CatmullRomSpline.H

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License
    This file is part of OpenFOAM.
 
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    the Free Software Foundation, either version 3 of the License, or
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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::CatmullRomSpline
 
Description
    An implementation of Catmull-Rom splines (sometimes known as Overhauser
    splines). This is a piecewise cubic spline that intersects all of its
    control points.
 
    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. Reflection is used to automatically create the extrapolated end
    points.
 
See also
    BSpline
 
SourceFiles
    CatmullRomSpline.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef CatmullRomSpline_H
#define CatmullRomSpline_H
 
#include "Spline.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                      Class CatmullRomSpline Declaration
\*---------------------------------------------------------------------------*/
 
class CatmullRomSpline
:
    public Spline<CatmullRomSpline>
{
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<CatmullRomSpline>::position;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //