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- J. Sánchez-Reyes, L. Fernández-Jambrina
- Computer Aided Geometric Design
- 2008

It has been recently proved that rational quadratic circles in standard Bézier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue… (More)

- L. Fernández-Jambrina
- Computer Aided Geometric Design
- 2007

In this paper a linear algorithm is derived for constructing B-spline control nets for spline developable surfaces of arbitrary degree and number of pieces. Control vertices are written in terms of five free parameters related to the type of developable surface. Aumann’s algorithm for constructing Bézier developable surfaces is recovered as a particular… (More)

- Alicia Cantón, L. Fernández-Jambrina, E. Rosado María
- Computer-Aided Design
- 2011

In the Bézier formalism, an arc of a conic is a rational curve of degree 2 with control polygon {P, Q, R} for which the weights can be normalized to {1, w, 1}. The parametrization of the conic arc is C(t) = (1 − t) 2 P + 2wt(1 − t)Q + t 2 R (1 − t) 2 + 2wt(1 − t) + t 2 , t ∈ [0, 1]. Abstract Synthetic derivation of closed for-mulae of the geometric… (More)

- Alicia Cantón, L. Fernández-Jambrina
- Curves and Surfaces
- 2010

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of nondegenerate developable triangular patches are provided.

- F. Pérez-Arribas, J. A. Suárez-Suárez, L. Fernández-Jambrina
- Computer-Aided Design
- 2006

When defining a ship hull surface, the main objective is to obtain a faired surface or surfaces that contain some specific points of the hull, that have been selected in the design process and give the ship its hydrodynamic, stability and other properties. So, the hull surface should be a compromise between fairness and precision, and this is not and easy… (More)

In this paper we provide a thorough classification of Friedman-Lemâıtre-RobertsonWalker (FLRW) cosmological models in terms of the strong or weak character of their singularities according to the usual definitions. The classification refers to a generalised Puiseux power expansion of the scale factor of the model around a singular event.

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz-Senovilla and Fernández-Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out. Since the… (More)

This talk will deal to a certain extent with the natural continuation of some work in progress that was introduced last year at the Spanish Relativity Meeting in Salamanca 1, 2 and that has recently been published 3. The reason for investigating geodesic completeness of Lorentzian manifolds is twofold. From the mathematical point of view, there is no… (More)

We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe. Assuming that the present matter content of the universe is a pressureless fluid, the possible singularities that may… (More)

- A. Rodríguez, L. Fernández-Jambrina
- Computer-Aided Design
- 2012