CatmullRomSpline.H

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    \\  /    A nd           | Copyright (C) 2009-2010 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.

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Class
    Foam::CatmullRomSpline

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 @e local interpolation on the interval t=[0..1] is
    described as follows:
    @verbatim
    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 ]
    @endverbatim

    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.

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

ToDo
    A future implementation could also handle closed splines.

SourceFiles
    CatmullRomSpline.C

\*---------------------------------------------------------------------------*/

#ifndef CatmullRomSpline_H
#define CatmullRomSpline_H

#include "polyLine.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

/*---------------------------------------------------------------------------*\
                      Class CatmullRomSpline Declaration
\*---------------------------------------------------------------------------*/

class CatmullRomSpline
:
    public polyLine
{
    // Private Member Functions

        //- Disallow default bitwise copy construct
        CatmullRomSpline(const CatmullRomSpline&);

        //- Disallow default bitwise assignment
        void operator=(const CatmullRomSpline&);


public:

    // Constructors

        //- Construct from components
        CatmullRomSpline
        (
            const pointField& knots,
            const bool notImplementedClosed = false
        );


    // Member Functions

        //- Return the point position corresponding to the curve parameter
        //  0 <= lambda <= 1
        point position(const scalar lambda) const;

        //- Return the point position corresponding to the local parameter
        //  0 <= lambda <= 1 on the given segment
        point position(const label segment, const scalar lambda) const;

        //- Return the length of the curve - not implemented
        scalar length() const;
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //