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.
Public Member Functions | |
BSpline (const pointField &knots, const bool notImplementedClosed=false) | |
Construct from components. | |
point | position (const scalar lambda) const |
Return the point position corresponding to the curve parameter. | |
point | position (const label segment, const scalar lambda) const |
Return the point position corresponding to the local parameter. | |
scalar | length () const |
Return the length of the curve. | |
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polyLine (const pointField &, const bool notImplementedClosed=false) | |
Construct from components. | |
const pointField & | points () const |
Return const-access to the control-points. | |
label | nSegments () const |
Return the number of line segments. |
Additional Inherited Members | |
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void | calcParam () |
Precalculate the rational cumulative parameter value. | |
label | localParameter (scalar &lambda) const |
Return the line segment and the local parameter [0..1]. | |
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pointField | points_ |
The control points or ends of each segments. | |
scalar | lineLength_ |
The real line length. | |
scalarList | param_ |
The rational (0-1) cumulative parameter value for each point. |
BSpline | ( | const pointField & | knots, |
const bool | notImplementedClosed = false |
||
) |
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.