eval_cshep2d
============

bidimensional cubic shepard interpolation evaluation



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [zp [,dzpdx, dzpdy [,d2zpdxx,d2zpdxy,d2zpdyy]]] = eval_cshep2d(xp, yp, tl_coef)




Arguments
~~~~~~~~~

:xp, yp two real vectors (or matrices) of the same size
: :tl_coef a tlist scilab structure (of type cshep2d) defining a cubic
  Shepard interpolation function (named `S` in the following)
: :zp vector (or matrix) of the same size than `xp` and `yp`,
  evaluation of the interpolant `S` at these points
: :dzpdx,dzpdy vectors (or matrices) of the same size than `xp` and
  `yp`, evaluation of the first derivatives of `S` at these points
: :d2zpdxx,d2zpdxy,d2zpdyy vectors (or matrices) of the same size than
  `xp` and `yp`, evaluation of the second derivatives of `S` at these
  points
:



Description
~~~~~~~~~~~

This is the evaluation routine for cubic Shepard interpolation
function computed with `cshep2d`_, that is :



Remark
~~~~~~

The interpolant *S* is C2 (twice continuously differentiable) but is
also extended by zero for *(x,y)* far enough the interpolation points.
This leads to a discontinuity in a region far outside the
interpolation points, and so, is not cumbersome in practice (in a
general manner, evaluation outside interpolation points (i.e.
extrapolation) leads to very inacurate results).



Examples
~~~~~~~~


::

    // see example section of cshep2d
    
    // this example shows the behavior far from the interpolation points ...
    `deff`_("z=f(x,y)","z = 1+ 50*(x.*(1-x).*y.*(1-y)).^2")
    x = `linspace`_(0,1,10);
    [X,Y] = `ndgrid`_(x,x);
    X = X(:); Y = Y(:); Z = f(X,Y);
    S = `cshep2d`_([X Y Z]);
    // evaluation inside and outside the square [0,1]x[0,1]
    m = 40;
    xx = `linspace`_(-1.5,0.5,m);
    [xp,yp] = `ndgrid`_(xx,xx);
    zp = eval_cshep2d(xp,yp,S);
    // compute facet (to draw one color for extrapolation region
    // and another one for the interpolation region)
    [xf,yf,zf] = `genfac3d`_(xx,xx,zp);
    `color`_ = 2*ones(1,`size`_(zf,2));
    // indices corresponding to facet in the interpolation region
    ind=`find`_( `mean`_(xf,"r")>0 & `mean`_(xf,"r")<1 & `mean`_(yf,"r")>0 & `mean`_(yf,"r")<1 );
    `color`_(ind)=3;
    `clf`_();
    `plot3d`_(xf,yf,`list`_(zf,`color`_), flag=[2 6 4])
    `legends`_(["extrapolation region","interpolation region"],[2 3],1)
    `show_window`_()




See Also
~~~~~~~~


+ `cshep2d`_ bidimensional cubic shepard (scattered) interpolation




History
~~~~~~~
Version Description 5.4.0 previously, imaginary part of input
arguments were implicitly ignored.
.. _cshep2d: cshep2d.html