CatmullRomSpline.H
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23 
24 Class
25  Foam::CatmullRomSpline
26 
27 Description
28  An implementation of Catmull-Rom splines
29  (sometimes known as Overhauser splines).
30 
31  In this implementation, the end tangents are created automatically
32  by reflection.
33 
34  In matrix form, the \e local interpolation on the interval t=[0..1] is
35  described as follows:
36  \verbatim
37  P(t) = 1/2 * [ t^3 t^2 t 1 ] * [ -1 3 -3 1 ] * [ P-1 ]
38  [ 2 -5 4 -1 ] [ P0 ]
39  [ -1 0 1 0 ] [ P1 ]
40  [ 0 2 0 0 ] [ P2 ]
41  \endverbatim
42 
43  Where P-1 and P2 represent the neighbouring points or the extrapolated
44  end points. Simple reflection is used to automatically create the end
45  points.
46 
47  The spline is discretized based on the chord length of the individual
48  segments. In rare cases (sections with very high curvatures), the
49  resulting distribution may be sub-optimal.
50 
51  A future implementation could also handle closed splines.
52 
53 See also
54  http://www.algorithmist.net/catmullrom.html provides a nice
55  introduction
56 
57 SourceFiles
58  CatmullRomSpline.C
59 
60 \*---------------------------------------------------------------------------*/
61 
62 #ifndef CatmullRomSpline_H
63 #define CatmullRomSpline_H
64 
65 #include "polyLine.H"
66 
67 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
68 
69 namespace Foam
70 {
71 
72 /*---------------------------------------------------------------------------*\
73  Class CatmullRomSpline Declaration
74 \*---------------------------------------------------------------------------*/
75 
76 class CatmullRomSpline
77 :
78  public polyLine
79 {
80  // Private Member Functions
81 
82  //- Disallow default bitwise copy construct
84 
85  //- Disallow default bitwise assignment
86  void operator=(const CatmullRomSpline&);
87 
88 
89 public:
90 
91  // Constructors
92 
93  //- Construct from components
95  (
96  const pointField& knots,
97  const bool notImplementedClosed = false
98  );
99 
100 
101  // Member Functions
102 
103  //- Return the point position corresponding to the curve parameter
104  // 0 <= lambda <= 1
105  point position(const scalar lambda) const;
106 
107  //- Return the point position corresponding to the local parameter
108  // 0 <= lambda <= 1 on the given segment
109  point position(const label segment, const scalar lambda) const;
110 
111  //- Return the length of the curve
112  scalar length() const;
113 };
114 
115 
116 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
117 
118 } // End namespace Foam
119 
120 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
121 
122 #endif
123 
124 // ************************************************************************* //
intWM_LABEL_SIZE_t label
A label is an int32_t or int64_t as specified by the pre-processor macro WM_LABEL_SIZE.
Definition: label.H:59
point position(const scalar lambda) const
Return the point position corresponding to the curve parameter.
An ordered pair of two objects of type <T> with first() and second() elements.
Definition: contiguous.H:49
A series of straight line segments, which can also be interpreted as a series of control points for s...
Definition: polyLine.H:53
dimensionedScalar lambda(laminarTransport.lookup("lambda"))
scalar length() const
Return the length of the curve.
An implementation of Catmull-Rom splines (sometimes known as Overhauser splines). ...
Namespace for OpenFOAM.