Planar C2 cubic spline interpolation under geometric boundary conditions

✍ Scribed by A.I. Ginnis; P.D. Kaklis

• Book ID: 104304919
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 214 KB
• Volume: 19
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(02)00091-2

✦ Synopsis

This paper deals with the problem of C 2 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 boundarydata 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.