def test_edge_surfaces(self):
# test 3D surface vs 2D rational surface
# more or less random 3D surface with p=[2,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 1], [1, 0, .5], [1, 1, 1],
[2, 1, 1], [2, 2, .5], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, .64, 2, 2, 2])
top = Surface(basis1, basis2, controlpoints)
# more or less random 2D rational surface with p=[1,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, .96], [0, 2, 1], [1, -1, 1], [1, 0, .8], [1, 1, 1],
[2, 1, .89], [2, 2, .9], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints, True)
vol = VolumeFactory.edge_surfaces(bottom, top)
# set parametric domain to [0,1]^2 for easier comparison
top.reparam()
bottom.reparam()
# verify on 7x7x2 evaluation grid
for u in np.linspace(0, 1, 7):
for v in np.linspace(0, 1, 7):
for w in np.linspace(0, 1, 2): # rational basis, not linear in w-direction
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
# test 3D surface vs 2D surface
controlpoints = [[0, 0], [-1, 1], [0, 2], [1, -1], [1, 0], [1, 1], [2, 1], [2, 2], [2, 3],
[3, 0], [4, 1], [3, 2]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints) # non-rational!
vol = VolumeFactory.edge_surfaces(bottom, top) # also non-rational!
# verify on 5x5x7 evaluation grid
for u in np.linspace(0, 1, 5):
for v in np.linspace(0, 1, 5):
for w in np.linspace(0, 1, 7): # include inner evaluation points
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
def test_edge_surfaces(self):
# test 3D surface vs 2D rational surface
# more or less random 3D surface with p=[2,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 1], [1, 0, .5], [1, 1, 1],
[2, 1, 1], [2, 2, .5], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, .64, 2, 2, 2])
top = Surface(basis1, basis2, controlpoints)
# more or less random 2D rational surface with p=[1,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, .96], [0, 2, 1], [1, -1, 1], [1, 0, .8], [1, 1, 1],
[2, 1, .89], [2, 2, .9], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints, True)
vol = vf.edge_surfaces(bottom, top)
# set parametric domain to [0,1]^2 for easier comparison
top.reparam()
bottom.reparam()
# verify on 7x7x2 evaluation grid
for u in np.linspace(0, 1, 7):
for v in np.linspace(0, 1, 7):
for w in np.linspace(0, 1, 2): # rational basis, not linear in w-direction
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
# test 3D surface vs 2D surface
controlpoints = [[0, 0], [-1, 1], [0, 2], [1, -1], [1, 0], [1, 1], [2, 1], [2, 2], [2, 3],
[3, 0], [4, 1], [3, 2]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints) # non-rational!
vol = vf.edge_surfaces(bottom, top) # also non-rational!
# verify on 5x5x7 evaluation grid
for u in np.linspace(0, 1, 5):
for v in np.linspace(0, 1, 5):
for w in np.linspace(0, 1, 7): # include inner evaluation points
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
def plane(self):
dim = int( self.read_next_non_whitespace().strip())
center = np.array(next(self.fstream).split(), dtype=float)
normal = np.array(next(self.fstream).split(), dtype=float)
x_axis = np.array(next(self.fstream).split(), dtype=float)
finite = next(self.fstream).strip() != '0'
if finite:
param_u= np.array(next(self.fstream).split(), dtype=float)
param_v= np.array(next(self.fstream).split(), dtype=float)
else:
param_u= [-state.unlimited, +state.unlimited]
param_v= [-state.unlimited, +state.unlimited]
swap = next(self.fstream).strip() != '0'
result = Surface() * [param_u[1]-param_u[0], param_v[1]-param_v[0]] + [param_u[0],param_v[0]]
result.rotate(rotate_local_x_axis(x_axis, normal))
result = flip_and_move_plane_geometry(result,center,normal)
result.reparam(param_u, param_v)
if(swap):
result.swap()
return result
def test_reparam(self):
# identity mapping, control points generated from knot vector
basis1 = BSplineBasis(4, [2, 2, 2, 2, 3, 6, 7, 7, 7, 7])
basis2 = BSplineBasis(3, [-3, -3, -3, 20, 30, 31, 31, 31])
surf = Surface(basis1, basis2)
self.assertAlmostEqual(surf.start(0), 2)
self.assertAlmostEqual(surf.end(0), 7)
self.assertAlmostEqual(surf.start(1), -3)
self.assertAlmostEqual(surf.end(1), 31)
surf.reparam((4, 10), (0, 9))
self.assertAlmostEqual(surf.start(0), 4)
self.assertAlmostEqual(surf.end(0), 10)
self.assertAlmostEqual(surf.start(1), 0)
self.assertAlmostEqual(surf.end(1), 9)
surf.reparam((5, 11), direction=0)
self.assertAlmostEqual(surf.start(0), 5)
self.assertAlmostEqual(surf.end(0), 11)
self.assertAlmostEqual(surf.start(1), 0)
self.assertAlmostEqual(surf.end(1), 9)
surf.reparam((5, 11), direction='v')
self.assertAlmostEqual(surf.start(0), 5)
self.assertAlmostEqual(surf.end(0), 11)
self.assertAlmostEqual(surf.start(1), 5)
self.assertAlmostEqual(surf.end(1), 11)
surf.reparam((-9, 9))
self.assertAlmostEqual(surf.start(0), -9)
self.assertAlmostEqual(surf.end(0), 9)
self.assertAlmostEqual(surf.start(1), 0)
self.assertAlmostEqual(surf.end(1), 1)
surf.reparam()
self.assertAlmostEqual(surf.start(0), 0)
self.assertAlmostEqual(surf.end(0), 1)
self.assertAlmostEqual(surf.start(1), 0)
self.assertAlmostEqual(surf.end(1), 1)
surf.reparam((4, 10), (0, 9))
surf.reparam(direction=1)
self.assertAlmostEqual(surf.start(0), 4)
self.assertAlmostEqual(surf.end(0), 10)
self.assertAlmostEqual(surf.start(1), 0)
self.assertAlmostEqual(surf.end(1), 1)
