A convex G^2 Hermite interpolation problem of concentric curvature elements is considered in this paper. It is first proved that there is no spiral arc solution with turning angle less than or equal to π and then, that any convex solution admits at least two vertices. The curvature and the evolute profiles of such an interpolant are analyzed. In particular, conditions for the existence of a G^2 convex interpolant with prescribed extremal curvatures are given.
On the interpolation of concentric curvature elements / Giannelli Carlotta; Biard Luc. - In: COMPUTER AIDED DESIGN. - ISSN 0010-4485. - STAMPA. - 43:(2011), pp. 586-597. [10.1016/j.cad.2011.02.003]
On the interpolation of concentric curvature elements
Giannelli Carlotta;
2011
Abstract
A convex G^2 Hermite interpolation problem of concentric curvature elements is considered in this paper. It is first proved that there is no spiral arc solution with turning angle less than or equal to π and then, that any convex solution admits at least two vertices. The curvature and the evolute profiles of such an interpolant are analyzed. In particular, conditions for the existence of a G^2 convex interpolant with prescribed extremal curvatures are given.
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