Support qhull options for alpha_shape_auto to resolve ill-conditioned inputs

[ljwolf]

• Platform information:

posix darwin
posix.uname_result(sysname='Darwin', nodename='wolfbook.local', release='22.3.0', version='Darwin Kernel Version 22.3.0: Mon Jan 30 20:42:11 PST 2023; root:xnu-8792.81.3~2/RELEASE_X86_64', machine='x86_64')

• Python version:

3.9.16 | packaged by conda-forge | (main, Feb  1 2023, 21:42:20)
[Clang 14.0.6 ]

• SciPy version:

1.10.0

• NumPy version:

1.23.5

Working with @LVConsult, we noted that when alpha_shape_auto() receives ill-conditioned input (such as collinear or coincident points), the underlying scipy.spatial.Delaunay() routine will fail with a scipy.spatial.QhullError. But, because we cannot access the underlying Delaunay() call, we cannot provide any qhull_options to resolve or address this error.

For an example testbench:

import numpy
from libpysal.cg import alpha_shape_auto

good = numpy.random.random(size=(20, 2))
alpha_shape_auto(good) # succeeds
collinear = numpy.column_stack((numpy.arange(6), numpy.arange(6)))
# alpha_shape_auto(collinear) # fails with a Qhull error, needs to be jittered
collinear_plus = numpy.row_stack((collinear, good))
alpha_shape_auto(collinear_plus) # succeeds
coincident = numpy.zeros((6, 2))
# alpha_shape_auto(coincident) # fails with a Qhull error, needs to have coincident points deleted
coincident_plus = numpy.row_stack((coincident, good))
alpha_shape_auto(coincident_plus) # succeeds
two_coincident = numpy.row_stack((numpy.zeros((3, 2)), numpy.ones((3, 2))))
#alpha_shape_auto(two_coincident) # fails with a Qhull error, needs to have coincident points deleted
col_and_coi = numpy.row_stack((collinear, coincident))
#alpha_shape_auto(col_and_coi) # fails with a Qhull error, needs to have coincident points deleted, then jittered

The usual solution to conditioning problems (either delete the coincident points or jitter the collinear points) can be done very efficiently by Qhull ( Delaunay(coords, qhull_options="Qbk:0Bk:0") or Delaunay(coords, qhull_options="QJ"), respectively) but the end user can't use these options because the alpha_shape_auto() does not deal with the options for Delaunay().

Think we could support these options?

[martinfleis]

Can we just pass kwargs to Delaunay()?

[ljwolf]

Yep!