6-point Scheme Research Articles

Engineering images designed by fractal subdivision scheme.

This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and visual demonstrations show that 6-point scheme is good choice for the generation of fractals for the modeling of fractal antennas, bearings, garari’s and rock etc.

A new non-stationary binary 6-point subdivision scheme

In this paper, the hyperbolic form of binary 6-point interpolating non-stationary subdivision scheme has been constructed using the hyperbolic function. Some of the important properties of the proposed scheme has been discussed. The comparison of the proposed scheme with the trigonometric form of binary 6-point interpolatory non-stationary scheme is depicted through examples which indicate that the proposed scheme not only accommodates and is more consistent with the control polygon, but also generates pleasing curves corresponding to the larger parametric values in and outside the parametric interval as compared to the trigonometric form of binary 6-point scheme developed by Daniel et al. Comparison with some other interpolating non-stationary subdivision schemes has also been demonstrated.

Construction of m-point binary approximating subdivision schemes

In this paper, an algorithm to construct m -point (for any integer m > 1 ) binary approximating subdivision schemes has been developed using the Cox–de Boor recursion formula. Some properties like symmetry of basis functions and polynomial reproduction are also discussed. It can be observed that most of the existing binary approximating schemes (corner cutting scheme developed by Chaikin, and 3-point, 4-point, 5-point and 6-point schemes introduced by Siddiqi and Ahmad) are either special cases or can be reproduced by the proposed algorithm.

Non-uniform interpolatory subdivision via splines

We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness Cn−1 are presented for n=2,3,4 and even higher order, as well as a variety of non-uniform 6-point schemes with C3 continuity.

Darboux transformations for a 6-point scheme

We introduce the Jonas transformation (a transformation of the Darboux type) for the general second-order differential equation in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate for the solution of a hyperbolic-type initial-boundary value problem. We discuss several reductions and specifications of the transformations.

A ternary 4-point approximating subdivision scheme

In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and 6-point schemes, ternary 3-point and 4-point schemes (see Table 2). The method is easily generalized to ternary (2 n + 2)-point approximating subdivision schemes. We choose a ternary scheme because a way to get smaller support is to raise arity. And we use polynomial reproduction to get higher approximation order easily.

Continuity Analysis and Construction of Uniform Stationary Univariate Subdivision Schemes

With the necessary and sufficient conditions for C k -continuity of uniform stationary subdivision schemes, the range of free parameter in several classical interpolating curve schemes is presented. For the first time, this paper points out that the arity-2 interpolating 6-point scheme is C 3 -continuous in certain range. A new C 3 -continuous arity-3 interpolating 6-point scheme is also proposed.

An efficient solution to the five-point relative pose problem

An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.

DEVELOPMENT OF NUMERICAL TECHNIQUE FOR ADVECTION WITH HIGH-ACCURACY AND RESOLUTION

This paper deals with development of a new numerical technique with high-accuracy and resolution for advection. The 6-point scheme, which is a numerical solver based on the characteristics method for advection, is modified in order to make it possible to be applied to the conservative advection equation. The modified 6-point scheme is named the conservative 6-point scheme. The universal limiter and a new discriminator are incorporated in the conservative 6-point scheme to obtain numerical solutions which are not only highaccurate but also free from numerical oscillations. It is found that the numerical technique presented in this paper is able to give good numerical results.

Accuracy of new dispersed-phase model for convective numerical simulation

The accuracy of GAL model, recently developed by the authors for a new formulation of dispersed-phase motion in a multiphase turbulent flow, is examined for convective numerical simulation. To reduce numerical diffusion inherent in the previous scheme of reallocation procedure of the GAL model, a new reallocation scheme is presented. The computational results for idealized convective transport show that the improved GAL model has high accuracy, being comparable to 6-point scheme, and high numerical stability even for the flow condition of Courant number greater than one.