def test_edge_surfaces_six_sides(self):
# create the unit cube
vol = Volume()
vol.raise_order(2,2,2)
vol.refine(3)
edges = vol.faces()
# edge_surface should give back the same unit cube
vol2 = VolumeFactory.edge_surfaces(edges)
# check discretization
self.assertEqual(vol2.order(0), 4)
self.assertEqual(vol2.order(1), 4)
self.assertEqual(vol2.order(2), 4)
self.assertEqual(len(vol2.knots(0)), 5) # [0,.25,.5,.75,1]
self.assertEqual(len(vol2.knots(1)), 5)
self.assertEqual(len(vol2.knots(2)), 5)
# check a 5x5x5 evaluation grid
u = np.linspace(0,1,5)
v = np.linspace(0,1,5)
w = np.linspace(0,1,5)
pt = vol( u,v,w)
pt2 = vol2(u,v,w)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def test_edge_surfaces_six_sides(self):
# create the unit cube
vol = Volume()
vol.raise_order(2,2,2)
vol.refine(3)
edges = vol.faces()
# edge_surface should give back the same unit cube
vol2 = vf.edge_surfaces(edges)
# check discretization
self.assertEqual(vol2.order(0), 4)
self.assertEqual(vol2.order(1), 4)
self.assertEqual(vol2.order(2), 4)
self.assertEqual(len(vol2.knots(0)), 5) # [0,.25,.5,.75,1]
self.assertEqual(len(vol2.knots(1)), 5)
self.assertEqual(len(vol2.knots(2)), 5)
# check a 5x5x5 evaluation grid
u = np.linspace(0,1,5)
v = np.linspace(0,1,5)
w = np.linspace(0,1,5)
pt = vol( u,v,w)
pt2 = vol2(u,v,w)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def test_controlpoint_access(self):
v = Volume()
v.refine(1)
self.assertAlmostEqual(v[0,0,0, 0] , 0)
self.assertAlmostEqual(v[0,0,0][0] , 0)
self.assertAlmostEqual(v[0,1,0][0] , 0)
self.assertAlmostEqual(v[0,1,0][1] , .5)
self.assertAlmostEqual(v[0,1,0, 1] , .5)
self.assertAlmostEqual(v[0,0,2][2] , 1)
self.assertAlmostEqual(v[4][0] , .5)
self.assertAlmostEqual(v[4][1] , .5)
self.assertAlmostEqual(v[4][2] , 0)
self.assertAlmostEqual(v[13][0] , .5)
self.assertAlmostEqual(v[13][1] , .5)
self.assertAlmostEqual(v[13][2] , .5)
self.assertAlmostEqual(v[14][0] , 1)
self.assertAlmostEqual(v[14][1] , .5)
self.assertAlmostEqual(v[14][2] , .5)
v[0] = [.1, .1, .1]
v[1,1,1] = [.6, .6, .6]
v[1,0,0][0] = .4
self.assertAlmostEqual(v[0,0,0][0], .1)
self.assertAlmostEqual(v[0,0,0][1], .1)
self.assertAlmostEqual(v[0,0,0][2], .1)
self.assertAlmostEqual(v[13][0] , .6)
self.assertAlmostEqual(v[13][1] , .6)
self.assertAlmostEqual(v[13][2] , .6)
self.assertAlmostEqual(v[1][0] , .4)
self.assertAlmostEqual(v[1][1] , 0)
self.assertAlmostEqual(v[1][2] , 0)
v[:,0,0] = 13
v[0,1,0][:] = 12
# v[0,2,1] = [9,8,7]
# v[0,2,0] = [9,8,7]
v[0,2,1::-1] = [9,8,7]
v[1,2,1::-1,:] = [[6,5,4],[3,2,1]]
self.assertAlmostEqual(v[1,0,0,0], 13)
self.assertAlmostEqual(v[1,0,0,1], 13)
self.assertAlmostEqual(v[2,0,0,2], 13)
self.assertAlmostEqual(v[0,1,0,0], 12)
self.assertAlmostEqual(v[0,1,0,2], 12)
self.assertAlmostEqual(v[0,2,2,1], 1)
self.assertAlmostEqual(v[0,2,1,0], 9)
self.assertAlmostEqual(v[0,2,1,1], 8)
self.assertAlmostEqual(v[0,2,0,2], 7)
self.assertAlmostEqual(v[1,2,1,0], 6)
self.assertAlmostEqual(v[1,2,1,1], 5)
self.assertAlmostEqual(v[1,2,1,2], 4)
self.assertAlmostEqual(v[1,2,0,0], 3)
self.assertAlmostEqual(v[1,2,0,1], 2)
self.assertAlmostEqual(v[1,2,0,2], 1)
def test_controlpoint_access(self):
v = Volume()
v.refine(1)
self.assertAlmostEqual(v[0, 0, 0, 0], 0)
self.assertAlmostEqual(v[0, 0, 0][0], 0)
self.assertAlmostEqual(v[0, 1, 0][0], 0)
self.assertAlmostEqual(v[0, 1, 0][1], .5)
self.assertAlmostEqual(v[0, 1, 0, 1], .5)
self.assertAlmostEqual(v[0, 0, 2][2], 1)
self.assertAlmostEqual(v[4][0], .5)
self.assertAlmostEqual(v[4][1], .5)
self.assertAlmostEqual(v[4][2], 0)
self.assertAlmostEqual(v[13][0], .5)
self.assertAlmostEqual(v[13][1], .5)
self.assertAlmostEqual(v[13][2], .5)
self.assertAlmostEqual(v[14][0], 1)
self.assertAlmostEqual(v[14][1], .5)
self.assertAlmostEqual(v[14][2], .5)
v[0] = [.1, .1, .1]
v[1, 1, 1] = [.6, .6, .6]
v[1, 0, 0][0] = .4
self.assertAlmostEqual(v[0, 0, 0][0], .1)
self.assertAlmostEqual(v[0, 0, 0][1], .1)
self.assertAlmostEqual(v[0, 0, 0][2], .1)
self.assertAlmostEqual(v[13][0], .6)
self.assertAlmostEqual(v[13][1], .6)
self.assertAlmostEqual(v[13][2], .6)
self.assertAlmostEqual(v[1][0], .4)
self.assertAlmostEqual(v[1][1], 0)
self.assertAlmostEqual(v[1][2], 0)
v[:, 0, 0] = 13
v[0, 1, 0][:] = 12
# v[0,2,1] = [9,8,7]
# v[0,2,0] = [9,8,7]
v[0, 2, 1::-1] = [9, 8, 7]
v[1, 2, 1::-1, :] = [[6, 5, 4], [3, 2, 1]]
self.assertAlmostEqual(v[1, 0, 0, 0], 13)
self.assertAlmostEqual(v[1, 0, 0, 1], 13)
self.assertAlmostEqual(v[2, 0, 0, 2], 13)
self.assertAlmostEqual(v[0, 1, 0, 0], 12)
self.assertAlmostEqual(v[0, 1, 0, 2], 12)
self.assertAlmostEqual(v[0, 2, 2, 1], 1)
self.assertAlmostEqual(v[0, 2, 1, 0], 9)
self.assertAlmostEqual(v[0, 2, 1, 1], 8)
self.assertAlmostEqual(v[0, 2, 0, 2], 7)
self.assertAlmostEqual(v[1, 2, 1, 0], 6)
self.assertAlmostEqual(v[1, 2, 1, 1], 5)
self.assertAlmostEqual(v[1, 2, 1, 2], 4)
self.assertAlmostEqual(v[1, 2, 0, 0], 3)
self.assertAlmostEqual(v[1, 2, 0, 1], 2)
self.assertAlmostEqual(v[1, 2, 0, 2], 1)
def test_operators(self):
v = Volume()
v.raise_order(1, 1, 2)
v.refine(3, 2, 1)
# test translation operator
v2 = v + [1, 0, 0]
v3 = [1, 0, 0] + v
v += [1, 0, 0]
self.assertTrue(np.allclose(v2.controlpoints, v3.controlpoints))
self.assertTrue(np.allclose(v.controlpoints, v3.controlpoints))
# test scaling operator
v2 = v * 3
v3 = 3 * v
v *= 3
self.assertTrue(np.allclose(v2.controlpoints, v3.controlpoints))
self.assertTrue(np.allclose(v.controlpoints, v3.controlpoints))
def test_make_identical(self):
basis1 = BSplineBasis(4, [-1, -1, 0, 0, 1, 1, 2, 2], periodic=1)
basis2 = BSplineBasis(3, [-1, 0, 0, 1, 1, 2], periodic=0)
basis3 = BSplineBasis(2)
vol1 = Volume()
vol2 = Volume(basis1, basis2, basis3)
vol1.refine(1)
Volume.make_splines_identical(vol1, vol2)
for v in (vol1, vol2):
self.assertEqual(v.periodic(0), False)
self.assertEqual(v.periodic(1), False)
self.assertEqual(v.periodic(2), False)
self.assertEqual(v.order(), (4, 3, 2))
self.assertAlmostEqual(len(v.knots(0, True)), 11)
self.assertAlmostEqual(len(v.knots(1, True)), 8)
self.assertAlmostEqual(len(v.knots(2, True)), 5)
def test_operators(self):
v = Volume()
v.raise_order(1,1,2)
v.refine(3,2,1)
# test translation operator
v2 = v + [1,0,0]
v3 = [1,0,0] + v
v += [1,0,0]
self.assertTrue(np.allclose(v2.controlpoints, v3.controlpoints))
self.assertTrue(np.allclose(v.controlpoints, v3.controlpoints))
# test scaling operator
v2 = v * 3
v3 = 3 * v
v *= 3
self.assertTrue(np.allclose(v2.controlpoints, v3.controlpoints))
self.assertTrue(np.allclose(v.controlpoints, v3.controlpoints))
def test_make_identical(self):
basis1 = BSplineBasis(4, [-1,-1,0,0,1,1,2,2], periodic=1)
basis2 = BSplineBasis(3, [-1,0,0,1,1,2], periodic=0)
basis3 = BSplineBasis(2)
vol1 = Volume()
vol2 = Volume(basis1, basis2, basis3)
vol1.refine(1)
Volume.make_splines_identical(vol1,vol2)
for v in (vol1, vol2):
self.assertEqual(v.periodic(0), False)
self.assertEqual(v.periodic(1), False)
self.assertEqual(v.periodic(2), False)
self.assertEqual(v.order(), (4,3,2))
self.assertAlmostEqual(len(v.knots(0, True)), 11)
self.assertAlmostEqual(len(v.knots(1, True)), 8)
self.assertAlmostEqual(len(v.knots(2, True)), 5)
def test_bounding_box(self):
vol = Volume()
bb = vol.bounding_box()
self.assertAlmostEqual(bb[0][0], 0)
self.assertAlmostEqual(bb[0][1], 1)
self.assertAlmostEqual(bb[1][0], 0)
self.assertAlmostEqual(bb[1][1], 1)
self.assertAlmostEqual(bb[2][0], 0)
self.assertAlmostEqual(bb[2][1], 1)
vol.refine(2)
vol.rotate(pi / 4, [1, 0, 0])
vol += (1, 0, 1)
bb = vol.bounding_box()
self.assertAlmostEqual(bb[0][0], 1)
self.assertAlmostEqual(bb[0][1], 2)
self.assertAlmostEqual(bb[1][0], -sqrt(2) / 2)
self.assertAlmostEqual(bb[1][1], sqrt(2) / 2)
self.assertAlmostEqual(bb[2][0], 1)
self.assertAlmostEqual(bb[2][1], 1 + sqrt(2))
def test_bounding_box(self):
vol = Volume()
bb = vol.bounding_box()
self.assertAlmostEqual(bb[0][0], 0 )
self.assertAlmostEqual(bb[0][1], 1 )
self.assertAlmostEqual(bb[1][0], 0 )
self.assertAlmostEqual(bb[1][1], 1 )
self.assertAlmostEqual(bb[2][0], 0 )
self.assertAlmostEqual(bb[2][1], 1 )
vol.refine(2)
vol.rotate(pi/4, [1,0,0])
vol += (1,0,1)
bb = vol.bounding_box()
self.assertAlmostEqual(bb[0][0], 1 )
self.assertAlmostEqual(bb[0][1], 2 )
self.assertAlmostEqual(bb[1][0], -sqrt(2)/2 )
self.assertAlmostEqual(bb[1][1], sqrt(2)/2 )
self.assertAlmostEqual(bb[2][0], 1 )
self.assertAlmostEqual(bb[2][1], 1+sqrt(2) )
