The Graph2d makes use of
Catmull-Rom spline interpolation. The user can configure these per group, or globally. In this example we
show all 4 possiblities. The differences are in the parametrization of the
curves. The options are
uniform
,
chordal
and
centripetal
. Alternatively you can disable the Catmull-Rom
interpolation and a linear interpolation will be used. The
centripetal
parametrization produces the best result (no self
intersection, yet follows the line closely) and is therefore the default
setting.
For both the
centripetal
and
chordal
parametrization, the distances between the points
have to be calculated and this makes these methods computationally
intensive if there are very many points. The
uniform
parametrization still has to do transformations,
though it does not have to calculate the distance between point. Finally,
the linear interpolation is the fastest method. For more on the
Catmull-Rom method,
C. Yuksel et al. have an interesting paper titled ″On the
parametrization of Catmull-Rom Curves″.