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An implementation of B-splines. More...
Public Member Functions | |
| BSpline (const pointField &knots, const bool notImplementedClosed=false) | |
| Construct from components. More... | |
| point | position (const scalar lambda) const |
| Return the point position corresponding to the curve parameter. More... | |
| point | position (const label segment, const scalar lambda) const |
| Return the point position corresponding to the local parameter. More... | |
| scalar | length () const |
| Return the length of the curve. More... | |
 Public Member Functions inherited from polyLine | |
| polyLine (const pointField &, const bool notImplementedClosed=false) | |
| Construct from components. More... | |
| const pointField & | points () const |
| Return const-access to the control-points. More... | |
| label | nSegments () const |
| Return the number of line segments. More... | |
| point | position (const scalar) const |
| Return the point position corresponding to the curve parameter. More... | |
| point | position (const label segment, const scalar) const |
| Return the point position corresponding to the local parameter. More... | |
| scalar | length () const |
| Return the length of the curve. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from polyLine | |
| void | calcParam () |
| Precalculate the rational cumulative parameter value. More... | |
| label | localParameter (scalar &lambda) const |
| Return the line segment and the local parameter [0..1]. More... | |
| Protected Attributes inherited from polyLine | |
| pointField | points_ |
| The control points or ends of each segments. More... | |
| scalar | lineLength_ |
| The real line length. More... | |
| scalarList | param_ |
| The rational (0-1) cumulative parameter value for each point. More... | |
An implementation of B-splines.
In this implementation, the end tangents are created automatically by reflection.
In matrix form, the local interpolation on the interval t=[0..1] is described as follows:
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 ]
Where P-1 and P2 represent the neighbouring points or the extrapolated end points. Simple reflection is used to automatically create the end points.
The spline is discretized based on the chord length of the individual segments. In rare cases (sections with very high curvatures), the resulting distribution may be sub-optimal.
A future implementation could also handle closed splines.
| BSpline | ( | const pointField & | knots, |
| const bool | notImplementedClosed = false |
||
| ) |
| Foam::point position | ( | const scalar | lambda | ) | const |
Return the point position corresponding to the curve parameter.
0 <= lambda <= 1
Definition at line 42 of file BSpline.C.
References UList< T >::first(), lambda(), UList< T >::last(), polyLine::localParameter(), Foam::constant::physicoChemical::mu, and polyLine::points().
Referenced by BSplineEdge::position().
| Foam::point position | ( | const label | segment, |
| const scalar | lambda | ||
| ) | const |
Return the point position corresponding to the local parameter.
0 <= lambda <= 1 on the given segment
Definition at line 61 of file BSpline.C.
References UList< T >::first(), UList< T >::last(), polyLine::nSegments(), and polyLine::points().
| Foam::scalar length | ( | ) | const |
Return the length of the curve.
Definition at line 132 of file BSpline.C.
References NotImplemented.
Referenced by BSplineEdge::length().
1.8.13