Complex transition-metal oxides are important functional materials in areas such as energy and information storage. The cubic ABO3 perovskite is an archetypal example of this class, formed by the occupation of small octahedral B-sites within an AO3 network defined by larger A cations. We show that introduction of chemically mismatched octahedral cations into a cubic perovskite oxide parent phas...

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 crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by definition curves over stations, bow and stern contours plan lines. Thus, new knots are created applying an equal spaced subdivision on defined B-spline Then, these transversal space knots, longitudinal subdivided into equally too. Subsequently, knots. Finally,...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...

Prior studies have shown that the biological mixture of the two hydrophobic surfactant proteins, SP-B and SP-C, produces faster adsorption of the surfactant lipids to an air/water interface, and that they induce 1-palmitoyl-2-oleoyl phosphatidylethanolamine (POPE) to form inverse bicontinuous cubic phases. Previous studies have shown that SP-B has a much greater effect than SP-C on adsorption. ...

We show that the number of non-trivial rational points of height at most B, which lie on the cubic surface x1x2x3 = x4(x1 + x2 + x3) , has order of magnitude B(log B). This agrees with Manin’s conjecture.

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...