def test_surface_loft(self):
crv1 = Curve(BSplineBasis(3, range(11), 1), [[1,-1], [1,0], [1,1], [-1,1], [-1,0], [-1,-1]])
crv2 = CurveFactory.circle(2) + (0,0,1)
crv3 = Curve(BSplineBasis(4, range(11), 2), [[1,-1,2], [1,1,2], [-1,1,2], [-1,-1,2]])
crv4 = CurveFactory.circle(2) + (0,0,3)
surf = SurfaceFactory.loft(crv1, crv2, crv3, crv4)
crv1.set_dimension(3) # for convenience when evaluating
t = np.linspace( 0, 1, 13)
u = np.linspace(crv1.start(0), crv1.end(0), 13)
pt = crv1(u)
pt2 = surf(t,0).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv2.start(0), crv2.end(0), 13)
pt = crv2(u)
pt2 = surf(t,1).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv3.start(0), crv3.end(0), 13)
pt = crv3(u)
pt2 = surf(t,2).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv4.start(0), crv4.end(0), 13)
pt = crv4(u)
pt2 = surf(t,3).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def test_surface_loft(self):
crv1 = Curve(BSplineBasis(3, range(11), 1), [[1,-1], [1,0], [1,1], [-1,1], [-1,0], [-1,-1]])
crv2 = cf.circle(2) + (0,0,1)
crv3 = Curve(BSplineBasis(4, range(11), 2), [[1,-1,2], [1,1,2], [-1,1,2], [-1,-1,2]])
crv4 = cf.circle(2) + (0,0,3)
surf = sf.loft(crv1, crv2, crv3, crv4)
crv1.set_dimension(3) # for convenience when evaluating
t = np.linspace( 0, 1, 13)
u = np.linspace(crv1.start(0), crv1.end(0), 13)
pt = crv1(u)
pt2 = surf(t,0).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv2.start(0), crv2.end(0), 13)
pt = crv2(u)
pt2 = surf(t,1).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv3.start(0), crv3.end(0), 13)
pt = crv3(u)
pt2 = surf(t,2).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
u = np.linspace(crv4.start(0), crv4.end(0), 13)
pt = crv4(u)
pt2 = surf(t,3).reshape(13,3)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def test_curvature(self):
# linear curves have zero curvature
crv = Curve()
self.assertAlmostEqual(crv.curvature(.3), 0.0)
# test multiple evaluation points
t = np.linspace(0, 1, 10)
k = crv.curvature(t)
self.assertTrue(np.allclose(k, 0.0))
# test circle
crv = cf.circle(r=3) + [1, 1]
t = np.linspace(0, 2 * pi, 10)
k = crv.curvature(t)
self.assertTrue(np.allclose(k, 1.0 / 3.0)) # circles: k = 1/r
# test 3D (np.cross has different behaviour in 2D/3D)
crv.set_dimension(3)
k = crv.curvature(t)
self.assertTrue(np.allclose(k, 1.0 / 3.0)) # circles: k = 1/r
def test_thicken(self):
c = Curve() # 2D curve from (0,0) to (1,0)
s = sf.thicken(c, .5) # extend to y=[-.5, .5]
self.assertTupleEqual(s.order(), (2, 2))
self.assertTupleEqual(s.start(), (0, 0))
self.assertTupleEqual(s.end(), (1, 1))
self.assertTupleEqual(s.bounding_box()[0], (0.0, 1.0))
self.assertTupleEqual(s.bounding_box()[1], (-.5, .5))
# test a case with vanishing velocity. x'(t)=0, y'(t)=0 for t=0
c = Curve(BSplineBasis(3),
[[0, 0], [0, 0], [1, 0]]) # x(t)=t^2, y(t)=0
s = sf.thicken(c, .5)
self.assertTupleEqual(s.order(), (3, 2))
self.assertTupleEqual(s.start(), (0, 0))
self.assertTupleEqual(s.end(), (1, 1))
self.assertTupleEqual(s.bounding_box()[0], (0.0, 1.0))
self.assertTupleEqual(s.bounding_box()[1], (-.5, .5))
def myThickness(t):
return t**2
c = Curve(BSplineBasis(3))
s = sf.thicken(c, myThickness)
self.assertTupleEqual(s.order(), (3, 2))
self.assertTupleEqual(s.start(), (0, 0))
self.assertTupleEqual(s.end(), (1, 1))
self.assertTupleEqual(s.bounding_box()[0], (0.0, 1.0))
self.assertTupleEqual(s.bounding_box()[1], (-1.0, 1.0))
# test 3D geometry
c = Curve()
c.set_dimension(3)
s = sf.thicken(c, 1) # cylinder along x-axis with h=1, r=1
for u in np.linspace(s.start(0), s.end(0), 5):
for v in np.linspace(s.start(1), s.end(1), 5):
x = s(u, v)
self.assertAlmostEqual(x[1]**2 + x[2]**2,
1.0**2) # distance to x-axis
self.assertAlmostEqual(x[0],
u) # x coordinate should be linear
def test_thicken(self):
c = Curve() # 2D curve from (0,0) to (1,0)
s = SurfaceFactory.thicken(c, .5) # extend to y=[-.5, .5]
self.assertTupleEqual(s.order(), (2,2))
self.assertTupleEqual(s.start(), (0,0))
self.assertTupleEqual(s.end(), (1,1))
self.assertTupleEqual(s.bounding_box()[0], (0.0,1.0))
self.assertTupleEqual(s.bounding_box()[1], (-.5, .5))
# test a case with vanishing velocity. x'(t)=0, y'(t)=0 for t=0
c = Curve(BSplineBasis(3), [[0,0],[0,0],[1,0]]) # x(t)=t^2, y(t)=0
s = SurfaceFactory.thicken(c, .5)
self.assertTupleEqual(s.order(), (3,2))
self.assertTupleEqual(s.start(), (0,0))
self.assertTupleEqual(s.end(), (1,1))
self.assertTupleEqual(s.bounding_box()[0], (0.0,1.0))
self.assertTupleEqual(s.bounding_box()[1], (-.5, .5))
def myThickness(t):
return t**2
c = Curve(BSplineBasis(3))
s = SurfaceFactory.thicken(c, myThickness)
self.assertTupleEqual(s.order(), (3,2))
self.assertTupleEqual(s.start(), (0,0))
self.assertTupleEqual(s.end(), (1,1))
self.assertTupleEqual(s.bounding_box()[0], ( 0.0, 1.0))
self.assertTupleEqual(s.bounding_box()[1], (-1.0, 1.0))
# test 3D geometry
c = Curve()
c.set_dimension(3)
s = SurfaceFactory.thicken(c, 1) # cylinder along x-axis with h=1, r=1
for u in np.linspace(s.start(0), s.end(0), 5):
for v in np.linspace(s.start(1), s.end(1), 5):
x = s(u, v)
self.assertAlmostEqual(x[1]**2+x[2]**2, 1.0**2) # distance to x-axis
self.assertAlmostEqual(x[0], u) # x coordinate should be linear
