125 lines
3.8 KiB
C++
125 lines
3.8 KiB
C++
/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | foam-extend: Open Source CFD
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\\ / O peration |
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\\ / A nd | For copyright notice see file Copyright
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of foam-extend.
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foam-extend is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation, either version 3 of the License, or (at your
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option) any later version.
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foam-extend is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with foam-extend. If not, see <http://www.gnu.org/licenses/>.
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Class
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Foam::CatmullRomSpline
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Description
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An implementation of Catmull-Rom splines
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(sometimes known as Overhauser splines).
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In this implementation, the end tangents are created automatically
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by reflection.
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In matrix form, the @e local interpolation on the interval t=[0..1] is
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described as follows:
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@verbatim
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P(t) = 1/2 * [ t^3 t^2 t 1 ] * [ -1 3 -3 1 ] * [ P-1 ]
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[ 2 -5 4 -1 ] [ P0 ]
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[ -1 0 1 0 ] [ P1 ]
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[ 0 2 0 0 ] [ P2 ]
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@endverbatim
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Where P-1 and P2 represent the neighbouring points or the extrapolated
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end points. Simple reflection is used to automatically create the end
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points.
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The spline is discretized based on the chord length of the individual
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segments. In rare cases (sections with very high curvatures), the
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resulting distribution may be sub-optimal.
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SeeAlso
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http://www.algorithmist.net/catmullrom.html provides a nice
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introduction
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ToDo
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A future implementation could also handle closed splines.
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SourceFiles
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CatmullRomSpline.C
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\*---------------------------------------------------------------------------*/
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#ifndef CatmullRomSpline_H
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#define CatmullRomSpline_H
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#include "polyLine.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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namespace Foam
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{
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/*---------------------------------------------------------------------------*\
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Class CatmullRomSpline Declaration
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\*---------------------------------------------------------------------------*/
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class CatmullRomSpline
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:
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public polyLine
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{
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// Private Member Functions
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//- Disallow default bitwise copy construct
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CatmullRomSpline(const CatmullRomSpline&);
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//- Disallow default bitwise assignment
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void operator=(const CatmullRomSpline&);
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public:
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// Constructors
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//- Construct from components
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CatmullRomSpline
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(
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const pointField& knots,
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const bool notImplementedClosed = false
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);
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// Member Functions
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//- Return the point position corresponding to the curve parameter
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// 0 <= lambda <= 1
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point position(const scalar lambda) const;
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//- Return the point position corresponding to the local parameter
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// 0 <= lambda <= 1 on the given segment
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point position(const label segment, const scalar lambda) const;
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//- Return the length of the curve - not implemented
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scalar length() const;
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};
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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} // End namespace Foam
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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#endif
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// ************************************************************************* //
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