C-1 Hermite interpolation with simple planar PH curves by speed reparametrization

Abstract

We introduce a new method of solving C-1 Hermite interpolation roblems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t-c)(2n+1) + d. Next, we introduce a speed reparametrization. Finally, we show that, for C-1 Hermite data, we can use PH curves of type K(t-c)(2n+1) + d or strongly regular PH quintics satisfying the G(1) reduction of C-1 data, and use these curves to solve the original Cl Hermite interpolation problem. (C) 2007 Elsevier B.V. All rights reserved.