A-patches[BCX94a] are implicit surfaces in Bernstein-Bezier(BB) form that are smooth and single-sheeted. In this paper, we present algorithms to utilize the extra degrees of freedom of these patches for local shape co·ntrol. A ray shooting scheme is also given to rapidly generate polygonal approximations of A-patches for graphic display. A distributed implementation of this scheme gives near "r...

Let Fn denote the set of polynomials of degree at most n with coefficients from {−1, 0, 1}. Let Gn be the collection of polynomials p of the form

Global parameterizations of parametric algebraic curves or surfaces are defined over infinite parameter domains. In this paper we show how to replace these global real parameterizations with a finite number of alternate bounded parameterizations, each defined over a fixed, bounded part of the real parameter domain space. The new bounded parameterizations together generate all real points of the...

S d := {x = (x1, . . . , xd) ∈ R : 0 6 x1, . . . , xd 6 1, 0 6 x1 + · · ·+ xd 6 1} denote the standard simplex in R. We denote by ∂S the boundary of S. We will also use barycentric coordinates on the simplex which we denote by the boldface symbol x = (x0, x1, . . . , xd), x0 := 1−x1−· · ·−xd. We will use standard multiindex notation such as x := x0 0 x α1 1 · · ·xd d and α n := (α0 n , α1 n , ·...

To Iosif Bernstein for his 60th birthday

A finite-dimensional commutative algebra A over a field K is called a Bernstein algebra if there exists a non-trivial homomorphism co: A -> K (baric algebra) such that the identity (x) = CO(X)JC holds in A (see [7]). The origin of Bernstein algebras lies in genetics (see [2,8]). Holgate (in [2]) was the first to translate the problem into the language of non-associative algebras. Information ab...

A first-order theory T has the Schröder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and non-multidimensional. We also prove that among superstable theories T , the class of a-saturated models of T has the SB property if and only if T has no nomadic ...

The aim of the paper is twofold. First, some results of Shiota and Plaza-Mart́ın on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given.