Birational quadrilateral maps

• 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]×[0,1][0,1]×[0,1] domain.
• Any planar quad mesh can be made piecewise C0C0 birational by using this method.

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.