cshep2d bidimensional cubic shepard (scattered) interpolation

## Syntax

    tl_coef = cshep2d(xyz)

## Arguments

xyz

  a n x 3 matrix of the (no gridded) interpolation points (the i th row given the (x,y) coordinates then the altitude z of the i th interpolation point)

tl_coef

  a tlist scilab structure (of type cshep2d)

## Description

This function is useful to define a 2d interpolation function when the interpolation points are not on a grid (you may use it in this case but splin2d is better for that purpose). The interpolant is a cubic shepard one and is a C2 (twice continuously differentiable) bivariate function s(x,y) such that : s(xi,yi)=zi for all i=1,..,n ((xi,yi,zi) being the i th row of `xyz`).

The evaluation of s at some points must be done by the eval_cshep2d function.

## Remark

The function works if n>= 10, if the nodes are not all colinears (i.e. the (x,y) coordinates of the interpolation points are not on the same straight line), and if there is no duplicate nodes (i.e. 2 or more interpolation points with the same (x,y) coordinates). An error is issued if these conditions are not respected.

## Examples

    // interpolation of cos(x)cos(y) with randomly chosen interpolation points
    n = 150; // nb of interpolation points
    xy = grand(n,2,"unf",0,2*%pi);
    z = cos(xy(:,1)).*cos(xy(:,2));
    xyz = [xy z];
    tl_coef = cshep2d(xyz);

    // evaluation on a grid
    m = 30;
    xx = linspace(0,2*%pi,m);
    [X,Y] = ndgrid(xx,xx);
    Z = eval_cshep2d(X,Y, tl_coef);
    clf()
    plot3d(xx,xx,Z,flag=[2 6 4])
    param3d1(xy(:,1),xy(:,2),list(z,-9), flag=[0 0])
    xtitle("Cubic Shepard Interpolation of cos(x)cos(y) with randomly chosen interpolation points")
    legends("interpolation points",-9,1)
    show_window()

n = 150; // nb of interpolation points xy = grand(n,2,"unf",0,2*%pi); z = cos(xy(:,1)).*cos(xy(:,2)); xyz = [xy z]; tl_coef = cshep2d(xyz); // evaluation on a grid m = 30; xx = linspace(0,2*%pi,m); [X,Y] = ndgrid(xx,xx); Z = eval_cshep2d(X,Y, tl_coef); clf() plot3d(xx,xx,Z,flag=[2 6 4]) param3d1(xy(:,1),xy(:,2),list(z,-9), flag=[0 0]) xtitle("Cubic Shepard Interpolation of cos(x)cos(y) with randomly chosen interpolation points") legends("interpolation points",-9,1) show_window()

## See also

- splin2d
- eval_cshep2d

## History

5.4.0 previously, imaginary part of input arguments were implicitly ignored.