Planar C2 cubic spline interpolation under geometric boundary conditions

A Ginnis
2002 Computer Aided Geometric Design  
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
more » ... e numerical solution of the quadratic system is presented, and the use of the new boundary conditions is illustrated in the context of three examples.
doi:10.1016/s0167-8396(02)00091-2 fatcat:sntghwttxfflljddsesziotvsi