Toric geometry applications to CAGD

Rimvydas Krasauskas, Vilnius University

Toric surfaces with their homogeneous coordinates (in the sense of David Cox) have several applications in Computer Aided Geometric Design (CAGD):
- many low degree rational surfaces used in CAGD appear to be real toric, or non-canonical real parts of complex toric surfaces;
- classical Bezier surface constructions can be naturally generalized to toric Bezier patches;
- all rational curves and natural subpatches of toric surfaces can be constructively described using the concept of universal rational parametrization.
The talk is devoted to various corollaries of recently proved (jointly with D. Cox and M. Mustata) Universal Rational Parametrization Theorem for toric varieties.