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 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); m = 41; direction = ["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(direction(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_example = 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_example), flag=[-1 6 4]) xtitle("3d spline interpolation of "+func) See Also linear_interpn interp3d bsplin3val History 5.4.0 previously, imaginary part of input arguments were implicitly ignored.