Shape of toric surfaces

We present an informal introduction to the theory of toric surfaces from the viewpoint of geometric modeling. Bezier surfaces and many well-known low-degree rational surfaces are found to be toric. Bezier-like control point schemes for toric surfaces are defined via mixed trigonometric-polynomial parametrizations. Many examples are considered: quadrics, cubic Mobius strip, quartic 'pillow', 'crosscap' and Dupin cyclides. A 'pear' shape modeling is presented.