def test_surface_torus(self):
# default torus
surf = SurfaceFactory.torus(1, 3)
start = surf.start()
end = surf.end()
# check a 13 evaluation points of v-evaluation (around the z-axis)
v = np.linspace(start[1], end[1], 13)
# check minor-circle u=0 (outmost ring)
x = surf.evaluate(0, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1], 4 * 4) # check radius=4
self.assertAlmostEqual(pt[2], 0) # check height=0
# check minor-circle u=pi (innermost ring)
x = surf.evaluate(pi, v)
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], 0) # check height=0
# check minor-circle u=pi/2 (topmost ring)
x = surf.evaluate(pi / 2, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1], 3 * 3) # check radius=3
self.assertAlmostEqual(pt[2], 1) # check height=1
# check minor-circle u=3*pi/2 (mid-evaluation)
x = surf.evaluate(3 * pi / 4, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1],
(3 - 1.0 / sqrt(2))**2) # check radius=3-1/sqrt(2)
self.assertAlmostEqual(pt[2], 1.0 / sqrt(2)) # check height=1/sqrt(2)
def test_surface_torus(self):
# default torus
surf = sf.torus(1, 3)
start = surf.start()
end = surf.end()
# check a 13 evaluation points of v-evaluation (around the z-axis)
v = np.linspace(start[1], end[1], 13)
# check minor-circle u=0 (outmost ring)
x = surf.evaluate(0, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1],
4 * 4) # check radius=4
self.assertAlmostEqual(pt[2], 0) # check height=0
# check minor-circle u=pi (innermost ring)
x = surf.evaluate(pi, v)
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], 0) # check height=0
# check minor-circle u=pi/2 (topmost ring)
x = surf.evaluate(pi / 2, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(pt[0] * pt[0] + pt[1] * pt[1],
3 * 3) # check radius=3
self.assertAlmostEqual(pt[2], 1) # check height=1
# check minor-circle u=3*pi/2 (mid-evaluation)
x = surf.evaluate(3 * pi / 4, v)
for pt in np.array(x[0, :, :]):
self.assertAlmostEqual(
pt[0] * pt[0] + pt[1] * pt[1],
(3 - 1.0 / sqrt(2))**2) # check radius=3-1/sqrt(2)
self.assertAlmostEqual(pt[2],
1.0 / sqrt(2)) # check height=1/sqrt(2)
def torus(self):
dim = int( self.read_next_non_whitespace().strip())
r2 = float( next(self.fstream).strip())
r1 = float( next(self.fstream).strip())
center = np.array(next(self.fstream).split(), dtype=float)
z_axis = np.array(next(self.fstream).split(), dtype=float)
x_axis = np.array(next(self.fstream).split(), dtype=float)
select_out= next(self.fstream).strip() != '0' # I have no idea what this does :(
param_u = np.array(next(self.fstream).split(), dtype=float)
param_v = np.array(next(self.fstream).split(), dtype=float)
swap = next(self.fstream).strip() != '0'
result = SurfaceFactory.torus(minor_r=r1, major_r=r2, center=center, normal=z_axis, xaxis=x_axis)
result.reparam(param_u, param_v)
if(swap):
result.swap()
return result
def test_periodic_split(self):
# create a double-periodic spline on the knot vector [-1,0,0,1,1,2,2,3,3,4,4,5]*pi/2
surf = sf.torus()
surf2 = surf.split(pi / 2, 0) # split on existing knot
surf3 = surf.split(1.23, 1) # split between knots
surf4 = surf2.split(pi, 1) # split both periodicities
# check periodicity tags
self.assertEqual(surf.periodic(0), True)
self.assertEqual(surf.periodic(1), True)
self.assertEqual(surf2.periodic(0), False)
self.assertEqual(surf2.periodic(1), True)
self.assertEqual(surf3.periodic(0), True)
self.assertEqual(surf3.periodic(1), False)
self.assertEqual(surf4.periodic(0), False)
self.assertEqual(surf4.periodic(1), False)
# check parametric domain boundaries
self.assertAlmostEqual(surf2.start(0), pi / 2)
self.assertAlmostEqual(surf2.end(0), 5 * pi / 2)
self.assertAlmostEqual(surf3.start(0), 0)
self.assertAlmostEqual(surf3.end(0), 2 * pi)
self.assertAlmostEqual(surf3.start(1), 1.23)
self.assertAlmostEqual(surf3.end(1), 1.23 + 2 * pi)
# check knot vector lengths
self.assertEqual(len(surf2.knots(0, True)), 12)
self.assertEqual(len(surf2.knots(1, True)), 12)
self.assertEqual(len(surf3.knots(0, True)), 12)
self.assertEqual(len(surf3.knots(1, True)), 14)
self.assertEqual(len(surf4.knots(0, True)), 12)
self.assertEqual(len(surf4.knots(1, True)), 12)
# check that evaluation is unchanged over a 9x9 grid of shared parametric coordinates
u = np.linspace(pi / 2, 2 * pi, 9)
v = np.linspace(pi, 2 * pi, 9)
pt = surf(u, v)
pt2 = surf2(u, v)
pt3 = surf3(u, v)
pt4 = surf4(u, v)
self.assertAlmostEqual(np.linalg.norm(pt - pt2), 0.0)
self.assertAlmostEqual(np.linalg.norm(pt - pt3), 0.0)
self.assertAlmostEqual(np.linalg.norm(pt - pt4), 0.0)
# Examples on how to write geometries to file
#
# Author: Kjetil Andre Johannessen
# Institute: Norwegian University of Science and Technology (NTNU)
# Date: March 2016
#
from sys import path
path.append('../')
from splipy.io import G2, STL
import splipy.surface_factory as surfaces
# create a NURBS torus
torus = surfaces.torus(minor_r=1, major_r=4)
# STL files are tessellated linear triangles. View with i.e. meshlab
with STL('torus.stl') as my_file:
my_file.write(torus, n=(50, 150)) # specify resolution of 50x150 evaluation pts
# G2 files are native GoTools (http://www.sintef.no/projectweb/geometry-toolkits/gotools/)
with G2('torus.g2') as my_file:
my_file.write(torus)