def test_half_space_pt_convex_2d(self):
n = np.array([[0, 0, 0, 0, 1, -1], [1, 1, -1, -1, 0, 0],
[0, 0, 0, 0, 0, 0]])
x0 = np.array([[0, 0, 0, 0, 0, 2. / 3.],
[0, 0, 1. / 3., 1. / 3., 0, 0], [0, 0, 0, 0, 0, 0]])
pts = np.array([[0, 2. / 3.], [0, 1. / 3.], [0, 0]])
pt = half_space.half_space_pt(n, x0, pts)
assert np.allclose(pt, [1. / 6., 1. / 6., 0.])
def test_half_space_pt_convex_3d(self):
n = np.array([[1, -1, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0],
[0, 0, 0, 0, 1, -1]])
x0 = np.array([[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1]])
pts = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
pt = half_space.half_space_pt(n, x0, pts)
assert np.allclose(pt, [1. / 2., 1. / 2., 1. / 2.])
def test_half_space_pt_star_shaped_2d(self):
n = np.array([[0, 0, 1, 0, -1, 0, 1], [1, 1, 0, 1, 0, -1, 0],
[0, 0, 0, 0, 0, 0, 0]])
x0 = np.array([[0, 0, 2. / 3., 0, 1, 0, 0],
[1. / 3., 1. / 3., 0, 0, 0, 2. / 3., 0],
[0, 0, 0, 0, 0, 0, 0]])
pts = np.array([[0, 1], [0, 2. / 3.], [0, 0]])
pt = half_space.half_space_pt(n, x0, pts)
assert np.allclose(pt, [5. / 6., 1. / 2., 0.])
def test_half_space_pt_convex_3d(self):
n = np.array([[1, -1, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0],
[0, 0, 0, 0, 1, -1]])
x0 = np.array([[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1]])
pts = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
pt = half_space.half_space_pt(n, x0, pts).reshape((-1, 1))
# Verify that the computed point is on the same side of the all normal
# vectors as a point known to be in the interior.
known_pt = np.array([1.0 / 2.0, 1.0 / 2.0, 1.0 / 2.0]).reshape((-1, 1))
self.assertTrue(
np.all(
np.sign(np.sum(n * (pt - x0), axis=0)) == np.sign(
np.sum(n * (known_pt - x0), axis=0))))
def test_half_space_pt_convex_2d(self):
n = np.array([[0, 0, 0, 0, 1, -1], [1, 1, -1, -1, 0, 0],
[0, 0, 0, 0, 0, 0]])
x0 = np.array([
[0, 0, 0, 0, 0, 2.0 / 3.0],
[0, 0, 1.0 / 3.0, 1.0 / 3.0, 0, 0],
[0, 0, 0, 0, 0, 0],
])
known_pt = np.array([1.0 / 6.0, 1.0 / 6.0, 0.0]).reshape((-1, 1))
pts = np.array([[0, 2.0 / 3.0], [0, 1.0 / 3.0], [0, 0]])
pt = half_space.half_space_pt(n, x0, pts).reshape((-1, 1))
self.assertTrue(
np.all(
np.sign(np.sum(n * pt, axis=0)) == np.sign(
np.sum(n * known_pt, axis=0))))
def test_half_space_pt_star_shaped_3d(self):
n = np.array([
[0, 0, 1, 0, -1, 0, 1, 0, 0],
[1, 1, 0, 1, 0, -1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, -1],
])
x0 = np.array([
[0, 0, 2.0 / 3.0, 0, 1, 0, 0, 0, 0],
[1.0 / 3.0, 1.0 / 3.0, 0, 0, 0, 2.0 / 3.0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 1],
])
known_pt = np.array([5.0 / 6.0, 1.0 / 2.0, 1.0 / 6.0]).reshape((-1, 1))
pts = np.array([[0, 1], [0, 2.0 / 3.0], [0, 1]])
pt = half_space.half_space_pt(n, x0, pts).reshape((-1, 1))
self.assertTrue(
np.all(
np.sign(np.sum(n * (pt - x0), axis=0)) == np.sign(
np.sum(n * (known_pt - x0), axis=0))))
def test_half_space_pt_test0(self):
n = np.array([[
-0.4346322145903923, -0.5837212981640826, -0.5545602917404856,
0.8874304062782964, 0.9432862408780104, -0.5285915818615673
],
[
-0.9006080379611606, -0.8119540911096134,
0.8321435470065893, -0.4609417251808932,
0.3319805231790443, 0.8488762804938574
], [0., -0., 0., -0., 0., 0.]])
pts = np.array([[
0.6264867087233955, 0.6264867087233955, 0.6292849480051679,
0.6767304875123992, 0.6767304875123992, 0.6622642106131997,
0.6598935979971375, 0.6012244303376967, 0.6012244303376967,
0.6598935979971375, 0.6622642106131997, 0.6292849480051679
],
[
0.8042920815320497, 0.8042920815320497,
0.8411535645991798, 0.8205852695643441,
0.8205852695643441, 0.8616896085330092,
0.7881699621908844, 0.8224533668748337,
0.8224533668748337, 0.7881699621908844,
0.8616896085330092, 0.8411535645991798
], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
x0 = np.array([[
0.6264867087233955, 0.6264867087233955, 0.6292849480051679,
0.6767304875123992, 0.6767304875123992, 0.6622642106131997
],
[
0.8042920815320497, 0.8042920815320497,
0.8411535645991798, 0.8205852695643441,
0.8205852695643441, 0.8616896085330092
], [0., 0., 0., 0., 0., 0.]])
x1 = pts[:, 6:12]
x0 = (x1 + x0) / 2
pt = half_space.half_space_pt(n, x0, pts)
pt_known = np.array([0.6484723969922208, 0.8225131504113889, 0.])
assert np.allclose(pt, pt_known)
def test_half_space_pt_test1(self):
n = np.array([[
1., 0.6773171037156254, -0.0965964317843146, 0.5615536850805473,
-0.8227124789179447, -0.8663868741056542, -0.3297308258566596
],
[
-0., -0.7356911994949217, 0.9953236304672657,
0.8274403052622333, 0.5684577178935039,
-0.4993733917395212, -0.9440749877419088
], [0., -0., 0., 0., -0., -0., 0.]])
pts = np.array(
[[
1., 1., 1., 0.9456767570553427, 0.9002821557415752,
0.9236181291669759, 0.9236181291669759, 1., 0.9689475893045396,
0.9456767570553427, 0.9188491193586552, 0.9188491193586552,
0.9002821557415752, 0.9689475893045396
],
[
0.3333333333328948, 0.3333333333328948, 0.3749999999996713,
0.3697279143475474, 0.3610634261905756, 0.3205767254478346,
0.3205767254478346, 0.3749999999996713, 0.3047448047626512,
0.3697279143475474, 0.3879348577545479, 0.3879348577545479,
0.3610634261905756, 0.3047448047626512
], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
x0 = np.array([[
1., 0.9844737946522698, 0.9728383785276713, 0.9322629382069989,
0.9095656375501152, 0.9119501424542755, 0.9462828592357577
],
[
0.354166666666283, 0.319039069047773,
0.3723639571736094, 0.3788313860510477,
0.3744991419725617, 0.3408200758192051,
0.3126607651052429
], [0., 0., 0., 0., 0., 0., 0.]])
pt = half_space.half_space_pt(n, x0, pts)
pt_known = np.array([0.9411337621203867, 0.3417142038105351, 0])
assert np.allclose(pt, pt_known)