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CatmullRomSpline.H
Go to the documentation of this file.
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2009-2010 OpenCFD Ltd.
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM 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
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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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 OpenFOAM. 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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// ************************************************************************* //