Rectangular v-Splines

This article describes and presents examples of some techniques for the representation and interactive design of surfaces based on a parametric surface representation that user v-spline curves. These v-spline curves, similar in mathematical structure to v-splines, were developed as a more computationally efficient alternative to splines in tension. Although splines in tension can be modified to allow tension to be applied at each control point, the procedure is computationally expensive. The v-spline curve, however, uses more computationally tractable piecewise cubic curves segments, resulting in curves that are just as smoothly joined as those of a standard cubic spline. After presenting a review of v-splines and some new properties, this article extends their application to a rectangular grid of control points. Three techniques and some application examples are presented.