Positive interpolation with rational quadratic splines

Shape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Biquadratic Splines

“…Shape control [17], shape design [18], shape representation [19][20] and shape preservation [10][11][12][13][14][15][16] are important areas for graphical presentation of data. The problem of shape preservation has been discussed by a number of authors.…”

“…The problem of shape preservation has been discussed by a number of authors. In recent years, a good amount of work has been published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] that focuses on shape preserving curves and surfaces. The motivation of the work, in this paper, is due to the past work of many authors.…”

“…They considered nonnegative data arranged over a triangular mesh and interpolated each triangular patch using a bivariate quadratic function. Schmidt and Hess [13] discussed quadratic and rational quadratic spline and developed necessary and sufficient conditions for the positivity.…”

A novel approach to the convexity control of interpolant curves

“…In recent years, the rational spline with parameters has received attention in the literature [22][23][24][25][26]. For the given interpolating data, the change of the parameters causes the change of the interpolating curve, so the interpolating curve may be modiÿed to the needed shape if suitable parameters exist.…”

Positivity of cubic polynomials on intervals and positive spline interpolation

“…Let (xo, Yo), ( Besides convex and monotone interpolation this is a further type of shape preserving interpolation being also of practical interest. In [7] the present authors dealt with the positive interpolation by quadratic splines. Now, cubic Cl-splines will be considered.…”