Graph2d | Interpolation

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″.