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# cshep2d

bidimensional cubic shepard (scattered) interpolation

### Calling Sequence

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 choosen 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 choosen interpolation points") legends("interpolation points",-9,1) show_window()

### See Also

- splin2d — bicubic spline gridded 2d interpolation
- eval_cshep2d — bidimensional cubic shepard interpolation evaluation

### Authors

- Robert J. Renka
- B. Pincon (scilab interface)

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