splin3d

spline gridded 3d interpolation

Calling Sequence

tl = splin3d(x, y, z, v, [order])

Arguments

:x,y,z strictly increasing row vectors (each with at least 3

components) defining the 3d interpolation grid

: :v nx x ny x nz hypermatrix (nx, ny, nz being the length of x, y

and z)

: :order (optional) a 1x3 vector [kx,ky,kz] given the order of the

tensor spline in each direction (default [4,4,4], i.e. tricubic spline)

: :tl a tlist of type splin3d defining the spline :

Description

This function computes a 3d tensor spline s which interpolates the (xi,yj,zk,vijk) points, ie, we have s(xi,yj,zk)=vijk for all i=1,..,nx, j=1,..,ny and k=1,..,nz. The resulting spline s is defined by tl which consists in a B-spline-tensor representation of s. The evaluation of s at some points must be done by the `interp3d`_ function (to compute s and its first derivatives) or by the `bsplin3val`_ function (to compute an arbitrary derivative of s) . Several kind of splines may be computed by selecting the order of the spline in each direction order=[kx,ky,kz].

Remark

This function works under the conditions:

an error being issued when they are not respected.

Examples

// example 1
// =============================================================================

func =  "v=cos(2*%pi*x).*sin(2*%pi*y).*cos(2*%pi*z)";
`deff`_("v=f(x,y,z)",func);
n = 10;  // n x n x n  interpolation points
x = `linspace`_(0,1,n); y=x; z=x; // interpolation grid
[X,Y,Z] = `ndgrid`_(x,y,z);
V = f(X,Y,Z);
tl = splin3d(x,y,z,V,[5 5 5]);
m = 10000;
// compute an approximated error
xp = `grand`_(m,1,"def"); yp = `grand`_(m,1,"def"); zp = `grand`_(m,1,"def");
vp_exact = f(xp,yp,zp);
vp_interp = `interp3d`_(xp,yp,zp, tl);
er = `max`_(`abs`_(vp_exact - vp_interp))
// now retry with n=20 and see the error

// example 2 (see linear_interpn help page which have the
//            same example with trilinear interpolation)
// =============================================================================

`exec`_("SCI/modules/interpolation/demos/interp_demo.sci")
func =  "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
`deff`_("v=f(x,y,z)",func);
n = 5;
x = `linspace`_(0,1,n); y=x; z=x;
[X,Y,Z] = `ndgrid`_(x,y,z);
V = f(X,Y,Z);
tl = splin3d(x,y,z,V);
// compute (and display) the 3d spline interpolant on some slices
m = 41;
`dir`_ = ["z="  "z="  "z="  "x="  "y="];
val = [ 0.1   0.5   0.9   0.5   0.5];
ebox = [0 1 0 1 0 1];
XF=[]; YF=[]; ZF=[]; VF=[];
for i = 1:`length`_(val)
  [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(`dir`_(i), val(i), ebox, m, m, m);
  Vm = `interp3d`_(Xm,Ym,Zm, tl);
  [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
  XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
  Vp = `interp3d`_(Xp,Yp,Zp, tl);
  [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
  XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
end
nb_col = 128;
vmin = `min`_(VF); vmax = `max`_(VF);
`color`_ = dsearch(VF,`linspace`_(vmin,vmax,nb_col+1));
`xset`_("colormap",`jetcolormap`_(nb_col));
`clf`_(); `xset`_("hidden3d",`xget`_("background"));
`colorbar`_(vmin,vmax)
`plot3d`_(XF, YF, `list`_(ZF,`color`_), flag=[-1 6 4])
`xtitle`_("3d spline interpolation of "+func)
`show_window`_()

See Also

• `linear_interpn`_ n dimensional linear interpolation
• `interp3d`_ 3d spline evaluation function
• `bsplin3val`_ 3d spline arbitrary derivative evaluation function

History

Version Description 5.4.0 previously, imaginary part of input arguments were implicitly ignored. .. _linear_interpn: linear_interpn.html .. _interp3d: interp3d.html .. _bsplin3val: bsplin3val.html