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Spherical Pythagorean-hodograph curves. (English) Zbl 0905.65019
Dæhlen, Morten (ed.) et al., Mathematical methods for curves and surfaces II. 2nd international conference, Lillehammer, Norway, July 3--8, 1997. Nashville, TN: Vanderbilt Univ. Press. 485-492 (1998).
Summary: Geometric inversion preserves Pythagorean hodographs. Stereographic projection, that is, a composition of the three mappings: translation, inversion and dilatation, maps Pythagorean hodograph (PH) plane curves onto the unit sphere. These stereographic image curves are spherical PH curves. The rotated curves and the geodesic offset curves of a spherical curve are also spherical PH curves. A great number of PH plane curves can be obtained as the preimage curves of such derived spherical PH curves. For the entire collection see [Zbl 0892.00046].

65D17Computer aided design (modeling of curves and surfaces)