Using Farin points for rational Bezier surfaces
Farin points (weight points) are a useful tool for handling the weights of rational Bezier curves. They describe the weights of the Bezier points uniquely and in a geometrically intuitive way. The main problem for using Farin points for triangular or tensorproduct rational Bezier 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 Bezier surfaces. They make Farin points useful for the design of rational Bezier surfaces. (C) 1999 Elsevier Science B.V. All rights reserved.
rational bezier surfaces farin points (weight points) weights