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))
def revolve(surf, theta=2 * pi, axis=(0, 0, 1)):
""" Revolve a volume by sweeping a surface in a rotational fashion around
an axis.
:param Surface surf: Surface to revolve
:param float theta: Angle to revolve, in radians
:param array-like axis: Axis of rotation
:return: The revolved surface
:rtype: Volume
"""
surf = surf.clone() # clone input surface, throw away old reference
surf.set_dimension(3) # add z-components (if not already present)
surf.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
surf.rotate(-normal_theta, [0, 0, 1])
surf.rotate(-normal_phi, [0, 1, 0])
path = CurveFactory.circle_segment(theta=theta)
n = len(surf) # number of control points of the surface
m = len(path) # number of control points of the sweep
cp = np.zeros((m * n, 4))
dt = np.sign(theta) * (path.knots(0)[1] - path.knots(0)[0]) / 2.0
for i in range(m):
weight = path[i, -1]
cp[i * n:(i + 1) * n, :] = np.reshape(
surf.controlpoints.transpose(1, 0, 2), (n, 4))
cp[i * n:(i + 1) * n, 2] *= weight
cp[i * n:(i + 1) * n, 3] *= weight
surf.rotate(dt)
result = Volume(surf.bases[0], surf.bases[1], path.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0, 1, 0])
result.rotate(normal_theta, [0, 0, 1])
return result
def revolve(surf, theta=2 * pi, axis=(0,0,1)):
""" Revolve a volume by sweeping a surface in a rotational fashion around
an axis.
:param Surface surf: Surface to revolve
:param float theta: Angle to revolve, in radians
:param array-like axis: Axis of rotation
:return: The revolved surface
:rtype: Volume
"""
surf = surf.clone() # clone input surface, throw away old reference
surf.set_dimension(3) # add z-components (if not already present)
surf.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
surf.rotate(-normal_theta, [0,0,1])
surf.rotate(-normal_phi, [0,1,0])
path = CurveFactory.circle_segment(theta=theta)
n = len(surf) # number of control points of the surface
m = len(path) # number of control points of the sweep
cp = np.zeros((m * n, 4))
dt = np.sign(theta)*(path.knots(0)[1] - path.knots(0)[0]) / 2.0
for i in range(m):
weight = path[i,-1]
cp[i * n:(i + 1) * n, :] = np.reshape(surf.controlpoints.transpose(1, 0, 2), (n, 4))
cp[i * n:(i + 1) * n, 2] *= weight
cp[i * n:(i + 1) * n, 3] *= weight
surf.rotate(dt)
result = Volume(surf.bases[0], surf.bases[1], path.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0,1,0])
result.rotate(normal_theta, [0,0,1])
return result
