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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 non-degenerate 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)

- Alicia Cantón, L. Fernández-Jambrina
- Frontiers of Information Technology & Electronic…
- 2015

In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both… (More)

We show that the solution published in Ref.1 is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyper-bolicity, causal symmetry and causal stability. A detailed discussion about which assumptions in the singularity theorems are not fulfilled is performed, and… (More)

- L Fernández-Jambrina, C Hoenselaers
- 2004

The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion… (More)

- L. Fernández-Jambrina
- ArXiv
- 2017

In this paper we address the issue of designing developable surfaces with Bézier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann's algorithm. We also obtain the set of polynomial developable surfaces which can be constructed using general polynomial… (More)

- Alicia Cantón, L. Fernández-Jambrina, E. Rosado María, M. J. Vázquez-Gallo
- J. Computational Applied Mathematics
- 2016

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product… (More)