The standard Clough-Tocher split-domain scheme constructs a surface element with quadratic precision. In this paper, I will look at methods for improving the degrees of freedom in Clough-Tocher schemes. In particular , I will discuss modiications to the cross-boundary construction that improve the interpolant from quadratic precision to cubic precision. In the general scattered data interpolati...

In this paper a class of quartic trigonometric Bézier curve, called QT Bézier curve, with two shape parameters is presented. These curves not only inherit most properties of the usual quartic Bézier curves in the polynomial space, but also enjoy some other advantageous properties for shape modelling. The shape of the curve can be adjusted by altering the values of shape parameters while the con...

Bernstein{B ezier two{point Hermite G 2 interpolants to plane and space curves can be of degree up to 5, depending on the situation. We give a complete characterization for the cases of degree 3 to 5 and prove that rational representations are only required for degree 3. x1. Introduction and Overview We consider recovery of curves from irregularly sampled data. If the curves are to be represent...

The statistical distributions are modeled in explaining nature of various types of data sets. Although these distributions are mostly uni-modal, it is quite common to see multiple modes in the observed distribution of the underlying variables, which make the precise modeling unrealistic. The observed data do not exhibit smoothness not necessarily due to randomness, but could also be due to non-...

Interpolation of a sequence of points by spline curves generally requires the solution of a large system of equations. In this paper we provide a method which requires only local computation instead of a global system of equations and works for a large class of curves. This is a generalization of a method which previously developed for Bspline, NURBS and trigonometric CB-spline curves. Moreover...

Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational curves and surfaces. Concerning computer aided geometric design, the unique normalized B-bases of such vector spaces ensure optimal shape preserving properties, i...

Here some formulae and results complete the explanations of http://www.tphys.uni-heidelberg.de/∼wegner/Fl2mvs/Movies.html. More details are given in [1]. The first section gives some basic formulae, the second section contains formulae in the limit, in which the curves can be represented by ’elementary’ functions like exponentialand trigonometric functions, whereas in the general case double-pe...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis        

A rational cubic trigonometric spline with two shape parameters which play an important role in manipulating the shape of the curve is described in this paper. Its algebraic analogue with shape parameters has been discussed. Spline is presented both in interpolatory and rational B-spline form and the properties of resulting Bsplines are also studied. Keywords— Computer aided geometric design, r...