In this paper, the motion planning problem is studied for nonlinear differentially flat systems using B-splines parametrization of the flat output history. In order to satisfy the constraints continuously in time, the motion planning problem is transformed into a B-splines positivity problem. The latter problem is formulated as a convex semidefinite programming problem by means of a non-negativ...

We investigate the functions of given approximation order L that have the smallest support. Those are shown to be linear combinations of the Bspline of degree .L 1 and its L 1 first derivatives. We then show how to And the functions that minimize the asymptotic approximation constant among this finite dimension space; in particular, a tractable induction relation is worked out. Using these func...

In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform Bspline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied t...

The effect of the modification of knot values on the shape of B-spline curves is examined in this paper. The modification of a knot of a Bspline curve of order k generates a one-parameter family of curves.This family has an envelope which is also a B-spline curve with the same control polygon and of order k 2 1: Applying this theoretical result, three shape control methods are provided for cubi...

A simulation framework for articial neural network models and electronic implementations (CMOS) is presented. Neural network models spanning from arti-cial biological models through mathematical or computational models such as back-propagation type networks to digital, analog or subthreshold analog implementations can be simulated concurrently. Neural and electronic variables (nodes) interact t...

Pen-input is not a new means for CAD designers, in particular, in the concept design phase. Meanwhile, B-Splines are well known curve and surface design tool in 3D shape modeling in the final modeling stages in which neat curves and surfaces should be produced. In this paper, an intuitive B-Spline design method that can be used for the CAD systems both in conceptual modeling phase and in later ...

We describe an extension of B-splines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mesh mu...

A well-documented problem of Catmull and Clark subdivision is that, in the neighborhood of extraordinary point, the curvature is unbounded and fluctuates. In fact, since one of the eigenvalues that determines elliptic shape is too small, the limit surface can have a saddle point when the designer’s input mesh suggests a convex shape. Here, we replace, near the extraordinary point, CatmullClark ...