Higher order interpolation for contour plots in python

Question

Is anybody of you aware of a higher order interpolation method (Catmull-Rom splines, cubic interpolation, etc.) for 2D contouring in Python?

Skimage, Matplotlib, and OpenCV provide the functions measure.find_contours(), contours() and findContours() respectively, but all are based on linear interpolation (also known as marching squares), I'm looking into something with higher accuracy in Python, preferably. Any pointers would be highly appreciated.

https://www.dropbox.com/s/orgr2yqhbbk2xnr/test.PNG

In the image above I'm trying to extract iso-value 25 from the scalar field of f(x,y)=x^3+y^3. I'm looking for 6 points with better accuracy than the 6 red points given by linear interpolation.

Answer 1

For unstructured 2d-data (or triangulated data), you might be interested by the following class:

http://matplotlib.org/api/tri_api.html?highlight=cubictriinterpolator#matplotlib.tri.CubicTriInterpolator

which provides a Clough-Tocher (cubic) interpolator from a user-defined Triangulation and field defined at triangulation nodes. It can also be used through the helper class UniformTriRefiner:

http://matplotlib.org/api/tri_api.html?highlight=refine_field#matplotlib.tri.UniformTriRefiner.refine_field http://matplotlib.org/mpl_examples/pylab_examples/tricontour_smooth_user.png

Nevertheless the choice of the adapted interpolation depends of course of your data set.