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Università della Svizzera italiana

New shape control tools for rational Bézier curve design

Ramanantoanina, Andriamahenina ; Hormann, Kai

In: Computer aided geometric design, 2021, vol. 88, p. 11

Bézier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties and provide the user with intuitive tools for editing the shape of a parametric polynomial curve. Even more control and flexibility can be achieved by associating a shape parameter with each control point and considering rational Bézier curves, which comes with the...

Università della Svizzera italiana

Using linear algebra in decomposition of Farkas interpolants

Blicha, Martin ; Hyvärinen, Antti E. J. ; Kofroň, Jan ; Sharygina, Natasha

In: International journal on software tools for technology transfer, 2021, p. 15

The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by ...

Consortium of Swiss Academic Libraries

Non-rationality of some fibrations associated to Klein surfaces

Blanc, Jérémy

In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015, vol. 56, no. 1, p. 351-371

Université de Fribourg

Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm

Berrut, Jean-Paul ; Marchi, S. De ; Elefante, Giacomo ; Marchetti, F.

In: Applied Mathematics Letters, 2020, vol. 103, p. 106196

In this work, we extend the so-called mapped bases or fake nodes approach to the barycentric rational interpolation of Floater–Hormann and to AAA approximants. More precisely, we focus on the reconstruction of discontinuous functions by the S-Gibbs algorithm introduced in De Marchi et al. (2020). Numerical tests show that it yields an accurate approximation of discontinuous functions.

Université de Fribourg

Adapting spherical-harmonics-based geometric morphometrics (SPHARM) for 3D images containing large cavity openings using ambient occlusion: a study with hermit crab claw shape variability

Ege, Yannic C. ; Foth, Christian ; Baum, Daniel ; Wirkner, Christian S. ; Richter, Stefan

In: Zoomorphology, 2020, p. -

One of the advantages of mesh-based geometric morphometrics (GM) over landmark-based approaches, is that it affords the possibility of the precise examination of highly irregular shapes and complex topographic surfaces. In the case of spherical-harmonic-based GM, the main prerequisite is a completely closed mesh surface, which is often lacking, particularly when dealing with natural objects....

Università della Svizzera italiana

On the Lebesgue constant of barycentric rational Hermite interpolants at equidistant nodes

Cirillo, Emiliano ; Hormann, Kai

In: Journal of computational and applied mathematics, 2019, vol. 349, p. 292-301

Barycentric rational Floater–Hormann interpolants compare favourably to classical polynomial interpolants in the case of equidistant nodes, because the Lebesgue constant associated with these interpolants grows logarithmically in this setting, in contrast to the exponential growth experienced by polynomials. In the Hermite setting, in which also the first derivatives of the interpolant are...

Università della Svizzera italiana

Behaviour of exponential three-point coordinates at the vertices of convex polygons

Anisimov, Dmitry ; Hormann , Kai ; Schneider

In: Journal of computational and applied mathematics, 2019, vol. 350, p. 114-129

Barycentric coordinates provide a convenient way to represent a point inside a triangle as a convex combination of the triangle’s vertices and to linearly interpolate data given at these vertices. Due to their favourable properties, they are commonly applied in geometric modelling, finite element methods, computer graphics, and many other fields. In some of these applications, it is desirable...

Università della Svizzera italiana

Advances in barycentric rational interpolation of a function and its derivatives

Cirillo, Emiliano ; Hormann, Kai (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2019 ; 2019INFO007.

Linear barycentric rational interpolants are a particular kind of rational interpolants, defined by weights that are independent of the function f. Such interpolants have recently proved to be a viable alternative to more classical interpolation methods, such as global polynomial interpolants and splines, especially in the equispaced setting. Other kinds of interpolants might indeed suffer...