메뉴 건너뛰기




Volumn 354, Issue 1714, 1996, Pages 1899-1940

On the complexity and computation of view graphs of piecewise smooth algebraic surfaces

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3242783490     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1996.0083     Document Type: Article
Times cited : (10)

References (43)
  • 1
    • 84891999913 scopus 로고
    • Singularities of systems of rays
    • Arnol'd, V. I. 1983 Singularities of systems of rays. Russ. Math. Surv. 38, 87-176.
    • (1983) Russ. Math. Surv. , vol.38 , pp. 87-176
    • Arnol'd, V.I.1
  • 2
    • 0021521367 scopus 로고
    • Cylindrical algebraic decomposition. I. The basic algorithm. II. An adjacency algorithm for the plane
    • Arnon, D. S., Collins, G. E. & McCallum, S. 1984 Cylindrical algebraic decomposition. I. The basic algorithm. II. An adjacency algorithm for the plane. SIAM J. Comput. 13, 865-877; 878-889.
    • (1984) SIAM J. Comput. , vol.13 , pp. 865-877
    • Arnon, D.S.1    Collins, G.E.2    McCallum, S.3
  • 3
    • 85034428367 scopus 로고
    • An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space
    • (Springer LNCS 204.) Berlin: Springer
    • Arnon, D. S., Collins, G. E. & McCallum, S. 1985 An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space. In Proc. Eurocal'85, vol. 2, pp. 246-261. (Springer LNCS 204.) Berlin: Springer.
    • (1985) Proc. Eurocal'85 , vol.2 , pp. 246-261
    • Arnon, D.S.1    Collins, G.E.2    McCallum, S.3
  • 6
    • 0002803133 scopus 로고
    • Gröbner bases: An algorithmic method in polynomial ideal theory
    • (ed. N. K. Bose), Dordrecht, Boston, and Lancaster: Reidel
    • Buchberger, B. 1985 Gröbner bases: an algorithmic method in polynomial ideal theory. In Multidimensional systems theory (ed. N. K. Bose), pp. 184-232. Dordrecht, Boston, and Lancaster: Reidel.
    • (1985) Multidimensional Systems Theory , pp. 184-232
    • Buchberger, B.1
  • 7
    • 85029837057 scopus 로고
    • Quantifier elimination for real closed fields by cylindrical algebraic decomposition
    • (Springer LNCS 33.) Berlin, Heidelberg and New York: Springer
    • Collins, G. E. 1975 Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Proc. 2nd GI Conf. Automata Theory and Formal Languages, pp. 134-183. (Springer LNCS 33.) Berlin, Heidelberg and New York: Springer.
    • (1975) Proc. 2nd GI Conf. Automata Theory and Formal Languages , pp. 134-183
    • Collins, G.E.1
  • 8
    • 0007205572 scopus 로고
    • The structure of TA(f), classification, and an application to differential geometry
    • American Mathematical Society
    • Gaffney, T. 1983 The structure of TA(f), classification, and an application to differential geometry. In Proc. Symp. Pure Math., vol. 40, pp. 409-427. American Mathematical Society.
    • (1983) Proc. Symp. Pure Math. , vol.40 , pp. 409-427
    • Gaffney, T.1
  • 9
    • 0025387820 scopus 로고
    • Computing the aspect graph for line drawings of polyhedral objects
    • Gigus, Z. & Malik, J. 1990 Computing the aspect graph for line drawings of polyhedral objects. IEEE Trans. Pattern Analysis Machine Intell. 12, 113-122.
    • (1990) IEEE Trans. Pattern Analysis Machine Intell , vol.12 , pp. 113-122
    • Gigus, Z.1    Malik, J.2
  • 10
    • 0000148308 scopus 로고
    • On spherical image maps whose Jacobians do not change sign
    • Hartman, P. & Nirenberg, L. 1959 On spherical image maps whose Jacobians do not change sign. Am. J. Math. 81, 901-920.
    • (1959) Am. J. Math. , vol.81 , pp. 901-920
    • Hartman, P.1    Nirenberg, L.2
  • 11
    • 0000516514 scopus 로고
    • Triangulations of algebraic sets
    • American Mathematical Society
    • Hironaka, H. 1975 Triangulations of algebraic sets. In Proc. Symp. Pure Math., vol. 29, pp. 165-185. American Mathematical Society.
    • (1975) Proc. Symp. Pure Math. , vol.29 , pp. 165-185
    • Hironaka, H.1
  • 12
    • 0001715693 scopus 로고
    • La famille des projections orthogonales d'une surface et ses singularites
    • Kergosien, Y. L. 1981 La famille des projections orthogonales d'une surface et ses singularites. C.R. Acad. Sci. Paris Ser. I Math. 292, 929-932.
    • (1981) C.R. Acad. Sci. Paris Ser. I Math. , vol.292 , pp. 929-932
    • Kergosien, Y.L.1
  • 13
    • 0001858013 scopus 로고
    • Multiple-point formulas. I. Iteration
    • Kleiman, S. L. 1981 Multiple-point formulas. I. Iteration. Acta Math. 147, 13-49.
    • (1981) Acta Math. , vol.147 , pp. 13-49
    • Kleiman, S.L.1
  • 14
    • 0017134710 scopus 로고
    • The singularities of the visual mapping
    • Koenderink, J. J. & van Doorn, A. J. 1976 The singularities of the visual mapping. Biol. Cybernet. 24, 51-59.
    • (1976) Biol. Cybernet. , vol.24 , pp. 51-59
    • Koenderink, J.J.1    Van Doorn, A.J.2
  • 15
    • 0018777412 scopus 로고
    • The internal representation of solid shape with respect to vision
    • Koenderink, J. J. & van Doorn, A. J. 1979 The internal representation of solid shape with respect to vision. Biol. Cybernet. 32, 211-216.
    • (1979) Biol. Cybernet. , vol.32 , pp. 211-216
    • Koenderink, J.J.1    Van Doorn, A.J.2
  • 17
    • 0000418851 scopus 로고
    • Triangulations of semi-analytic sets
    • Lojasiewicz, S. 1964 Triangulations of semi-analytic sets. Ann. Scuola Norm. Sup. Pisa 18, 449-474.
    • (1964) Ann. Scuola Norm. Sup. Pisa , vol.18 , pp. 449-474
    • Lojasiewicz, S.1
  • 18
    • 0001945369 scopus 로고
    • ∞ mappings. I
    • ∞ mappings. I. Ann. Math. 87, 89-104.
    • (1968) Ann. Math. , vol.87 , pp. 89-104
    • Mather, J.N.1
  • 20
    • 0000167702 scopus 로고
    • ∞ mappings. II
    • ∞ mappings. II. Ann. Math. 89, 259-291.
    • (1969) Ann. Math. , vol.89 , pp. 259-291
    • Mather, J.N.1
  • 22
    • 49849118512 scopus 로고
    • ∞ mappings. V
    • ∞ mappings. V. Adv. Math. 4, 301-335.
    • (1970) Adv. Math. , vol.4 , pp. 301-335
    • Mather, J.N.1
  • 23
    • 0001399303 scopus 로고
    • ∞ mappings. VI
    • ∞ mappings. VI. Springer LNM 192, 207-255.
    • (1971) Springer LNM , vol.192 , pp. 207-255
    • Mather, J.N.1
  • 24
    • 0040436083 scopus 로고
    • Stable map-germs and algebraic geometry
    • Mather, J. N. 19716 Stable map-germs and algebraic geometry. Springer LNM 197, 176-193.
    • (1971) Springer LNM , vol.197 , pp. 176-193
    • Mather, J.N.1
  • 25
    • 0002279198 scopus 로고
    • Generic projections
    • Mather, J. N. 1973 Generic projections. Ann. Math. 98, 226-245.
    • (1973) Ann. Math. , vol.98 , pp. 226-245
    • Mather, J.N.1
  • 26
    • 3242774302 scopus 로고
    • Preprint, Mathematics Institute, University of Warwick, England
    • McCrory, C. 1980 Profiles of surfaces. Preprint, Mathematics Institute, University of Warwick, England.
    • (1980) Profiles of Surfaces
    • McCrory, C.1
  • 27
    • 84966260816 scopus 로고
    • On the Betti numbers of real varieties
    • Milnor, J. 1964 On the Betti numbers of real varieties. Proc. Am. Math. Soc. 15, 275-280.
    • (1964) Proc. Am. Math. Soc. , vol.15 , pp. 275-280
    • Milnor, J.1
  • 29
    • 0000413093 scopus 로고
    • Counting real zeros in the multivariate case
    • (ed. F. Eyssette & A. Galligo), Boston, Basel and Berlin: Birkhäuser
    • Pedersen, P., Roy, M.-F. & Szpirglas A. 1992 Counting real zeros in the multivariate case. In Computational Algebraic Geometry, Prog. in Math. (ed. F. Eyssette & A. Galligo), vol. 109, pp. 203-224. Boston, Basel and Berlin: Birkhäuser.
    • (1992) Computational Algebraic Geometry, Prog. in Math. , vol.109 , pp. 203-224
    • Pedersen, P.1    Roy, M.-F.2    Szpirglas, A.3
  • 30
    • 0026971802 scopus 로고
    • Computing exact aspect graphs of curved objects: Algebraic surfaces
    • Petitjean, S., Ponce, J. & Kriegman, D. J. 1992 Computing exact aspect graphs of curved objects: algebraic surfaces. Int. J. Comput. Vision 9(3), 231-255.
    • (1992) Int. J. Comput. Vision , vol.9 , Issue.3 , pp. 231-255
    • Petitjean, S.1    Ponce, J.2    Kriegman, D.J.3
  • 31
    • 0022719569 scopus 로고
    • On the classification of views of piecewise smooth objects
    • Rieger, J. H. 1987a On the classification of views of piecewise smooth objects. Image Vision Comput. 5, 91-97.
    • (1987) Image Vision Comput. , vol.5 , pp. 91-97
    • Rieger, J.H.1
  • 32
    • 84959850452 scopus 로고
    • Families of maps from the plane to the plane
    • Rieger, J. H. 19876 Families of maps from the plane to the plane. J. Lond. Math. Soc. 36, 351-369.
    • (1987) J. Lond. Math. Soc. , vol.36 , pp. 351-369
    • Rieger, J.H.1
  • 33
    • 84974449938 scopus 로고
    • Versal tppological stratification and the bifurcation geometry of map-germs of the plane
    • Rieger, J. H. 1990 Versal tppological stratification and the bifurcation geometry of map-germs of the plane. Math. Proc. Camb. Phil. Soc. 107, 127-147.
    • (1990) Math. Proc. Camb. Phil. Soc. , vol.107 , pp. 127-147
    • Rieger, J.H.1
  • 34
    • 0026842029 scopus 로고
    • Global bifurcation sets and stable projections of non-singular algebraic surfaces
    • Rieger, J. H. 1992 Global bifurcation sets and stable projections of non-singular algebraic surfaces. Int. J. Comput. Vision 7(3), 171-194.
    • (1992) Int. J. Comput. Vision , vol.7 , Issue.3 , pp. 171-194
    • Rieger, J.H.1
  • 35
    • 38249003237 scopus 로고
    • Computing view graphs of algebraic surfaces
    • Rieger, J. H. 1993a Computing view graphs of algebraic surfaces. J. Symbolic Computation 16(3), 259-272.
    • (1993) J. Symbolic Computation , vol.16 , Issue.3 , pp. 259-272
    • Rieger, J.H.1
  • 36
    • 3242788576 scopus 로고
    • Projections of generic surfaces of revolution
    • Rieger, J. H. 1993b Projections of generic surfaces of revolution. Geometriae Dedicata 48, 211-230.
    • (1993) Geometriae Dedicata , vol.48 , pp. 211-230
    • Rieger, J.H.1
  • 37
    • 3242816662 scopus 로고
    • Semi-algebraic solids in 3-space: A survey of modelling schemes and implications for view graphs
    • Rieger, J. H. & Rohr, K. 1994 Semi-algebraic solids in 3-space: a survey of modelling schemes and implications for view graphs. Image Vision Comput. 12, 395-410.
    • (1994) Image Vision Comput. , vol.12 , pp. 395-410
    • Rieger, J.H.1    Rohr, K.2
  • 40
    • 84980085825 scopus 로고
    • Developable surfaces in the large
    • Stoker, J. J. 1961 Developable surfaces in the large. Communs Pure Appl. Math. XIV, 627-635.
    • (1961) Communs Pure Appl. Math. , vol.14 , pp. 627-635
    • Stoker, J.J.1
  • 41
    • 84959831347 scopus 로고
    • Projections of piecewise smooth surfaces
    • Tari, F. 1991 Projections of piecewise smooth surfaces. J. Lond. Math. Soc. 44, 155-172.
    • (1991) J. Lond. Math. Soc. , vol.44 , pp. 155-172
    • Tari, F.1
  • 42
    • 0000521365 scopus 로고
    • Finite determinacy of smooth map-germs
    • Wall, C. T. C. 1981 Finite determinacy of smooth map-germs. Bull. Lond. Math. Soc. 13, 481-539.
    • (1981) Bull. Lond. Math. Soc. , vol.13 , pp. 481-539
    • Wall, C.T.C.1
  • 43
    • 0000770380 scopus 로고
    • On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
    • Whitney, H. 1955 On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane. Ann. Math. 62, 374-410.
    • (1955) Ann. Math. , vol.62 , pp. 374-410
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.