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Zbl 1210.65040
Kurnosenko, A.I.
Two-point $G^{2}$ Hermite interpolation with spirals by inversion of hyperbola. (English)
[J] Comput. Aided Geom. Des. 27, No. 6, 474-481 (2010). ISSN 0167-8396

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.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
65D05 Interpolation (numerical methods)

Keywords: lens; rational curve; inversion of hyperbola; Möbius map; graphical examples; rational spirals; convex spiral arcs; non-convex data

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Zentralblatt MATH Berlin [Germany]