CatmullRomSpline Class Reference

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

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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 pointFieldpoints () 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< pointFieldconcat (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().

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