def sphere(r=1, center=(0, 0, 0), type='radial'):
""" Create a solid sphere
:param float r: Radius
:param array-like center: Local origin of the sphere
:param string type: The type of parametrization ('radial' or 'square')
:return: A solid ball
:rtype: Volume
"""
if type == 'radial':
shell = SurfaceFactory.sphere(r, center)
midpoint = shell * 0 + center
return edge_surfaces(shell, midpoint)
elif type == 'square':
# based on the work of James E.Cobb: "Tiling the Sphere with Rational Bezier Patches"
# University of Utah, July 11, 1988. UUCS-88-009
b = BSplineBasis(order=5)
sr2 = sqrt(2)
sr3 = sqrt(3)
sr6 = sqrt(6)
cp = [
[-4 * (sr3 - 1), 4 * (1 - sr3), 4 * (1 - sr3),
4 * (3 - sr3)], # row 0
[-sr2, sr2 * (sr3 - 4), sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[
0, 4. / 3 * (1 - 2 * sr3), 4. / 3 * (1 - 2 * sr3),
4. / 3 * (5 - sr3)
],
[sr2, sr2 * (sr3 - 4), sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[4 * (sr3 - 1), 4 * (1 - sr3), 4 * (1 - sr3), 4 * (3 - sr3)],
[-sr2 * (4 - sr3), -sr2, sr2 * (sr3 - 4),
sr2 * (3 * sr3 - 2)], # row 1
[
-(3 * sr3 - 2) / 2, (2 - 3 * sr3) / 2, -(sr3 + 6) / 2,
(sr3 + 6) / 2
],
[0, sr2 * (2 * sr3 - 7) / 3, -5 * sr6 / 3, sr2 * (sr3 + 6) / 3],
[(3 * sr3 - 2) / 2, (2 - 3 * sr3) / 2, -(sr3 + 6) / 2,
(sr3 + 6) / 2],
[sr2 * (4 - sr3), -sr2, sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[
-4. / 3 * (2 * sr3 - 1), 0, 4. / 3 * (1 - 2 * sr3),
4 * (5 - sr3) / 3
], # row 2
[-sr2 / 3 * (7 - 2 * sr3), 0, -5 * sr6 / 3, sr2 * (sr3 + 6) / 3],
[0, 0, 4 * (sr3 - 5) / 3, 4 * (5 * sr3 - 1) / 9],
[sr2 / 3 * (7 - 2 * sr3), 0, -5 * sr6 / 3, sr2 * (sr3 + 6) / 3],
[
4. / 3 * (2 * sr3 - 1), 0, 4. / 3 * (1 - 2 * sr3),
4 * (5 - sr3) / 3
],
[-sr2 * (4 - sr3), sr2, sr2 * (sr3 - 4),
sr2 * (3 * sr3 - 2)], # row 3
[
-(3 * sr3 - 2) / 2, -(2 - 3 * sr3) / 2, -(sr3 + 6) / 2,
(sr3 + 6) / 2
],
[0, -sr2 * (2 * sr3 - 7) / 3, -5 * sr6 / 3, sr2 * (sr3 + 6) / 3],
[(3 * sr3 - 2) / 2, -(2 - 3 * sr3) / 2, -(sr3 + 6) / 2,
(sr3 + 6) / 2],
[sr2 * (4 - sr3), sr2, sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[-4 * (sr3 - 1), -4 * (1 - sr3), 4 * (1 - sr3),
4 * (3 - sr3)], # row 4
[-sr2, -sr2 * (sr3 - 4), sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[
0, -4. / 3 * (1 - 2 * sr3), 4. / 3 * (1 - 2 * sr3),
4. / 3 * (5 - sr3)
],
[sr2, -sr2 * (sr3 - 4), sr2 * (sr3 - 4), sr2 * (3 * sr3 - 2)],
[4 * (sr3 - 1), -4 * (1 - sr3), 4 * (1 - sr3), 4 * (3 - sr3)]
]
wmin = Surface(b, b, cp, rational=True)
wmax = wmin.clone().mirror([0, 0, 1])
vmax = wmin.clone().rotate(pi / 2, [1, 0, 0])
vmin = vmax.clone().mirror([0, 1, 0])
umax = vmin.clone().rotate(pi / 2, [0, 0, 1])
umin = umax.clone().mirror([1, 0, 0])
# ideally I would like to call edge_surfaces() now, but that function
# does not work with rational surfaces, so we'll just manually try
# and add some inner controlpoints
cp = np.zeros((5, 5, 5, 4))
cp[:, :, 0, :] = wmin[:, :, :]
cp[:, :, -1, :] = wmax[:, :, :]
cp[:, 0, :, :] = vmin[:, :, :]
cp[:, -1, :, :] = vmax[:, :, :]
cp[0, :, :, :] = umin[:, :, :]
cp[-1, :, :, :] = umax[:, :, :]
inner = np.linspace(-.5, .5, 3)
Y, X, Z = np.meshgrid(inner, inner, inner)
cp[1:4, 1:4, 1:4, 0] = X
cp[1:4, 1:4, 1:4, 1] = Y
cp[1:4, 1:4, 1:4, 2] = Z
cp[1:4, 1:4, 1:4, 3] = 1
ball = Volume(b, b, b, cp, rational=True, raw=True)
return r * ball + center
else:
raise ValueError('invalid type argument')
def sphere(r=1, center=(0,0,0), type='radial'):
""" Create a solid sphere
:param float r: Radius
:param array-like center: Local origin of the sphere
:param string type: The type of parametrization ('radial' or 'square')
:return: A solid ball
:rtype: Volume
"""
if type == 'radial':
shell = SurfaceFactory.sphere(r, center)
midpoint = shell*0 + center
return edge_surfaces(shell, midpoint)
elif type == 'square':
# based on the work of James E.Cobb: "Tiling the Sphere with Rational Bezier Patches"
# University of Utah, July 11, 1988. UUCS-88-009
b = BSplineBasis(order=5)
sr2 = sqrt(2)
sr3 = sqrt(3)
sr6 = sqrt(6)
cp = [[ -4*(sr3-1), 4*(1-sr3), 4*(1-sr3), 4*(3-sr3) ], # row 0
[ -sr2 , sr2*(sr3-4), sr2*(sr3-4), sr2*(3*sr3-2)],
[ 0 , 4./3*(1-2*sr3), 4./3*(1-2*sr3),4./3*(5-sr3) ],
[ sr2 , sr2*(sr3-4), sr2*(sr3-4), sr2*(3*sr3-2)],
[ 4*(sr3-1), 4*(1-sr3), 4*(1-sr3), 4*(3-sr3) ],
[ -sr2*(4-sr3), -sr2, sr2*(sr3-4), sr2*(3*sr3-2)], # row 1
[ -(3*sr3-2)/2, (2-3*sr3)/2, -(sr3+6)/2, (sr3+6)/2],
[ 0 , sr2*(2*sr3-7)/3, -5*sr6/3, sr2*(sr3+6)/3],
[ (3*sr3-2)/2, (2-3*sr3)/2, -(sr3+6)/2, (sr3+6)/2],
[ sr2*(4-sr3), -sr2, sr2*(sr3-4), sr2*(3*sr3-2)],
[ -4./3*(2*sr3-1), 0, 4./3*(1-2*sr3), 4*(5-sr3)/3], # row 2
[-sr2/3*(7-2*sr3), 0, -5*sr6/3, sr2*(sr3+6)/3],
[ 0 , 0, 4*(sr3-5)/3, 4*(5*sr3-1)/9],
[ sr2/3*(7-2*sr3), 0, -5*sr6/3, sr2*(sr3+6)/3],
[ 4./3*(2*sr3-1), 0, 4./3*(1-2*sr3), 4*(5-sr3)/3],
[ -sr2*(4-sr3), sr2, sr2*(sr3-4), sr2*(3*sr3-2)], # row 3
[ -(3*sr3-2)/2, -(2-3*sr3)/2, -(sr3+6)/2, (sr3+6)/2],
[ 0 ,-sr2*(2*sr3-7)/3, -5*sr6/3, sr2*(sr3+6)/3],
[ (3*sr3-2)/2, -(2-3*sr3)/2, -(sr3+6)/2, (sr3+6)/2],
[ sr2*(4-sr3), sr2, sr2*(sr3-4), sr2*(3*sr3-2)],
[ -4*(sr3-1), -4*(1-sr3), 4*(1-sr3), 4*(3-sr3) ], # row 4
[ -sr2 , -sr2*(sr3-4), sr2*(sr3-4), sr2*(3*sr3-2)],
[ 0 , -4./3*(1-2*sr3), 4./3*(1-2*sr3),4./3*(5-sr3) ],
[ sr2 , -sr2*(sr3-4), sr2*(sr3-4), sr2*(3*sr3-2)],
[ 4*(sr3-1), -4*(1-sr3), 4*(1-sr3), 4*(3-sr3) ]]
wmin = Surface(b,b,cp, rational=True)
wmax = wmin.clone().mirror([0,0,1])
vmax = wmin.clone().rotate(pi/2, [1,0,0])
vmin = vmax.clone().mirror([0,1,0])
umax = vmin.clone().rotate(pi/2, [0,0,1])
umin = umax.clone().mirror([1,0,0])
# ideally I would like to call edge_surfaces() now, but that function
# does not work with rational surfaces, so we'll just manually try
# and add some inner controlpoints
cp = np.zeros((5,5,5,4))
cp[ :, :, 0,:] = wmin[:,:,:]
cp[ :, :,-1,:] = wmax[:,:,:]
cp[ :, 0, :,:] = vmin[:,:,:]
cp[ :,-1, :,:] = vmax[:,:,:]
cp[ 0, :, :,:] = umin[:,:,:]
cp[-1, :, :,:] = umax[:,:,:]
inner = np.linspace(-.5,.5, 3)
Y, X, Z = np.meshgrid(inner,inner,inner)
cp[1:4,1:4,1:4,0] = X
cp[1:4,1:4,1:4,1] = Y
cp[1:4,1:4,1:4,2] = Z
cp[1:4,1:4,1:4,3] = 1
ball = Volume(b,b,b,cp,rational=True, raw=True)
return r*ball + center
else:
raise ValueError('invalid type argument')
