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)
	Construct from components. More...

point	position (const scalar lambda) const
	Return the point position corresponding to the curve parameter. More...

point	position (const label segment, const scalar lambda) const
	Return the point position corresponding to the local parameter. More...

scalar	length () const
	Return the length of the curve. More...

Public Member Functions inherited from polyLine
	polyLine (const pointField &, const bool notImplementedClosed=false)
	Construct from components. More...

const pointField &	points () const
	Return const-access to the control-points. More...

label	nSegments () const
	Return the number of line segments. More...

point	position (const scalar) const
	Return the point position corresponding to the curve parameter. More...

point	position (const label segment, const scalar) const
	Return the point position corresponding to the local parameter. More...

scalar	length () const
	Return the length of the curve. More...

Private Member Functions
	BSpline (const BSpline &)
	Disallow default bitwise copy construct. More...

void	operator= (const BSpline &)
	Disallow default bitwise assignment. More...

Additional Inherited Members
Protected Member Functions inherited from polyLine
void	calcParam ()
	Precalculate the rational cumulative parameter value. More...

label	localParameter (scalar &lambda) const
	Return the line segment and the local parameter [0..1]. More...

Protected Attributes inherited from polyLine
pointField	points_
	The control points or ends of each segments. More...

scalar	lineLength_
	The real line length. More...

scalarList	param_
	The rational (0-1) cumulative parameter value for each point. More...

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.