An implementation of B-splines. More...

Inheritance diagram for BSpline:

Collaboration diagram for BSpline:

Public Member Functions
	BSpline (const pointField &knots, const bool notImplementedClosed=false)

point	position (const scalar lambda) const

point	position (const label segment, const scalar lambda) const

scalar	length () const

Public Member Functions inherited from polyLine
	polyLine (const pointField &points, const bool notImplementedClosed=false)

	polyLine (const point &start, const pointField &intermediate, const point &end, const bool notImplementedClosed=false)

const pointField &	points () const noexcept

label	nSegments () const noexcept

point	position (const scalar) const

point	position (const label segment, const scalar) const

scalar	length () const noexcept

Additional Inherited Members
Static Public Member Functions inherited from polyLine
static tmp< pointField >	concat (const point &start, const pointField &intermediate, const point &end)

Protected Member Functions inherited from polyLine
void	calcParam ()

label	localParameter (scalar &lambda) const

Protected Attributes inherited from polyLine
pointField	points_

scalar	lineLength_

scalarList	param_

Detailed Description

An implementation of B-splines.

In this implementation, the end tangents are created automatically by reflection.

In matrix form, the local interpolation on the interval t=[0..1] is described as follows:

P(t) = 1/6 * [ t^3 t^2 t 1 ] * [ -1  3 -3  1 ] * [ P-1 ]
                               [  3 -6  3  0 ]   [ P0 ]
                               [ -3  0  3  0 ]   [ P1 ]
                               [  1  4  1  0 ]   [ P2 ]

Where P-1 and P2 represent the neighbouring points or the extrapolated end points. Simple reflection is used to automatically create the end points.

The spline is discretized based on the chord length of the individual segments. In rare cases (sections with very high curvatures), the resulting distribution may be sub-optimal.

A future implementation could also handle closed splines.