def test_revolve(self):
# square torus
square = CurveFactory.n_gon(4)
square.rotate(pi / 2, (1, 0, 0))
square.translate((2, 0, 0)) # in xz-plane with corners at (3,0),(2,1),(1,0),(2,-1)
surf = SurfaceFactory.revolve(square)
surf.reparam() # set parametric space to (0,1)^2
v = np.linspace(0, 1, 13)
x = surf.evaluate(0, v) # outer ring evaluation u=0
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(np.linalg.norm(pt, 2), 3.0) # check radius=3
x = surf.evaluate(.25, v) # top ring evaluation u=.25
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1], 2 * 2) # check radius=2
self.assertAlmostEqual(pt[2], 1) # check height=1
x = surf.evaluate(.375, v) # mid inner ring evaluation u=.375
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1], 1.5 * 1.5) # check radius=1.5
self.assertAlmostEqual(pt[2], .5) # check height=0.5
# incomplete revolve
c = CurveFactory.line([1,0], [0,1], relative=True)
surf = SurfaceFactory.revolve(c, theta=4.2222, axis=[0,1,0])
surf.reparam()
u = np.linspace(0,1,7)
v = np.linspace(0,1,7)
x = surf(u,v)
for uPt in x:
for pt in uPt:
self.assertAlmostEqual(pt[0]**2 + pt[2]**2, 1.0) # radius 1 from y-axis
def test_revolve(self):
# square torus
square = cf.n_gon(4)
square.rotate(pi / 2, (1, 0, 0))
square.translate(
(2, 0, 0)) # in xz-plane with corners at (3,0),(2,1),(1,0),(2,-1)
surf = sf.revolve(square)
surf.reparam() # set parametric space to (0,1)^2
v = np.linspace(0, 1, 13)
x = surf.evaluate(0, v) # outer ring evaluation u=0
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(np.linalg.norm(pt, 2),
3.0) # check radius=3
x = surf.evaluate(.25, v) # top ring evaluation u=.25
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1],
2 * 2) # check radius=2
self.assertAlmostEqual(pt[2], 1) # check height=1
x = surf.evaluate(.375, v) # mid inner ring evaluation u=.375
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1],
1.5 * 1.5) # check radius=1.5
self.assertAlmostEqual(pt[2], .5) # check height=0.5
# incomplete revolve
c = cf.line([1, 0], [0, 1], relative=True)
surf = sf.revolve(c, theta=4.2222, axis=[0, 1, 0])
surf.reparam()
u = np.linspace(0, 1, 7)
v = np.linspace(0, 1, 7)
x = surf(u, v)
for uPt in x:
for pt in uPt:
self.assertAlmostEqual(pt[0]**2 + pt[2]**2,
1.0) # radius 1 from y-axis
def test_2d_self_connection(self):
c = curve_factory.line([1, 0], [2, 0])
surf = surface_factory.revolve(c)
surf = surf.split(surf.knots('v')[0],
direction='v') # break periodicity
surf.set_dimension(2)
model = SplineModel(2, 2)
model.add(surf)
writer = IFEMWriter(model)
expected = [IFEMConnection(1, 1, 3, 4, 0)]
for connection, want in zip(writer.connections(), expected):
self.assertEqual(connection, want)
c1 = curves.circle_segment(pi/3)
c2 = c1.clone().rotate(2*pi/3) + [1,0]
c3 = c1.clone().rotate(4*pi/3) + [cos(pi/3), sin(pi/3)]
# merge the three circles into one, and center it at the origin
c = c1.append(c2).append(c3)
c -= c.center()
# plot the reuleaux triangle
t = np.linspace(c.start(0), c.end(0), 151) # 151 parametric evaluation points
x = c(t) # evaluate (x,y)-coordinates
plt.plot(x[:,0], x[:,1])
plt.axis('equal')
plt.show()
# split the triangle in two, and align this with the y-axis
two_parts = c.split((c.start(0) + c.end(0)) / 2.0)
half_curve = two_parts[0].rotate(2*pi/3)
# create a surface by revolving around its symmetry axis (y-axis)
surf = surfaces.revolve(half_curve, axis=[0,1,0])
# plot the resulting surface on a uniform grid of 71x71 evaluation points
u = np.linspace(surf.start(0), surf.end(0), 71)
v = np.linspace(surf.start(1), surf.end(1), 71)
x = surf(u,v)
ax = plt.figure().gca(projection='3d')
ax.plot_wireframe(x[:,:,0], x[:,:,1], x[:,:,2])
plt.show()
# create the three sides of the triangle, each consisting of a circle segment
c1 = curves.circle_segment(pi / 3)
c2 = c1.clone().rotate(2 * pi / 3) + [1, 0]
c3 = c1.clone().rotate(4 * pi / 3) + [cos(pi / 3), sin(pi / 3)]
# merge the three circles into one, and center it at the origin
c = c1.append(c2).append(c3)
c -= c.center()
# plot the reuleaux triangle
t = np.linspace(c.start(0), c.end(0), 151) # 151 parametric evaluation points
x = c(t) # evaluate (x,y)-coordinates
plt.plot(x[:, 0], x[:, 1])
plt.axis('equal')
plt.show()
# split the triangle in two, and align this with the y-axis
two_parts = c.split((c.start(0) + c.end(0)) / 2.0)
half_curve = two_parts[0].rotate(2 * pi / 3)
# create a surface by revolving around its symmetry axis (y-axis)
surf = surfaces.revolve(half_curve, axis=[0, 1, 0])
# plot the resulting surface on a uniform grid of 71x71 evaluation points
u = np.linspace(surf.start(0), surf.end(0), 71)
v = np.linspace(surf.start(1), surf.end(1), 71)
x = surf(u, v)
ax = plt.figure().gca(projection='3d')
ax.plot_wireframe(x[:, :, 0], x[:, :, 1], x[:, :, 2])
plt.show()
