Optimal twist vectors as a tool for interpolating a network of curves with a minimum energy surface

This paper provides a new answer to the old problem of specifying the mixed partial derivatives (MPDs) or ‘twist vectors’ at the grid points for an interpolating surface over a rectangular network of curves. An algorithm is presented for finding the MPDs that minimizes a generalized energy integral over the entire surface. The integrand may be any quadratic form in the second partial derivatives of the surface. This results in a surface design technique for interpolating over a network of curves by automatically selecting the optimal twist vectors at the grid points.