Trimmed NURBS are the standard surface representation used in CAD/CAM systems and accurate visualization of trimmed NURBS models at interactive frame rates is of great interest for industry. To support modification and/or animation of such surfaces, a GPU-based trimming and tessellation algorithm has been developed recently. First, the NURBS is approximated with a bi-cubic hierarchy of Bézier p...

Trimmed NURBS are the standard surface representation used in CAD/CAM systems and accurate visualization of trimmed NURBS models at interactive frame rates is of great interest for industry. To support modification and/or animation of such surfaces, a GPU-based trimming and tessellation algorithm has been developed recently. First, the NURBS is approximated with a bi-cubic hierarchy of Bézier p...

Highly crystalline Bi3+-doped cadmium oxide (CdO) sub-micron structures were synthesized by calcination the obtained precursor from a sol-gel reaction. The reaction was carried out with cadmium nitrate (Cd(NO3)2.4H2O), bismuth nitrate (Bi(NO3)3.5H2O) and ethylene glycol (C2H6O2) reactan...

This paper presents an investigative account of arbitrary cubic function fields. We present an elementary classification of the signature of a cubic extension of a rational function field of finite characteristic at least five; the signature can be determined solely from the coefficients of the defining curve. We go on to study such extensions from an algorithmic perspective, presenting efficie...

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.

A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...

In this paper we study cubic del Pezzo fibrations f : X → P such that the 3-fold X is smooth and rkPic(X) = 2. These are the examples of smooth 3-fold Mori fibre spaces. The 3-fold X is a divisor in the linear system |3M + nL| on the rational scroll Proj(⊕ i=1 OP1(di)), where n and di are integers, d1 ≥ d2 ≥ d3 ≥ d4 = 0, M is a tautological line bundle, and L is a fibre of the projection to P. ...

We consider cubic surfaces with rational coefficients that contain a rational point and satisfy a certain condition regarding their coefficients. Each such cubic surface is shown to be birationally equivalent to a surface of the form z2 = f(x, y), where f(x, y) is a polynomial of degree at most 4. Our method is similar to that which Tate and Silverman used in [2] to put cubic curves into Weiers...

This paper gives a construction to complete, at extraordinary points, an otherwise bi-cubic spline surface – so that the resulting surface is curvature continuous everywhere. To fill the n-sided gap in the bi-cubic surface, a cap is constructed from n spline patches, each consisting of 2× 2 pieces of polynomial degree bi-5. Particular care is taken to continue the curvature distribution from th...