Region control and approximation of a weighted rational interpolating curves

Abstract

SUMMARYA weighted rational cubic spline interpolation has been constructed using two kinds of rational cubic spline with quadratic denominator. The su cient conditions that constrain the interpolant curves to be in the given region are derived, also the error estimate formulas of this interpolation are obtained.

A Novel Approach to Surface Interpolation: Marriage of Coons Technique and Univariate Fractal Functions

“…(4.1) in [14] or Eq. (2) in [11]). The feasibility of the above construction depends on the existence and uniqueness of the solution of the linear system corresponding to a fixed choice of the scaling factors and the shape parameters, which follows from the existence and uniqueness of the fixed point of Read-Bajraktarévic operator (see [5]).…”

A class of $$C^1$$ rational interpolation splines in one and two dimensions with region control

“…Later, in Duan et al (2000) and Duan et al (2005), the problems of generating interpolation curves lying strictly between two given piecewise linear curves were solved using weighted rational cubic/linear interpolation splines. In Duan et al (2006), based on the idea of adding more parameters into the interpolating spline to enhance the constraining ability, a weighted rational cubic spline interpolation was constructed using two kinds of rational cubic spline with quadratic denominator. However, the conditions for interpolation curves lying strictly between two given piecewise linear curves given in Duan et al (1999Duan et al ( , 2000Duan et al ( , 2005 and Duan et al (2006) were non-explicit.…”

“…In Duan et al (2006), based on the idea of adding more parameters into the interpolating spline to enhance the constraining ability, a weighted rational cubic spline interpolation was constructed using two kinds of rational cubic spline with quadratic denominator. However, the conditions for interpolation curves lying strictly between two given piecewise linear curves given in Duan et al (1999Duan et al ( , 2000Duan et al ( , 2005 and Duan et al (2006) were non-explicit. Therefore, these conditions are inconvenient in pratical application.…”

The EH Interpolation Spline and Its Approximation

“…For the given interpolation condition, how to improve the approximation accuracy of the interpolation spline is an important problem in the computer aided geometric design. In recent years, many authors have presented some new method to modify the shape of the interpolation curve to satisfy the industrial product design with several kinds of new interpolation splines with parameters [7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…In [7][8][9][10][11][12][13][14][15][16][17], many rational form interpolation splines with multiple parameters were presented. For the given interpolation data, the change of the parameters causes the change of the interpolation curve.…”