We introduce a view–point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally–approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant featu...

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods.

A piecewise rational cubic spline has been introduced to visualize the positive data in its natural form. It is attempted that the spline method preserves the shape of the data when it is positive. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters, in the description of the rational cubic, have been constrained in such a way that they cont...

The behavior of Catmull-Rom curves heavily depends on the choice of parameter values at the control points. We analyze a class of parameterizations ranging from uniform to chordal parameterization and show that, within this class, curves with centripetal parameterization contain properties that no other curves in this family possess. Researchers have previously indicated that centripetal parame...

In this paper we present a novel interpolation technique for Vlasov simulations of intense space charge dominated beams. This new technique enables to localize the cubic spline interpolation generally performed in semi-Lagrangian Vlasov codes and thus to improve the scalability of the parallel version. This new method is applied to the propagation of a potassium beam in a periodic focusing chan...

We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We p...

e o A technique for limiting the knot slopes of hermite cubic splines in order to eliminat vershoot is proposed. It is proven that constraining each knot’s slope to lie between 0 and l three times the slope to the knot on either side forces all extrema to occur at knots. This al ows overshoot to be eliminated without sacrificing slope continuity. The technique has appli1 cations in keyframe int...