An implementation of B-splines. 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.
Definition at line 75 of file BSpline.H.
Public Member Functions | |
BSpline (const pointField &knots, const bool notImplementedClosed=false) | |
Construct from components.
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point | position (const scalar lambda) const |
Return the point position corresponding to the curve parameter.
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point | position (const label segment, const scalar lambda) const |
Return the point position corresponding to the local parameter.
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scalar | length () const |
Return the length of the curve.
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BSpline | ( | const pointField & | knots, |
const bool | notImplementedClosed = false
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||
) |
Construct from components.
point position | ( | const scalar | lambda ) | const |
Return the point position corresponding to the curve parameter.
0 <= lambda <= 1
Reimplemented from polyLine.
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
Reimplemented from polyLine.
scalar length | ( | ) | const |
Return the length of the curve.
Reimplemented from polyLine.