The semi-Lagrangian method using the hybrid-cubic-rational interpolation function [M. Ida, Comput. Fluid Dyn. J. 10 (2001) 159] is modified to a conservative method by incorporating the concept discussed in [R. Tanaka et al., Comput. Phys. Commun. 126 (2000) 232]. In the method due to Tanaka et al., not only a physical quantity but also its integrated quantity within a computational cell are us...

We consider the problem of finding parametric rational Bézier cubic spirals (planar curves of monotonic curvature) that interpolate end conditions consisting of positions, tangents and curvatures. Rational cubics give more design flexibility than polynomial cubics for creating spirals, making them suitable for many applications. The problem is formulated to enable the numerical robustness and e...

An explicit expression for the unique implicitization of any planar rational cubic Bézier curve is presented, the only exception being when the tangents at the ends of the curve are parallel. The representation is in the form of a cubic Bernstein-Bézier triangle and is invariant under affine transformations of the curve. The implicitization degenerates to zero if and only if the curve degenerat...

In this paper, we are interested in the evaluation of the zeta function of the simplest cubic field. We first introduce Siegel’s formula for values of the zeta function of a totally real number field at negative odd integers. Next, we will develop a method of computing the sum of a divisor function for ideals, and will give a full description for a Siegel lattice of the simplest cubic field. Us...

A rational quadratic trigonometric Bézier curve with two shape parameters, which is analogous to cubic Bézier curve, is presented in this paper. The shape of the curve can be adjusted as desired, by simply altering the value of shape parameters, without changing the control polygon. The rational quadratic trigonometric Bézier curve can be made close to the rational cubic Bézier curve or closer ...

For a group T and a subset S of T , the bi-Cayley graph BCay(T, S) of T with respect to S is the bipartite graph with vertex set T×{0, 1} and edge set {{(g, 0), (sg, 1)} | g ∈ T, s ∈ S}. In this paper, we investigate cubic bi-Cayley graphs of finite nonabelian simple groups. We give several sufficient or necessary conditions for a bi-Cayley graph to be semisymmetric, and construct several infin...

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

In this paper, a rational Bézier surface is proposed as a uniform approach to modeling all three types of molecular surfaces (MS): the van der Waals surface (vdWS), solvent accessible surface (SAS) and solvent excluded surface (SES). Each molecular surface can be divided into molecular patches, which can be defined by their boundary arcs. The solution consists of three steps: topology modeling,...