First order hermite interpolation with spherical Pythagorean-hodograph curves - Kim, Gwang-Il; Kong, Jae-Hoon; Lee, Sunhong (Journal of applied mathematics & computing, 2007)
The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the Pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatialC^sup 1^ Hermite data, we construct a spatial PH curve on a sphere that is aC^sup 1^ Hermite interpolant of the given data as follows: First, we solveC^sup 1^ Hermite interpolation problem for the stereographically projected planar data of the given data in ^sup 3^ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in ^sup 3^ using the inverse general stereographic projection.[PUBLICATION ABSTRACT]