A weighted bivariate blending rational interpolation based on function values

Bivariate polynomial and continued fraction interpolation over ortho-triples

“…(2.10) is called the barycentric coordinates transformation of P, is also called the barycentric coordinates expression as introduced in [5]. Obviously, this kind of expression is unique.…”

“…Many authors have contributed valuable insights into the mathematical topics in terms of the bivariate B-net method in [5], and [12], among which is the novel result on the equivalence of the smoothness conditions obtained by the conformality method of smoothing cofactor and the B-net one for any given simplex partition, respectively in [12].…”

“…As a result, new tools have been developed, such as wavelets, multivariate splines [10], radial-basis functions [1], rational approximation [7,9,13], etc. Besides these new developments are results on nonlinear interpolation with parameters [2], and with branched continued fractions [5,9,11]. But the former should be done by selecting suitable parameters, while the latter is done by means of partially inverse differences at points one by one.…”

A New Approach to Newton-Type Polynomial Interpolation with Parameters

“…ese methods are used, for instance, for shaping the outer hull of aircraft and a ship [28]. However, the disadvantage of polynomial interpolation lies in its global property, that is, it is difficult to control the local constraint of a given interpolation point under the condition that the values of the interpolant points are fixed [29,30]. To construct the polynomial spline, the derivative values of the interpolating data are required additionally to the function values.…”

“…In recent years, many scholars have studied parametric spline interpolation. Zhang et al [29,30] proposed new types of weighted blending spline interpolation. By selecting appropriate parameters and different coefficients, the value of the spline interpolation function can be modified at any point in the interpolant interval, under the condition that the values of the interpolant points are fixed, so that the geometric surfaces can be adjusted.…”