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_swap(self):
# more or less random 3D volume with p=[3,2,1] and n=[4,3,2]
controlpoints = [[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, 0],
[4, 1, 0], [3, 2, 0], [0, 0, 3], [-1, 1,
3], [0, 2, 3],
[1, -1, 5], [1, 0, 5], [1, 1, 5], [2, 1, 4],
[2, 2, 4], [2, 3, 4], [3, 0, 2], [4, 1, 2], [3, 2, 2]]
basis1 = BSplineBasis(4, [0, 0, 0, 0, 2, 2, 2, 2])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints)
evaluation_point1 = vol(0.23, .56, .12)
control_point1 = vol[
1] # this is control point i=(1,0,0), when n=(4,3,2)
self.assertEqual(vol.order(), (4, 3, 2))
vol.swap(0, 1)
evaluation_point2 = vol(0.56, .23, .12)
control_point2 = vol[
3] # this is control point i=(0,1,0), when n=(3,4,2)
self.assertEqual(vol.order(), (3, 4, 2))
# ensure that volume has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# check that the control points have re-ordered themselves
self.assertEqual(control_point1[0], control_point2[0])
self.assertEqual(control_point1[1], control_point2[1])
self.assertEqual(control_point1[2], control_point2[2])
vol.swap(1, 2)
evaluation_point3 = vol(.56, .12, .23)
control_point3 = vol[
6] # this is control point i=(0,0,1), when n=(3,2,4)
self.assertEqual(vol.order(), (3, 2, 4))
# ensure that volume has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point3[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point3[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point3[2])
# check that the control points have re-ordered themselves
self.assertEqual(control_point1[0], control_point3[0])
self.assertEqual(control_point1[1], control_point3[1])
self.assertEqual(control_point1[2], control_point3[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_evaluate(self):
# creating the identity mapping by different size for all directions
vol = Volume(BSplineBasis(7), BSplineBasis(6), BSplineBasis(5))
# call evaluation at a 2x3x4 grid of points
u_val = np.linspace(0, 1, 2)
v_val = np.linspace(0, 1, 3)
w_val = np.linspace(0, 1, 4)
value = vol(u_val, v_val, w_val)
self.assertEqual(value.shape[0], 2) # 2 u-evaluation points
self.assertEqual(value.shape[1], 3) # 3 v-evaluation points
self.assertEqual(value.shape[2], 4) # 4 w-evaluation points
self.assertEqual(value.shape[3], 3) # 3 dimensions (x,y,z)
self.assertEqual(vol.order(), (7, 6, 5))
for i, u in enumerate(u_val):
for j, v in enumerate(v_val):
for k, w in enumerate(w_val):
self.assertAlmostEqual(value[i, j, k, 0], u) # identity map x=u
self.assertAlmostEqual(value[i, j, k, 1], v) # identity map y=v
self.assertAlmostEqual(value[i, j, k, 2], w) # identity map z=w
# test errors and exceptions
with self.assertRaises(ValueError):
val = vol(-10, .5, .5) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(+10, .3, .3) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, -10, .123) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, +10, .123) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, .2, +10) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, .2, -10) # evalaute outside parametric domain
def test_evaluate(self):
# creating the identity mapping by different size for all directions
vol = Volume(BSplineBasis(7), BSplineBasis(6), BSplineBasis(5))
# call evaluation at a 2x3x4 grid of points
u_val = np.linspace(0, 1, 2)
v_val = np.linspace(0, 1, 3)
w_val = np.linspace(0, 1, 4)
value = vol(u_val, v_val, w_val)
self.assertEqual(value.shape[0], 2) # 2 u-evaluation points
self.assertEqual(value.shape[1], 3) # 3 v-evaluation points
self.assertEqual(value.shape[2], 4) # 4 w-evaluation points
self.assertEqual(value.shape[3], 3) # 3 dimensions (x,y,z)
self.assertEqual(vol.order(), (7, 6, 5))
for i, u in enumerate(u_val):
for j, v in enumerate(v_val):
for k, w in enumerate(w_val):
self.assertAlmostEqual(value[i, j, k, 0], u) # identity map x=u
self.assertAlmostEqual(value[i, j, k, 1], v) # identity map y=v
self.assertAlmostEqual(value[i, j, k, 2], w) # identity map z=w
# test errors and exceptions
with self.assertRaises(ValueError):
val = vol(-10, .5, .5) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(+10, .3, .3) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, -10, .123) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, +10, .123) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, .2, +10) # evalaute outside parametric domain
with self.assertRaises(ValueError):
val = vol(.5, .2, -10) # evalaute outside parametric domain
def test_swap(self):
# more or less random 3D volume with p=[3,2,1] and n=[4,3,2]
controlpoints = [[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, 0], [4, 1, 0], [3, 2, 0],
[0, 0, 3], [-1, 1, 3], [0, 2, 3], [1, -1, 5], [1, 0, 5], [1, 1, 5],
[2, 1, 4], [2, 2, 4], [2, 3, 4], [3, 0, 2], [4, 1, 2], [3, 2, 2]]
basis1 = BSplineBasis(4, [0, 0, 0, 0, 2, 2, 2, 2])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis3 = BSplineBasis(2, [0, 0, 1, 1])
vol = Volume(basis1, basis2, basis3, controlpoints)
evaluation_point1 = vol(0.23, .56, .12)
control_point1 = vol[1] # this is control point i=(1,0,0), when n=(4,3,2)
self.assertEqual(vol.order(), (4, 3, 2))
vol.swap(0, 1)
evaluation_point2 = vol(0.56, .23, .12)
control_point2 = vol[3] # this is control point i=(0,1,0), when n=(3,4,2)
self.assertEqual(vol.order(), (3, 4, 2))
# ensure that volume has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# check that the control points have re-ordered themselves
self.assertEqual(control_point1[0], control_point2[0])
self.assertEqual(control_point1[1], control_point2[1])
self.assertEqual(control_point1[2], control_point2[2])
vol.swap(1, 2)
evaluation_point3 = vol(.56, .12, .23)
control_point3 = vol[6] # this is control point i=(0,0,1), when n=(3,2,4)
self.assertEqual(vol.order(), (3, 2, 4))
# ensure that volume has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point3[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point3[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point3[2])
# check that the control points have re-ordered themselves
self.assertEqual(control_point1[0], control_point3[0])
self.assertEqual(control_point1[1], control_point3[1])
self.assertEqual(control_point1[2], control_point3[2])
