Carlotta Giannelli

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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)
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)
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)
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)
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)
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)