# BSpline (3) - Linux Manuals

## BSpline: B-spline basis functions.

## NAME

QuantLib::BSpline - B-spline basis functions.

## SYNOPSIS

#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>

$ (p+1) $-th order B-spline (or p degree polynomial) basis functions $ N_{i,p}(x), i = 0,1,2

knot vector of size $ p+n+2 $ defined at the increasingly sorted points $ (x_0, x_1

ratic B-spline has $ p=2 $, a cubic B-spline has $ p=3 $, etc.

The B-spline basis functions are defined recursively as follows:

[ xtrm{

xtrm{

## Author

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