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# 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

### Authors

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

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