Spline Toolbox

Vector-Valued Functions

The toolbox supports vector-valued splines. For example, if you want a spline curve through given planar points

, then the statements

• xy = [x;y]; df = diff(xy.').'; 
  t = cumsum([0, sqrt([1 1]*(df.*df))]); 
  cv = csapi(t,xy);
  

provide such a spline curve, using chord-length parametrization and cubic spline interpolation with the not-a-knot end condition, as can be verified by the statements

• fnplt(cv), hold on, plot(x,y,'o'), hold off
  

As another example of the use of vector-valued functions, suppose that you have solved the equations of motion of a particle in some specified force field in the plane, obtaining, at discrete times , the position as well as the velocity stored in the 4-vector , as you would if, in the standard way, you had solved the equivalent first-order system numerically. Then the following statement, which uses cubic Hermite interpolation, will produce a plot of the particle path:

• fnplt(spapi(augknt(t,4,2),t,reshape(z,2,2*n)))
  

Using the Spline Fits

Fitting Values at N-D Grid