Birational quadrilateral maps

A generic planar quadrilateral defines a 2:1 bilinear map. We show that by assigning an appropriate weight to one vertex of any planar quadrilateral, we can create a map whose inverse is rational linear. We show how to make a quad map be birational by assigning one control point weight.The weight is computed using a simple closed-form equation.For convex quads, the weight is positive and the pre-image is the [ 0 , 1 ] i? [ 0 , 1 ] domain.Any planar quad mesh can be made piecewise C 0 birational by using this method.