Planar C2 cubic spline interpolation under geometric boundary conditions

Authors:
A. I. Ginnis;P. D. Kaklis
Affiliations:
National Technical University of Athens, Department of Naval Architecture and Marine Engineering, Ship Design Laboratory, 9 Heroon Polytechneiou, Zografou, Athens, 15773, Greece;National Technical University of Athens, Department of Naval Architecture and Marine Engineering, Ship Design Laboratory, 9 Heroon Polytechneiou, Zografou, Athens, 15773, Greece
Venue:
Computer Aided Geometric Design
Year:
2002

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Abstract

This paper deals with the problem of C2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to necessary and sufficient conditions for all possible boundary-data configurations. A robust scheme for the numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples.