- Published 1992 in ACM Trans. Graph.

Rational Be´zier surfaces provide an effective tool for geometric design. One aspect of the theory of rational surfaces that is not well understood is what happens when a rational parameterization takes on the value (0/0, 0/0, 0/0) for some parameter value. Such parameter values are called base points of the parameterization. Base points can be introduced into a rational parameterization in Be´zier form by setting weights of appropriate control points to zero. By judiciously introducing base points, one can create parameterizations of four-, five- and six-sided surface patches using rational Be´zier surfaces defined over triangular domains. Subdivision techniques allow rendering and smooth meshing of such surfaces. Properties of base points also lead to a new understanding of incompatible edge twist methods such as Gregory's patch.

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@article{Warren1992CreatingMR,
title={Creating Multisided Rational B{\'e}zier Surfaces Using Base Points},
author={J David Warren},
journal={ACM Trans. Graph.},
year={1992},
volume={11},
pages={127-139}
}