BSpline.H

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    Copyright (C) 2011-2016 OpenFOAM Foundation
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License
    This file is part of OpenFOAM.
 
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    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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    for more details.
 
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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
{
    // Private Member Functions
 
        //- No copy construct
        BSpline(const BSpline&) = delete;
 
        //- No copy assignment
        void operator=(const BSpline&) = delete;
 
 
public:
 
    // Constructors
 
        //- Construct from components
        BSpline
        (
            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
        scalar length() const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //