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Two-point $G^{2}$ Hermite interpolation with spirals by inversion of hyperbola. (English) Zbl 1210.65040
Summary: Planar, 4th degree rational spirals, matching given $G^{2}$ Hermite data, are constructed by inversion of hyperbola. The proposed method handles any data for convex spiral arcs, and a great deal of non-convex data. Non-convex data are either with an inflection, or with big angular winding.

65D17Computer aided design (modeling of curves and surfaces)
65D05Interpolation (numerical methods)
Full Text: DOI
[1] Kurnosenko, A. I.: Long spirals, Zapiski nauch. Sem. POMI 372, 44-52 (2009)
[2] Kurnosenko, A. I.: Applying inversion to construct planar, rational, spiral curves that satisfy two-point G2 Hermite data, Comp. aided geom. Design 27, 262-280 (2010) · Zbl 1210.65039 · doi:10.1016/j.cagd.2009.12.004