An implementation of Catmull-Rom splines (sometimes known as Overhauser splines). More...

Inheritance diagram for CatmullRomSpline:

Collaboration diagram for CatmullRomSpline:

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

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

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

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

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

	polyLine (const point &start, const pointField &intermediate, const point &end, const bool notImplementedClosed=false)
	Construct from begin, intermediate, end points. More...

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

label	nSegments () const noexcept
	The number of line segments. More...

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

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

scalar	length () const noexcept
	The length of the curve. More...

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

Protected Member Functions inherited from polyLine
void	calcParam ()

label	localParameter (scalar &lambda) const

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

scalar	lineLength_
	The real (total) line length. More...

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

Detailed Description

An implementation of Catmull-Rom splines (sometimes known as Overhauser 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) = 1/2 * [ t^3 t^2 t 1 ] * [ -1  3 -3  1 ] * [ P-1 ]
                               [  2 -5  4 -1 ]   [ P0 ]
                               [ -1  0  1  0 ]   [ P1 ]
                               [  0  2  0  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.

See also: http://www.algorithmist.net/catmullrom.html provides a nice introduction

Source files

Definition at line 78 of file CatmullRomSpline.H.

Constructor & Destructor Documentation

◆ CatmullRomSpline()

CatmullRomSpline	(	const pointField &	knots,
		const bool	notImplementedClosed = `false`
	)

explicit

Construct from components.

Definition at line 83 of file CatmullRomSpline.C.

Member Function Documentation

◆ position() [1/2]

Foam::point position ( const scalar lambda ) const

The point position corresponding to the curve parameter.

0 <= lambda <= 1

Definition at line 94 of file CatmullRomSpline.C.

References lambda(), Foam::constant::physicoChemical::mu, and points.

Referenced by splineEdge::position().

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◆ position() [2/2]

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

The point position corresponding to the local parameter.

0 <= lambda <= 1 on the given segment

Definition at line 113 of file CatmullRomSpline.C.

References Foam::constant::physicoChemical::mu, p0, and points.

◆ length()

Foam::scalar length ( ) const

The length of the curve.

Definition at line 184 of file CatmullRomSpline.C.

References Foam::sum().

Referenced by splineEdge::length().