BSpline.H

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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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    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::BSpline
 
Description
    An implementation of B-splines. This is a piecewise cubic spline that
    intersects its given end points, but does not intersect and of its
    intermediate control points.
 
    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. Reflection is used to automatically create the extrapolated end
    points.
 
See also
    CatmullRomSpline
 
SourceFiles
    BSpline.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef BSpline_H
#define BSpline_H
 
#include "Spline.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                           Class BSpline Declaration
\*---------------------------------------------------------------------------*/
 
class BSpline
:
    public Spline<BSpline>
{
public:
 
    // Constructors
 
        //- Inherit constructors
        using Spline::Spline;
 
 
    // Member Functions
 
        //- Return the point position corresponding to the segment parameter
        point position(const label segmenti, const scalar segmentLambda) const;
 
        //- Inherit the base class' position methods
        using Spline<BSpline>::position;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //