Spline Toolbox

ppform

The items breaks, coefs, l, and k, make up the ppform of , along with the dimension d of its coefficients; usually d equals 1. The basic interval of this form is the interval [breaks(1) .. breaks(l+1)]. It is the default interval over which a function in ppform is plotted by the plot command fnplt.

In these terms, the precise description of the piecewise-polynomial is

• (*)     = polyval(coefs(j,:),  - breaks(j))
  

for

.

Here, polyval(a,x) is the MATLAB function; it returns the number

This defines only for in the half-open interval [breaks(1)..breaks(l+1)). For any other , is defined by

i.e., by extending the first, respectively last, polynomial piece. In this way, a function in ppform has possible jumps, in its value and/or its derivatives, only across the interior breaks, break(2:l). The end breaks, break([1,l+1]), mainly serve to define the basic interval of the ppform.

Breaks

Construction