The C2 continuous cubic spline can be viewed as the solution of a variational problem. The spline derived in this paper is obtained by solving a slightly different variational problem that depends on the input data. The goal is to obtain a spline that may have high second derivatives at the interpolated points and low second derivatives between two consecutive interpolated points. The solution is a C2 continuous quartic spline.

Given a set of points, and normals on a surface and triangulation associated with them a simple scheme for approximating the principal curvatures at these points is developed. The approximation is based on the fact that a surface can locally be represented as the graph of a bivariate function. Quadratic polynomials are used for this local approximation. The principal curvatures at the point on the graph of such a quadratic polynomial is used as the approximation of the principal curvatures at the original surface point.