Implements the "Fast generation of 2-D node distributions for mesh-free PDE discretizations" algorithm by [Fornberg and Flyer] (see: https://amath.colorado.edu/faculty/fornberg/Docs/2015_FF_Node_placing_CMA.pdf)
Fornberg, B., & Flyer, N. (2015). Fast generation of 2-D node distributions for mesh-free PDE discretizations. Computers & Mathematics with Applications, 69(7), 531-544.
This only implements the code for laying out points in a rectangular domain. The paper presents a method for an iterative repulsion model to clean up edges when non-rectangular regions are cut out; this is not implemented here.
Simply pass a function returning the number of points per unit area at a given point to moving_front_nodes:
# simple function; flat everywhere, with dense point in the centre
def density_fn(x,y):
return np.maximum(100, (5000.0*np.exp(-((x**2+y**2)*10.0))))
nodes = moving_front_nodes(density_fn, (-1,-1,1,1))
See VariableDensity.ipynb for some basic tests of the uniformity of the layout.
See PyrRetina.ipynb for an application in building a simple foveated (retinal) transform for imaging purposes using the layout algorithm.
