def test_incremental(self, name):
# Test incremental construction of the triangulation
if INCREMENTAL_DATASETS[name][0][0].shape[1] > 3:
# too slow (testing of the result --- qhull is still fast)
return
chunks, opts = INCREMENTAL_DATASETS[name]
points = np.concatenate(chunks, axis=0)
obj = qhull.Voronoi(chunks[0], incremental=True, qhull_options=opts)
for chunk in chunks[1:]:
obj.add_points(chunk)
obj2 = qhull.Voronoi(points)
obj3 = qhull.Voronoi(chunks[0], incremental=True, qhull_options=opts)
if len(chunks) > 1:
obj3.add_points(np.concatenate(chunks[1:], axis=0), restart=True)
# -- Check that the incremental mode agrees with upfront mode
assert_equal(len(obj.point_region), len(obj2.point_region))
assert_equal(len(obj.point_region), len(obj3.point_region))
# The vertices may be in different order or duplicated in
# the incremental map
for objx in obj, obj3:
vertex_map = {-1: -1}
for i, v in enumerate(objx.vertices):
for j, v2 in enumerate(obj2.vertices):
if np.allclose(v, v2):
vertex_map[i] = j
def remap(x):
if hasattr(x, '__len__'):
return tuple(set([remap(y) for y in x]))
try:
return vertex_map[x]
except KeyError as e:
raise AssertionError(
"incremental result has spurious vertex at %r" %
(objx.vertices[x], )) from e
def simplified(x):
items = set(map(sorted_tuple, x))
if () in items:
items.remove(())
items = [x for x in items if len(x) > 1]
items.sort()
return items
assert_equal(simplified(remap(objx.regions)),
simplified(obj2.regions))
assert_equal(simplified(remap(objx.ridge_vertices)),
simplified(obj2.ridge_vertices))
def _compare_qvoronoi(self, points, output, **kw):
"""Compare to output from 'qvoronoi o Fv < data' to Voronoi()"""
# Parse output
output = [list(map(float, x.split())) for x in output.strip().splitlines()]
nvertex = int(output[1][0])
vertices = list(map(tuple, output[3:2+nvertex])) # exclude inf
nregion = int(output[1][1])
regions = [[int(y)-1 for y in x[1:]]
for x in output[2+nvertex:2+nvertex+nregion]]
ridge_points = [[int(y) for y in x[1:3]]
for x in output[3+nvertex+nregion:]]
ridge_vertices = [[int(y)-1 for y in x[3:]]
for x in output[3+nvertex+nregion:]]
# Compare results
vor = qhull.Voronoi(points, **kw)
def sorttuple(x):
return tuple(sorted(x))
assert_allclose(vor.vertices, vertices)
assert_equal(set(map(tuple, vor.regions)),
set(map(tuple, regions)))
p1 = list(zip(list(map(sorttuple, ridge_points)), list(map(sorttuple, ridge_vertices))))
p2 = list(zip(list(map(sorttuple, vor.ridge_points.tolist())),
list(map(sorttuple, vor.ridge_vertices))))
p1.sort()
p2.sort()
assert_equal(p1, p2)
def test_ridges(self, name):
# Check that the ridges computed by Voronoi indeed separate
# the regions of nearest neighborhood, by comparing the result
# to KDTree.
points = DATASETS[name]
tree = KDTree(points)
vor = qhull.Voronoi(points)
for p, v in vor.ridge_dict.items():
# consider only finite ridges
if not np.all(np.asarray(v) >= 0):
continue
ridge_midpoint = vor.vertices[v].mean(axis=0)
d = 1e-6 * (points[p[0]] - ridge_midpoint)
dist, k = tree.query(ridge_midpoint + d, k=1)
assert_equal(k, p[0])
dist, k = tree.query(ridge_midpoint - d, k=1)
assert_equal(k, p[1])