共查询到20条相似文献,搜索用时 15 毫秒
1.
Inspired by the classic γ-spline, we propose a method for constructing a G2 rational γ-spline curve that interpolates a given set of distinct ordered data-points (planar or spatial). The only input of our method is just these data-points. We also present a procedure to solve the key problem of determining the tension parameters γi which are computed in terms of exponential functions that determine the eccentricities of the common conic osculants at the junction points while keeping in geometrical agreement with data-points. This allows the resulting curve to be modified in the close vicinity of each data-point. 相似文献
2.
In the present paper, C1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonie interpolant
to a given monotonie data set. It is observed that under certain conditions the interpolant preserves the convexity property
of the data set. The existence and uniqueness of a C2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given. 相似文献
3.
《Journal of Computational and Applied Mathematics》1999,102(1):87-117
A scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves. An initial curve is obtained by patching together rational cubic and straight line segments. This scheme has, in general, geometric continuity of order 2(G2 continuity) and preserves the local convexity of the data. A method for interactively modifying such curves, while maintaining their desirable properties, is discussed in detail. In particular, attention is focused upon local changes to the curve, while retaining G2 continuity and shape preserving properties. This is achieved by interactive adjustment of the Bézier control points, followed by automatic adjustment of the values of weights and curvatures in a prescribed manner. A number of examples are presented. 相似文献
4.
We report on our project to construct non-singular cubic surfaces over
\mathbbQ{\mathbb{Q}} with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For these, we develop an
explicit version of Galois descent. 相似文献
5.
We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods. 相似文献
6.
C. M. C. Roque A. J. M. Ferreira 《Numerical Methods for Partial Differential Equations》2010,26(3):675-689
A numerical investigation on a technique for choosing an optimal shape parameter is proposed. Radial basis functions (RBFs) and their derivatives are used as interpolants in the asymmetric collocation radial basis method, for solving systems of partial differential equations. The shape parameter c in RBFs plays a major role in obtaining high quality solutions for boundary value problems. As c is a user defined value, inexperienced users may compromise the quality of the solution, often a problem of this meshless method. Here we propose a statistical technique to choose the shape parameter in radial basis functions. We use a cross‐validation technique suggested by Rippa 6 for interpolation problems to find a cost function Cost(c) that ideally has the same behavior as an error function. If that is the case, the parameter c that minimizes the cost function will be an optimal shape parameter, in the sense that it minimizes the error function. The form of the cost and error functions are analized for several examples, and for most cases the two functions have a similar behavior. The technique produced very accurate results, even with a small number of points and irregular grids. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
7.
First we derive conditions that a parametric rational cubic curve segment, with a parameter, interpolating to plane Hermite data {(x
i
(k)
,y
i
(k)
),i = 0, 1;k = 0, 1} contains neither inflection points nor singularities on its segment. Next we numerically determine the distribution of inflection points and singularities on a segment which gives conditions that aC
2 parametric rational cubic curve interpolating to dataS = {(x
i
(k)
,y
i
(k)
), 0 i n} is free of inflection points and singularities. When the parametric rational cubic curve reduces to the well-known parametric cubic one, we obtain a theorem on the distribution of the inflection points and singularities on the cubic curve segment which has been widely used for finding aC
1 fair parametric cubic curve interpolating toS. 相似文献
8.
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a combination of the “determinant method” with an m-descent on the curve. 相似文献
9.
10.
John C. Clements 《Numerische Mathematik》1992,63(1):165-171
Summary AC
2 parametric rational cubic interpolantr(t)=x(t)
i+y(t)
j,t[t
1,t
n] to data S={(xj, yj)|j=1,...,n} is defined in terms of non-negative tension parameters
j
,j=1,...,n–1. LetP be the polygonal line defined by the directed line segments joining the points (x
j
,y
j
),t=1,...,n. Sufficient conditions are derived which ensure thatr(t) is a strictly convex function on strictly left/right winding polygonal line segmentsP. It is then proved that there always exist
j
,j=1,...,n–1 for whichr(t) preserves the local left/righ winding properties of any polygonal lineP. An example application is discussed.This research was supported in part by the natural Sciences and Engineering Research Council of Canada. 相似文献
11.
12.
Scott T. Parsell 《Transactions of the American Mathematical Society》2000,352(11):5045-5062
We provide a lower bound for the density of rational lines on the hypersurface defined by an additive cubic equation in at least 57 variables. In the process, we obtain a result on the paucity of non-trivial solutions to an associated system of Diophantine equations.
13.
Manabu Sakai 《Numerische Mathematik》1997,76(3):403-417
Summary. This paper considers the distribution of inflection points and singularity on the parametric rational cubic curve, using
much algebraic manipulation. Its use allows one to find a shape preserving interpolatory rational cubic curve of a planar
data. Some numerical examples are given to illustrate usefulness of the method.
Received April 30, 1995 / Revised version received January 15, 1996 相似文献
14.
《Journal of Computational and Applied Mathematics》1999,103(2):221-237
The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory's rational cubic C1 splines as well as related rational quintic C2 splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range restricted interpolation is successful. 相似文献
15.
We discuss multivariate interpolation with some radial basis function, called radial basis function under tension (RBFT). The RBFT depends on a positive parameter which provides a convenient way of controlling the behavior of the interpolating surface. We show that our RBFT is conditionally positive definite of order at least one and give a construction of the native space, namely a semi-Hilbert space with a semi-norm, minimized by such an interpolant. Error estimates are given in terms of this semi-norm and numerical examples illustrate the behavior of interpolating surfaces. 相似文献
16.
This paper describes a method for joining two circles with an S-shaped or with a broken back C-shaped transition curve, composed of at most two spiral segments. In highway and railway route design or car-like robot path planning, it is often desirable to have such a transition. It is shown that a single cubic curve can be used for blending or for a transition curve preserving G2 continuity with local shape control parameter and more flexible constraints. Provision of the shape parameter and flexibility provide freedom to modify the shape in a stable manner which is an advantage over previous work by Meek, Walton, Sakai and Habib. 相似文献
17.
18.
19.
We compute the number of rational degree d plane curves having prescribed fixed and moving contacts to a smooth plane cubic E. We use twisted stable maps to the stack for r large, where is the rth root of along E. We prove that certain Gromov–Witten invariants of this stack are enumerative, and establish recursive formulas for these numbers. 相似文献
20.
It is shown that each rational approximant to (ω,ω2)τ given by the Jacobi–Perron algorithm (JPA) or modified Jacobi–Perron algorithm (MJPA) is optimal, where ω is an algebraic function (a formal Laurent series over a finite field) satisfying ω3+kω-1=0 or ω3+kdω-d=0. A result similar to the main result of Ito et al. [On simultaneous approximation to (α,α2) with α3+kα-1=0, J. Number Theory 99 (2003) 255–283] is obtained. 相似文献