech. rep. 5658, Institut National de Recherche en Informatique et en Automatique (INRIA). August.
    • (2005) Tech. Rep. , vol.5658
    • Mourrain, B.1    Pavone, J.-P.2
  • 34
    • 33748958202 scopus 로고    scopus 로고
    • Bernstein's basis and real root isolation
    • J. Goodman et al., Eds. Mathematical Sciences Research Institute. Cambridge University Press
    • MOURRAIN, B., ROUILLIER, F., AND ROY, M.-F. 2005. Bernstein's basis and real root isolation. In Current Trends in Combinatorial and Computational Geometry, J. Goodman et al., Eds. Mathematical Sciences Research Institute. Cambridge University Press, 459-478.
    • (2005) Current Trends in Combinatorial and Computational Geometry , pp. 459-478
    • Mourrain, B.1    Rouillier, F.2    Roy, M.-F.3
  • 35
    • 0025475508 scopus 로고
    • Merging BSP trees yields polyhedral set operations
    • NAYLOR, B., AMANATIDES, J., AND THIBAULT, W. 1990. Merging BSP trees yields polyhedral set operations. Comput. Graphics 24, 4, 115-124.
    • (1990) Comput. Graphics , vol.24 , Issue.4 , pp. 115-124
    • Naylor, B.1    Amanatides, J.2    Thibault, W.3
  • 39
    • 0031518093 scopus 로고    scopus 로고
    • Adaptive precision floating-point arithmetic and fast robust geometric predicates
    • SHEWCHUK, J. 1997. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geom. 18, 3, 305-363.
    • (1997) Discrete Comput. Geom. , vol.18 , Issue.3 , pp. 305-363
    • Shewchuk, J.1
  • 40
    • 0026889111 scopus 로고
    • Interval arithmetic for computer graphics
    • SNYDER, J. 1992. Interval arithmetic for computer graphics. In Computer Graphics. Vol.26. 121-130.
    • (1992) Computer Graphics , vol.26 , pp. 121-130
    • Snyder, J.1
  • 41
    • 79953298368 scopus 로고
    • Ḿemoire sur la ŕesolution des ́equationsnuḿ eriques
    • STURM, C.-F. 1829. Ḿemoire sur la ŕesolution des ́equationsnuḿeriques. Le Bulletin des Sciences de F́erussac 11.
    • (1829) Le Bulletin des Sciences de F́erussac , vol.11
    • Sturm, C.-F.1
  • 43
    • 0003382414 scopus 로고
    • Ray tracing with the BSP tree
    • Academic Press
    • SUNG, K. AND SHIRLEY, P. 1992. Ray tracing with the BSP tree. In Graphics Gems. Vol.3. Academic Press, 271-274.
    • (1992) Graphics Gems , vol.3 , pp. 271-274
    • Sung, K.1    Shirley, P.2
  • 44
    • 0023380251 scopus 로고
    • Set operations on polyhedra using binary space partition trees
    • THIBAULT,W. ANDNAYLOR, B. 1987. Set operations on polyhedra using binary space partition trees. Comput. Graphics 21, 4, 153-162.
    • (1987) Comput. Graphics , vol.21 , Issue.4 , pp. 153-162
    • Thibault, W.1    Naylor, B.2
  • 45
    • 70349661016 scopus 로고    scopus 로고
    • Article 17, Publication date: April
    • ACM Transactions on Graphics, Vol.28, No.2, Article 17, Publication date: April 2009.
    • (2009) ACM Transactions on Graphics , vol.28 , Issue.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.