Direction-consistent tangent vectors for generating interpolation curves

In this paper, monotonicity-preserving interpolation is generalized to direction-consistent interpolation. The conditions for constructing direction-consistent tangent vectors are given. The conditions on the tangent vectors are also obtained such that the piecewise cubic Hermite interpolation curves are tangent direction-consistent with the direction of data polygon. Based on geometric insights, the balanced tangent vectors are presented and proved to be direction-consistent tangent vectors. With the balanced tangent vectors, the generated cubic Hermite interpolation curves are tangent direction-consistent, and the generated quintic Hermite interpolation curves are also tangent direction-consistent provided that we use the accumulative chord length parametrization. Some graphic examples are given to show that the generated interpolation curves preserve satisfactorily the shape of the given data control polygon.