Using Farin points for rational Bézier surfaces Original Research Article

Farin points (weight points) are a useful tool for handling the weights of rational Bézier curves. They describe the weights of the Bézier points uniquely and in a geometrically intuitive way. The main problem for using Farin points for triangular or tensorproduct rational Bézier surfaces is the fact that they are not independent of each other and therefore overdefine the weights. To overcome this problem we present two approaches: moving a Farin point, we adjust the adjacent Farin points automatically in such a way that the system of all Farin points stays contradiction-free. In the other approach we present an appropriate subset of Farin points which are independent of each other and define the weights uniquely. Both approaches are presented for triangular and tensorproduct Bézier surfaces. They make Farin points useful for the design of rational Bézier surfaces.