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