Thin plate splines with tension (Q1074290)

This paper investigates a scheme for representing surfaces by incorporating the concept of tension in a way which models a physical process. In particular, the deflection of a thin plate under the imposition of point loads in the lateral direction and midplane forces is considered. The properties of the (infinite) thin plate (function) as the tension goes to zero or becomes large is investigated. This function is then used to interpolate scattered data, allowing the tension parameter as control over overshoot when the surface has large gradients. Three examples are given.