bidimensional cubic shepard (scattered) interpolation
tl_coef = cshep2d(xyz)
: :tl_coef a tlist scilab structure (of type cshep2d) :
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.
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.
// 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`_()
Version Description 5.4.0 previously, imaginary part of input arguments were implicitly ignored. .. _eval_cshep2d: eval_cshep2d.html .. _splin2d: splin2d.html