Shape preserving approximation by spatial cubic splines

摘要

Shape preserving curve approximation is considered for an ordered set of spatial data points. Linear sufficient conditions for shape preserving criteria on convexity, inflection, collinearity and coplanarity are derived to ensure the approximant mimics the shape of the data. The cubic B-spline is used to generate the C~2 shape preserving approximation curve as this type of spline enables the shape preserving constraints to be formulated in a simple way.