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Aide Scilab >> Interpolation > cshep2d

# 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()```

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

### Authors

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