Spline Toolbox

Fitting Values at N-D Grid

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 satisfying  for  , . 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]))
  

Both plots are shown below.

Figure 2-6: A Sphere Made by a 3-D-Valued Bivariate Tensor Product Spline

Figure 2-7: A Planar Projection of the Above Spline Sphere

Vector-Valued Functions

Fitting Values at Scattered 2-D Sites