FIRST ORDER HERMITE INTERPOLATION WITH SPHERICAL PYTHAGOREAN-HODOGRAPH CURVES

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 spatial C-1 Hermite data, we construct a spatial PH curve on a sphere that is a C-1 Hermite interpolant of the given data as follows: First, we solve C-1 Hermite interpolation problem for the stereographically projected planar data of the given data in R-3 with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in R-3 using the inverse general stereographic projection. AMS Mathematics Subject Classification : 65D17, 68U05