Applying Rational Envelope curves for skinning purposes

Applying inversion to construct rational spiral curves

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including those, assuming inflection.

Rational Curves

Rational curves and splines are one of the building blocks of computer graphics and geometric modeling. Although a rational curve is more exible than its polynomial counterpart , many properties of polynomial curves are not applicable to it. For this reason it is very useful to know if a curve presented as a rational space curve has a polynomial parametrization. In this paper, we present an alg...

Similarity Detection for Rational Curves

In Pattern Recognition, there is a vast literature concerning the question how to detect whether two curves are similar. Essentially, the problem is to recognize a certain curve as the result of applying a movement to another curve in a database. Most of the strategies proposed so far deal with curves in implicit form, and ultimately resort to numerics to decide whether such curves are related ...

K3 Surfaces, Rational Curves, and Rational Points

We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...

Rational Curves on Varieties