A set of one-to-one two-dimensional biquadratic transformations

Abstract

AbstractIt is proved that a simple constraint on the parameters of the biquadratic form will produce a set of geometrical transformations that are one-to-one over a rectangular region of the plane. The transformations are treated as interpolations from discrete mappings specified at a finite set of points within the region. The constraint, which is less stringent than a previously proposed constraint of the same form, is shown to be minimal. Because of their polynomial form, these transformations are continuous, smooth, and computationally simple. Comparisons with transformations of other forms are made and applications are discussed