BSpline.H

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    Copyright (C) 2020 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
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    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
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Class
    Foam::BSpline
 
Description
    An implementation of B-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) = 1/6 * [ 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 ]
    \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.
 
    A future implementation could also handle closed splines.
 
See also
    CatmullRomSpline
 
SourceFiles
    BSpline.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef BSpline_H
#define BSpline_H
 
#include "polyLine.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                           Class BSpline Declaration
\*---------------------------------------------------------------------------*/
 
class BSpline
:
    public polyLine
{
public:
 
    // Constructors
 
        //- Construct from components
        explicit BSpline
        (
            const pointField& knots,
            const bool notImplementedClosed = false
        );
 
 
    // Member Functions
 
        //- The point position corresponding to the global curve parameter
        //  0 <= lambda <= 1
        point position(const scalar lambda) const;
 
        //- The point position corresponding to the local lambda (0-1)
        //- on the given segment
        point position(const label segment, const scalar lambda) const;
 
        //- The length of the curve
        //  \note NotImplemented
        scalar length() const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //