Spline Toolbox

Construction and Use

You are most likely to construct such a form by looking for an interpolant or approximant to gridded data. For example, if you know the values

, of some function at all the points in a rectangular grid, then, assuming that the strictly increasing sequence x satisfies the Schoenberg-Whitney conditions with respect to the above knot sequence , and that the strictly increasing sequence y satisfies the Schoenberg-Whitney conditions with respect to the above knot sequence , the command

constructs the unique bivariate spline of the above form that matches the given values. The command fnplt(sp) gives you a quick plot of this interpolant. The command pp = fn2fm(sp,'pp') gives you the ppform of this spline, which is probably what you want when you want to evaluate the spline at a fine grid ((xx(i),yy(j)) for i=1:M, j=1:N), by the command:

• values = fnval(pp,{xx,yy});
  

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