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Fitting Values at N-D Grid with Tensor-Product Splines

Vector-valued splines are also used in the approximation to gridded data, in any number of variables, using tensor-product splines. The same spline-construction commands are used, only the form of the input differs. For example, if x is an m-vector, y is an n-vector, and z is an array of size [m,n], then cs = csapi({x,y},z); describes a bicubic spline f satisfying f(x(i),y(j))=z(i,j) for i=1:m, j=1:n. Such a multivariate spline can be vector-valued. For example,

x = 0:4; y=-2:2; s2 = 1/sqrt(2);
z(3,:,:) = [0 1 s2 0 -s2 -1 0].'*[1 1 1 1 1];
z(2,:,:) = [1 0 s2 1 s2 0 -1].'*[0 1 0 -1 0];
z(1,:,:) = [1 0 s2 1 s2 0 -1].'*[1 0 -1 0 1];
sph = csape({x,y},z,{'clamped','periodic'});
fnplt(sph), axis equal, axis off

gives a perfectly acceptable sphere. Its projection onto the -plane is plotted by

fnplt(fncmb(sph,[1 0 0; 0 0 1])), axis equal, axis off

Both plots are shown below.

A Sphere Made by a 3-D-Valued Bivariate Tensor Product Spline

Planar Projection of Spline Sphere