This paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. We construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the ...

There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization. Optimality criteria such as low degrees in the parametrization or low degree field extensions are met by some parametrization algorithms. In this paper we investigate real curves. Given a parametrizable plane curve ov...

In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We analyze the main properties of the varieties defined by these parametrizations and we prove that they are exactly the ...

A rational parametrization of an algebraic curve establishes a rational correspondence of this curve with the affine or projective line. This correspondence is a birational equivalence if the parametrization is proper. So, intuitively speaking, a rational parametrization determines a linear tracing of the curve, when the parameter takes values in the algebraic closure of the ground field. Such ...

In this paper we give an explicit parametrization for all two-qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two-qubit density matrices. The important group-theoretical properties of such a description are t...

Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric a...

If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to...

We investigate by numerical experiment the use of discrete-time stochastic parametrization to account for model error due to unresolved scales in ensemble Kalman filters. The parametrization quantifies the model error and produces an improved non-Markovian forecast model, which generates high-quality forecast ensembles and improves filter performance. We compare this with the methods of dealing...