Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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11 Nov 2010
TL;DR: A brief algorithm that can obtain the shape feature points of cubic B'ezier and B-spline curves is proposed that is rapid, accurate, and robust.
Abstract: After analyzing the curvature expression, the inflection points were given by the known planar cubic B'ezier control polygon information. Based on that, we proposed a brief algorithm that can obtain the shape feature points of cubic B'ezier and B-spline curves. Experimental results show that the method is rapid, accurate, and robust.
4 citations
TL;DR: In this paper, the problem of constructing C2 quartic spline surface interpolation is discussed, and an approach to determining the freedom degrees is given, the continuity equations for constructing C 2 quartic Spline curve are discussed and a new method for constructing the C2 Spline surface is presented.
Abstract: This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.
4 citations
TL;DR: In this paper, the authors put forward a kind of Hermite interpolation scheme on the unit sphere, which is an extension and a development of Lagrange interpolation on the sphere.
4 citations
01 Jan 1979
TL;DR: It is shown that the Pade or Hermite formulation is a hybrid method resulting from two different poly nomial splines, and an extension to sixth-order is presented in this paper.
Abstract: Polynomial spline interpolation has been used to develop a variety of higher-order collocation methods Only those polynomials resulting in tridiagonal, or at worst 3×3 block- tridiagonal, matrix systems have been evaluatedIt is- shown that the Pade or Hermite formulation is a hybrid method resulting from two different poly nomial splinesAn extension to sixth-order is presented in this paper Of the fourth-order methods, Spline 4(5,6 has the smallest truncation error The sixth-order Hermite formulation leads to extraordinary accuracy even with very coarse grids
4 citations
Journal Article•
TL;DR: In this paper, a new interpolation method using cubic spline function is presented for range migration correction, which is smooth and convergent and has been used in SAR range-Doppler imaging algorithm.
Abstract: In SAR Range-Doppler Imaging algorithm,range migration results in the coupling between range and azimuth,and affects on imaging quality.Typical interpolation algorithms such as nearest neighbor interpolation,Newton interpolation,and sinc interpolation have been proposed for range migration correction.However,the smoothness and convergence of these methods are not satisfactory.Because cubic spline function can be a piecewise,and its second order derivative is continuous,it is smooth and convergent.In this paper,therefore,a new interpolation method using cubic spline function is presented for range migration correction.Using the method we presented,SAR imaging simulation of point target has been done and the experiment results are satisfactory.
4 citations