CatmullRomSpline Class Reference

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

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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.

See also:

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

Todo:

A future implementation could also handle closed splines.

Source files

• applications/utilities/mesh/generation/blockMesh/curvedEdges/CatmullRomSpline.H
• applications/utilities/mesh/generation/blockMesh/curvedEdges/CatmullRomSpline.C

Definition at line 77 of file CatmullRomSpline.H.

Inheritance diagram for CatmullRomSpline:

Collaboration diagram for CatmullRomSpline:

List of all members.

Public Member Functions
	CatmullRomSpline (const pointField &knots, const bool notImplementedClosed=false)
	Construct from components.
point	position (const scalar lambda) const
	Return the point position corresponding to the curve parameter.
point	position (const label segment, const scalar lambda) const
	Return the point position corresponding to the local parameter.
scalar	length () const
	Return the length of the curve - not implemented.

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Constructor & Destructor Documentation

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

Construct from components.

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Member Function Documentation

point position

(

const scalar

lambda  )

const

Return the point position corresponding to the curve parameter.

0 <= lambda <= 1

Reimplemented from polyLine.

Reimplemented in splineEdge.

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

Return the point position corresponding to the local parameter.

0 <= lambda <= 1 on the given segment

Reimplemented from polyLine.

scalar length

(

)

const

Return the length of the curve - not implemented.

Reimplemented from polyLine.

Reimplemented in splineEdge.

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The documentation for this class was generated from the following file:

• applications/utilities/mesh/generation/blockMesh/curvedEdges/CatmullRomSpline.H