We define the curvilinear rank of a degree d form P in n+1 variables as the minimum length of a curvilinear scheme, contained in the d-th Veronese embedding of Pn, whose span contains the projective class of P . Then, we give a bound for rank of any homogenous polynomial, in dependance on its curvilinear rank.

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curv...

This paper presents a splatting algorithm for volume rendering of curvilinear grids. A stochastic sampling technique called Poisson sphere/ellipsoid sampling is employed to adaptively resample a curvilinear grid with a set of randomly distributed points whose energy support extents are well approximated by spheres and ellipsoids. Filter kernels corresponding to these spheres and ellipsoids are ...

Dimension reduction techniques are widely used for the analysis and visualization of complex sets of data. This paper compares two recently published methods for nonlinear projection: Isomap and Curvilinear Distance Analysis (CDA). Contrarily to the traditional linear PCA, these methods work like multidimensional scaling, by reproducing in the projection space the pairwise distances measured in...

A NURBS-based isogeometric finite element formulation is developed and adopted to the free vibration analysis of finite square and skew laminated plates. Variable stiffness plies are assumed due to implementation of curvilinear fiberreinforcements. It is assumed due to employment of tow placement technology, in each ply of variable stiffness composite laminated plate the fiber reinforceme...

Recollection has long been thought to play a key role in associative recognition tasks. Evidence that associative recollection might be a threshold process has come from analyses of the associative recognition receiver operating characteristic (ROC). Specifically, the ROC is not as curvilinear as a signal detection theory requires. In addition, the Z-ROC is usually curvilinear, as a threshold r...