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 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`_()




See Also
~~~~~~~~


+ `splin2d`_ bicubic spline gridded 2d interpolation
+ `eval_cshep2d`_ bidimensional cubic shepard interpolation evaluation




History
~~~~~~~
Version Description 5.4.0 previously, imaginary part of input
arguments were implicitly ignored.
.. _eval_cshep2d: eval_cshep2d.html
.. _splin2d: splin2d.html