def test_incremental_volume_area_random_input(self):
"""Test that incremental mode gives the same volume/area as
non-incremental mode and incremental mode with restart"""
nr_points = 20
dim = 3
points = np.random.random((nr_points, dim))
inc_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True)
inc_restart_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True)
for i in range(dim+1, nr_points):
hull = qhull.ConvexHull(points[:i+1, :])
inc_hull.add_points(points[i:i+1, :])
inc_restart_hull.add_points(points[i:i+1, :], restart=True)
assert_allclose(hull.volume, inc_hull.volume, rtol=1e-7)
assert_allclose(hull.volume, inc_restart_hull.volume, rtol=1e-7)
assert_allclose(hull.area, inc_hull.area, rtol=1e-7)
assert_allclose(hull.area, inc_restart_hull.area, rtol=1e-7)
def test_volume_area(self):
# Basic check that we get back the correct volume and area for a cube
points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0),
(0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)])
tri = qhull.ConvexHull(points)
assert_allclose(tri.volume, 1., rtol=1e-14)
assert_allclose(tri.area, 6., rtol=1e-14)
def test_incremental(self, name):
# Test incremental construction of the convex hull
chunks, _ = INCREMENTAL_DATASETS[name]
points = np.concatenate(chunks, axis=0)
obj = qhull.ConvexHull(chunks[0], incremental=True)
for chunk in chunks[1:]:
obj.add_points(chunk)
obj2 = qhull.ConvexHull(points)
obj3 = qhull.ConvexHull(chunks[0], incremental=True)
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_hulls_equal(points, obj.simplices, obj2.simplices)
assert_hulls_equal(points, obj.simplices, obj3.simplices)
def test_good2d(self, incremental):
# Make sure the QGn option gives the correct value of "good".
points = np.array([[0.2, 0.2], [0.2, 0.4], [0.4, 0.4], [0.4, 0.2],
[0.3, 0.6]])
hull = qhull.ConvexHull(points=points,
incremental=incremental,
qhull_options='QG4')
expected = np.array([False, True, False, False], dtype=bool)
actual = hull.good
assert_equal(actual, expected)
def test_volume_area(self):
#Basic check that we get back the correct volume and area for a cube
points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0),
(0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)])
hull = qhull.ConvexHull(points)
assert_allclose(hull.volume, 1., rtol=1e-14,
err_msg="Volume of cube is incorrect")
assert_allclose(hull.area, 6., rtol=1e-14,
err_msg="Area of cube is incorrect")
def test_good2d_inside(self, incremental):
# Make sure the QGn option gives the correct value of "good".
# When point n is inside the convex hull of the rest, good is
# all False.
points = np.array([[0.2, 0.2], [0.2, 0.4], [0.4, 0.4], [0.4, 0.2],
[0.3, 0.3]])
hull = qhull.ConvexHull(points=points,
incremental=incremental,
qhull_options='QG4')
expected = np.array([False, False, False, False], dtype=bool)
actual = hull.good
assert_equal(actual, expected)
def test_vertices_2d(self):
# The vertices should be in counterclockwise order in 2-D
np.random.seed(1234)
points = np.random.rand(30, 2)
hull = qhull.ConvexHull(points)
assert_equal(np.unique(hull.simplices), np.sort(hull.vertices))
# Check counterclockwiseness
x, y = hull.points[hull.vertices].T
angle = np.arctan2(y - y.mean(), x - x.mean())
assert_(np.all(np.diff(np.unwrap(angle)) > 0))
def test_good3d(self, incremental):
# Make sure the QGn option gives the correct value of "good"
# for a 3d figure
points = np.array([[0.0, 0.0, 0.0],
[0.90029516, -0.39187448, 0.18948093],
[0.48676420, -0.72627633, 0.48536925],
[0.57651530, -0.81179274, -0.09285832],
[0.67846893, -0.71119562, 0.18406710]])
hull = qhull.ConvexHull(points=points,
incremental=incremental,
qhull_options='QG0')
expected = np.array([True, False, False, False], dtype=bool)
assert_equal(hull.good, expected)
def test_good2d_no_option(self, incremental):
# handle case where good attribue doesn't exist
# because Qgn or Qg-n wasn't specified
points = np.array([[0.2, 0.2], [0.2, 0.4], [0.4, 0.4], [0.4, 0.2],
[0.3, 0.6]])
hull = qhull.ConvexHull(points=points, incremental=incremental)
actual = hull.good
assert actual is None
# preserve None after incremental addition
if incremental:
hull.add_points(np.zeros((1, 2)))
actual = hull.good
assert actual is None
def test_good2d_incremental_changes(self, new_gen, expected, visibility):
# use the usual square convex hull
# generators from test_good2d
points = np.array([[0.2, 0.2], [0.2, 0.4], [0.4, 0.4], [0.4, 0.2],
[0.3, 0.6]])
hull = qhull.ConvexHull(points=points,
incremental=True,
qhull_options=visibility)
hull.add_points(new_gen)
actual = hull.good
if '-' in visibility:
expected = np.invert(expected)
assert_equal(actual, expected)
def test_hull_consistency_tri(self, name):
# Check that a convex hull returned by qhull in ndim
# and the hull constructed from ndim delaunay agree
points = DATASETS[name]
tri = qhull.Delaunay(points)
hull = qhull.ConvexHull(points)
assert_hulls_equal(points, tri.convex_hull, hull.simplices)
# Check that the hull extremes are as expected
if points.shape[1] == 2:
assert_equal(np.unique(hull.simplices), np.sort(hull.vertices))
else:
assert_equal(np.unique(hull.simplices), hull.vertices)
def test_random_volume_area(self):
#Test that the results for a random 10-point convex are
#coherent with the output of qconvex Qt s FA
points = np.array([(0.362568364506, 0.472712355305, 0.347003084477),
(0.733731893414, 0.634480295684, 0.950513180209),
(0.511239955611, 0.876839441267, 0.418047827863),
(0.0765906233393, 0.527373281342, 0.6509863541),
(0.146694972056, 0.596725793348, 0.894860986685),
(0.513808585741, 0.069576205858, 0.530890338876),
(0.512343805118, 0.663537132612, 0.037689295973),
(0.47282965018, 0.462176697655, 0.14061843691),
(0.240584597123, 0.778660020591, 0.722913476339),
(0.951271745935, 0.967000673944, 0.890661319684)])
hull = qhull.ConvexHull(points)
assert_allclose(hull.volume, 0.14562013, rtol=1e-07,
err_msg="Volume of random polyhedron is incorrect")
assert_allclose(hull.area, 1.6670425, rtol=1e-07,
err_msg="Area of random polyhedron is incorrect")
