BSpline Class Reference
B-spline basis functions. More...
#include <ql/math/bspline.hpp>
Public Member Functions | |
BSpline (Natural p, Natural n, const std::vector< Real > &knots) | |
Real | operator() (Natural i, Real x) const |
Detailed Description
B-spline basis functions.
Follows treatment and notation from:
Weisstein, Eric W. "B-Spline." From MathWorld--A Wolfram Web Resource. <http://mathworld.wolfram.com/B-Spline.html>
-th order B-spline (or p degree polynomial) basis functions
, with
control points, or equivalently, an associated knot vector of size
defined at the increasingly sorted points
. A linear B-spline has
, quadratic B-spline has
, a cubic B-spline has
, etc.
The B-spline basis functions are defined recursively as follows: