Minkowski Pythagorean hodograph curves are polynomial curves with polynomial speed, measured with respect to Minkowski norm. Curves of this special class are particularly well suited for representing medial axis transforms of planar domains. In the present paper we generalize this polynomial class to a rational class of curves in Minkowski 3-space. We show that any rational Minkowski Pythagorea...

A polynomial curve of degree 5, α, is a helix if and only if both ||α′|| and ||α′ ∧ α′′|| are polynomial functions.

We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector eld in R n and an algebraic hypersurface. The answer is polynomial in the height (the magnitude of coeecients) of the equation and the size of the curve in the space-time, with the exponent depending only on the degree and the dimension. The problem turns out to be closely r...

Some time ago, Shpilrain and Yu reported an algorithm for deciding whether or not a polynomial p ∈ K[x, y] is a coordinate, or, equivalently, whether or not a plane curve p(x, y) = 0 is isomorphic to a line. Here K is any constructible field of characteristic 0. In this paper, we show that their algorithm requires O(n log2 n) field operations, where n is the degree of a given polynomial. We als...

Abstract. We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined by the area of its interior domain and its exterior harmonic moments which are all given as parameters of the potential. Then we consider the ortho...