def test_edge_surfaces_six_sides_issue_141(self):
# create the unit cube
vol = Volume()
# modify slightly one edge: umin(w=0) is now a parabola instead of a line
vol.raise_order(0,1,0)
vol.controlpoints[-1, 1, 0, 0] += 1
faces = vol.faces()
# edge_surface should give back the same modified unit cube
vol2 = vf.edge_surfaces(faces)
# check discretization
self.assertEqual(vol2.order(0),2)
self.assertEqual(vol2.order(1),3)
self.assertEqual(vol2.order(2),2)
self.assertEqual(len(vol2.knots(0)),2) # [0, 1]
self.assertEqual(len(vol2.knots(1)),2)
self.assertEqual(len(vol2.knots(2)),2)
# 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.assertTrue(np.allclose(pt, pt2))
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_raise_order(self):
# more or less random 3D volume with p=[2,2,1] and n=[4,3,2]
controlpoints = [[0, 0, 0], [-1, 1, 0], [0, 2, 0], [1, -1,
0], [1, 0, 0],
[1, 1, 0], [2, 1, 0], [2, 2, 0], [2, 3, 0], [3, 0, 0],
[4, 1, 0], [3, 2, 0], [0, 0, 1], [-1, 1,
1], [0, 2, 1],
[1, -1, 2], [1, 0, 2], [1, 1, 2], [2, 1, 2],
[2, 2, 2], [2, 3, 2], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, .4, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints)
self.assertEqual(vol.order(), (3, 3, 2))
evaluation_point1 = vol(
0.23, 0.37, 0.44) # pick some evaluation point (could be anything)
vol.raise_order(1, 2, 4)
self.assertEqual(vol.order(), (4, 5, 6))
evaluation_point2 = vol(0.23, 0.37, 0.44)
# evaluation before and after RaiseOrder should remain unchanged
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test a rational 3D volume
controlpoints = [[0, 0, 1, 1], [-1, 1, .96, 1], [0, 2, 1, 1],
[1, -1, 1, 1], [1, 0, .8, 1], [1, 1, 1, 1],
[2, 1, .89, 1], [2, 2, .9, 1], [2, 3, 1, 1],
[3, 0, 1, 1], [4, 1, 1, 1], [3, 2, 1, 1],
[0, 0, 1, 2], [-1, 1, .7, 2], [0, 2, 1.3, 2],
[1, -1, 1, 2], [1, 0, .77, 2], [1, 1, 1, 2],
[2, 1, .89, 1], [2, 2, .8, 4], [2, 3, 1, 1],
[3, 0, 1, 1], [4, 1, 1, 1], [3, 2, 1, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, .4, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints, True)
self.assertEqual(vol.order()[0], 3)
self.assertEqual(vol.order()[1], 3)
evaluation_point1 = vol(0.23, 0.37, 0.44)
vol.raise_order(1, 2, 1)
self.assertEqual(vol.order(), (4, 5, 3))
evaluation_point2 = vol(0.23, 0.37, 0.44)
# evaluation before and after RaiseOrder should remain unchanged
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
def test_raise_order(self):
# more or less random 3D volume with p=[2,2,1] and n=[4,3,2]
controlpoints = [[0, 0, 0], [-1, 1, 0], [0, 2, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0],
[2, 1, 0], [2, 2, 0], [2, 3, 0], [3, 0, 0], [4, 1, 0], [3, 2, 0],
[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 2], [1, 0, 2], [1, 1, 2],
[2, 1, 2], [2, 2, 2], [2, 3, 2], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, .4, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints)
self.assertEqual(vol.order(), (3, 3, 2))
evaluation_point1 = vol(0.23, 0.37, 0.44) # pick some evaluation point (could be anything)
vol.raise_order(1, 2, 4)
self.assertEqual(vol.order(), (4, 5, 6))
evaluation_point2 = vol(0.23, 0.37, 0.44)
# evaluation before and after RaiseOrder should remain unchanged
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# test a rational 3D volume
controlpoints = [[0, 0, 1, 1], [-1, 1, .96, 1], [0, 2, 1, 1], [1, -1, 1, 1], [1, 0, .8, 1],
[1, 1, 1, 1], [2, 1, .89, 1], [2, 2, .9, 1], [2, 3, 1, 1], [3, 0, 1, 1],
[4, 1, 1, 1], [3, 2, 1, 1], [0, 0, 1, 2], [-1, 1, .7, 2], [0, 2, 1.3, 2],
[1, -1, 1, 2], [1, 0, .77, 2], [1, 1, 1, 2], [2, 1, .89, 1], [2, 2, .8, 4],
[2, 3, 1, 1], [3, 0, 1, 1], [4, 1, 1, 1], [3, 2, 1, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, .4, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints, True)
self.assertEqual(vol.order()[0], 3)
self.assertEqual(vol.order()[1], 3)
evaluation_point1 = vol(0.23, 0.37, 0.44)
vol.raise_order(1, 2, 1)
self.assertEqual(vol.order(), (4, 5, 3))
evaluation_point2 = vol(0.23, 0.37, 0.44)
# evaluation before and after RaiseOrder should remain unchanged
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
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_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))
