On geometric invariants of plane curves
DOI:
https://doi.org/10.5540/03.2022.009.01.0286Palavras-chave:
Geometric modeling, plane curves, inflections, vertices, graphs of stable maps.Resumo
In this paper, we study some geometric invariants of closed plane curves, that can help us classify these curves. We focus on two invariants: the number of inflection points and the number of vertex points. We intend to end models of curves with a number of predefined double points and with the smallest possible number of inflection points and vertex points.
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Referências
Kamenosono A. e Yamamoto T.The minimal number of singularities of stable maps between surfaces. Em: Topology and Its Appl. 156 (2009), pp. 23902405. doi: 10.1016/j.topol. 2009.06.010.
V. A. Arnold. Plane curves, their invariants, Perestroikas and Classifcations. Em: Advanced in Soviet Math. 21 (1994), pp. 3391. doi: https://doi.org/10.1090/S1061-0022- 04-00826-X.
J. W. Bruce e Giblin. P. J. Curves and singularities. University of Liverpool, 1984. isbn:9781139172615.
H. Pomerleano D. DeTurck D. Gluck e D. S. Vick. The four vertex theorem and its converse. Em: Notices Amer. Math. Soc. 54 (2007), pp. 192207. doi: https://doi.org/10.2307/ 2323126.
Whitney H.On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane into the Plane. Em: Ann. of Math. 62 (1955), pp. 374410. doi: https://doi.org/10. 2307/1970070.
Whitney W. H. On regular closed curves in the plane. Em: Comp. Math. 4 (1937), pp. 276 284. doi: http://www.numdam.org/item?id=CM_1937__4__276_0. 7
Mendes de Jesus C. Hacon D. e Romero Fuster M. C. Fold maps from the sphere to the plane. Em: Experimental Math. 15:4 (2006), pp. 491498. doi: https://doi.org/10. 1080/10586458.2006.10128973.
Mendes de Jesus C. Hacon D. e Romero Fuster M. C. Stable maps from surfaces to the plane with prescribed branching data. Em: Topology and Its Appl. 154 (2007), pp. 166175. doi: 10.1016/j.topol.2006.04.005.
Mehdipour P. Mendes de Jesus C. e Salarinoghabi M. Geometric surgeries of plane curves. Em: (preparação).
Salarinoghabi M. e Tari F. Flat and round singularity theory of plane curves. Em: C. R. Acad. Sci. Paris Ser. I. Math. 61 (2017), pp. 12891312. doi: https://doi.org/10. 1093/qmath/hax022.
Yamamoto M. Immersions of surfaces with boundary into the plane. Em: Pacic J. Maths. 212 (2012), pp. 371376. doi: 10.2140/PJM.2003.212.371.
Pignoni R. Minimal arrangements of singularities for apparent contours. Em: C. R. Acad. Sci. Paris Ser. I. Math. 313 (12) (1991), pp. 873878. doi: https://doi.org/10.2206/ kyushujm.64.1.
Ohmoto T. First Order Local Invariants of Apparent Coutours. Em: Topology 45 (2006), pp. 2745. doi: 10.1016/j.top.2005.04.005
