/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | www.openfoam.com
     \\/     M anipulation  |
-------------------------------------------------------------------------------
    Copyright (C) 2011-2016 OpenFOAM Foundation
    Copyright (C) 2020-2021 OpenCFD Ltd.
-------------------------------------------------------------------------------
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.

    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    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
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.

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.

    A future implementation could also handle closed splines.

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

SourceFiles
    CatmullRomSpline.C

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

#ifndef CatmullRomSpline_H
#define CatmullRomSpline_H

#include "polyLine.H"

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

namespace Foam
{

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

class CatmullRomSpline
:
    public polyLine
{

    //- Derivative of spline
    scalar derivative
    (
        const label segment,
        const scalar mu
    ) const;


public:

    // Constructors

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


    // Member Functions

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

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

        //- The length of the curve
        scalar length() const;
};


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

} // End namespace Foam

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

#endif

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