A method for construction of surfaces under tension

Abstract

We describe and develop the properties of a method for interpolation of scattered data based on a generalization of the univariate spline under tension defined on a triangulation of the domain. Examples are given showing that the surface responds in a predictable way to the application of tension. As in the univariate case, tension parameters offer the promise of a way for the user to control the behavior of surfaces which have steep gradients implied by the data. © 1984 Rocky Mountain Journal of Mathematics.