SplineΒΆ
| Type: | section |
|---|---|
| Appearance: | simple |
A Spline is a polynomial curve interpolating the given sequential list of Points. Its Degree controls the polynomial order of the curve with higher degrees leading to smoother curves. The start and end points of the replaced linear segment must be contained in the Points list.
The mapping
![\begin{eqnarray*}
t \mapsto \gamma(t)=(X(t),Y(t)),\quad t \in [0,1]
\end{eqnarray*}](_images/math/24d6082f33b03f48ce3a1a518b76dbd457608f8d.png)
is chosen such that 
are splines of the desired order and the curve parameterization in 
follows the linearized arc length. This means the interpolation points 
where 
for the i-th point of the Points list are approximately the ratio of the length of the polygon up to 
to the total length. For the best interpolation result the linear sampling provided by the Points should already yield a good approximation to the desired curve.
Note
A single Spline may be used to replace multiple linear segments of the polygonal chain. In this case it is required that all start/end points of the segments are in the Points list of the Spline.