Toric surface patches (Q1599375)

A rational surface patch generalizing the classical Bézier surface is defined. It is associated with a convex polygon with vertices at integer coordinates. The main properties of toric patches: multisided forms, singular corner points, a wider variety of implicit degrees. A method is described for subdivision of a toric patch into smaller tensor product patches. A definition of real projective varieties of arbitrary dimension via global coordinates is also introduced. Moreover, the concept of Bézier polytope is presented which develops a multidimensional variant of the theory.