Constrained Spline Interpolation

The research on constrained approximation and interpolation is important in industrial applications. Today, there are many results about interpolation of convexity or monotonically constrain. Another important constraint is the preservation of area of a surface. In univariate analogue, this constraint is just the preservation of length of the curve. In this paper, this constraint is discussed. For the space curve with length constraint and the surface of revolution area constraint, algorithms and estimation of the error are given. The key of the algorithm is how to estimate the derived vector of the surface curve or the first derivative of the surface of revolution according to the given length or area constraint. A length function and Fritsch-Carlson algorithm are used to solve the problem of the surface curve with length constraints. In the same way, an area function and Fritsch-Carlson algorithm is used to solve the problem of the preservation of area of the surface of revolution. In this paper, the error estimate is also given.