Constrained interpolation with rational cubics Original Research Article

For a given set of ordered points lying on one side of a polyline, the problem of constructing a planar interpolating G2 curve to these planar data which lies on the same side of the polyline as the data is considered. An existing method addresses this problem using rational cubics with multiple lines as constraints and where all the data points lie strictly on one side of these lines. The method presented here extends that method to allow a polyline as a more general constraint where all the data points need not lie on one side of the infinite line through each of its edges. It also allows data points to lie on the constraint polyline. The interpolating curve is shape preserving in the sense that it has the minimal number of inflections consistent with the data.