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- Carlotta Giannelli, Bert Jüttler, Hendrik Speleers
- Computer Aided Geometric Design
- 2012

The construction of classical hierarchical B–splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only… (More)

- Carlotta Giannelli, Bert Jüttler
- J. Computational Applied Mathematics
- 2013

We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain.… (More)

- Carlotta Giannelli, Bert Jüttler, Hendrik Speleers
- Adv. Comput. Math.
- 2014

- Rida T. Farouki, Carlotta Giannelli, Carla Manni, Alessandra Sestini
- Computer Aided Geometric Design
- 2008

- Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini
- J. Symb. Comput.
- 2009

- Rida T. Farouki, Carlotta Giannelli, Carla Manni, Alessandra Sestini
- Math. Comput.
- 2012

The construction of space curves with rational rotationminimizing frames (RRMF curves) by the interpolation of G1 Hermite data, i.e., initial/final points pi and pf and frames (ti,ui,vi) and (tf ,uf ,vf ), is addressed. Noting that the RRMF quintics form a proper subset of the spatial Pythagorean–hodograph (PH) quintics, characterized by a vector constraint… (More)

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 or, equivalently, the derivatives of fj , fk are both parallel to fi. The Frenet frame (t,p,b) is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect… (More)

- Dominik Mokris, Bert Jüttler, Carlotta Giannelli
- J. Computational Applied Mathematics
- 2014

Given a grid in R, consisting of d bi-infinite sequences of hyperplanes (possibly with multiplicities) orthogonal to the d axes of the coordinate system, we consider the spaces of tensor-product spline functions of a given degree on a multi-cell domain. Such a domain consists of finite set of cells which are defined by the grid. A piecewise polynomial… (More)

- Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini
- J. Symb. Comput.
- 2009

For regular polynomial curves r(t) in R3, relations between the helicity condition, existence of rational Frenet frames, and a certain ‘‘double’’ Pythagorean-hodograph (PH) structure are elucidated in terms of the quaternion and Hopf map representations of spatial PH curves. After reviewing the definitions and properties of these representations, and… (More)

- Gábor Kiss, Carlotta Giannelli, Bert Jüttler
- MMCS
- 2012

Tensor–product B–spline surfaces are commonly used as standard modeling tool in Computer Aided Geometric Design and for numerical simulation in Isogeometric Analysis. However, when considering tensor–product grids, there is no possibility of a localized mesh refinement without propagation of the refinement outside the region of interest. The recently… (More)