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eval_cshep2d
bidimensional cubic shepard interpolation evaluation
Syntax
zp = eval_cshep2d(xp, yp, tl_coef) [zp, dzpdx, dzpdy] = eval_cshep2d(xp, yp, tl_coef) [zp, dzpdx, dzpdy, d2zpdxx, d2zpdyy, d2zpdxy] = 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
andyp
, evaluation of the interpolantS
at these points- dzpdx,dzpdy
vectors (or matrices) of the same size than
xp
andyp
, evaluation of the first derivatives ofS
at these points- d2zpdxx,d2zpdxy,d2zpdyy
vectors (or matrices) of the same size than
xp
andyp
, evaluation of the second derivatives ofS
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 inaccurate 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); colors = 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 ); colors(ind)=3; clf(); plot3d(xf,yf,list(zf,colors), flag=[2 6 4]) legends(["extrapolation region","interpolation region"],[2 3],1) show_window()
See also
- cshep2d — bidimensional cubic shepard (scattered) interpolation
History
Версия | Описание |
5.4.0 | previously, imaginary part of input arguments were implicitly ignored. |
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