def plane(self):
dim = int( self.read_next_non_whitespace().strip())
center = np.array(next(self.fstream).split(), dtype=float)
normal = np.array(next(self.fstream).split(), dtype=float)
x_axis = np.array(next(self.fstream).split(), dtype=float)
finite = next(self.fstream).strip() != '0'
if finite:
param_u= np.array(next(self.fstream).split(), dtype=float)
param_v= np.array(next(self.fstream).split(), dtype=float)
else:
param_u= [-state.unlimited, +state.unlimited]
param_v= [-state.unlimited, +state.unlimited]
swap = next(self.fstream).strip() != '0'
result = Surface() * [param_u[1]-param_u[0], param_v[1]-param_v[0]] + [param_u[0],param_v[0]]
result.rotate(rotate_local_x_axis(x_axis, normal))
result = flip_and_move_plane_geometry(result,center,normal)
result.reparam(param_u, param_v)
if(swap):
result.swap()
return result
def test_swap(self):
# more or less random 3D surface with p=[2,2] and n=[4,3]
controlpoints = [[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 1],
[1, 0, .5], [1, 1, 1], [2, 1, 1], [2, 2, .5],
[2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, .64, 2, 2, 2])
basis2 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
surf = Surface(basis1, basis2, controlpoints)
evaluation_point1 = surf(0.23, .56)
control_point1 = surf[1] # this is control point i=(1,0), when n=(4,3)
surf.swap()
evaluation_point2 = surf(0.56, .23)
control_point2 = surf[3] # this is control point i=(0,1), when n=(3,4)
# ensure that surface has not chcanged, by comparing evaluation of it
self.assertAlmostEqual(evaluation_point1[0], evaluation_point2[0])
self.assertAlmostEqual(evaluation_point1[1], evaluation_point2[1])
self.assertAlmostEqual(evaluation_point1[2], evaluation_point2[2])
# check that the control points have re-ordered themselves
self.assertEqual(control_point1[0], control_point2[0])
self.assertEqual(control_point1[1], control_point2[1])
self.assertEqual(control_point1[2], control_point2[2])
def test_rational_derivative(self):
# testing the parametrization x(u,v) = [.5*u^3*(1-v)^3 / ((1-v)^3*(1-u)^3 + .5*u^3*(1-v)^3), 0]
# dx/du = (6*u^2*(u - 1)^2)/(u^3 - 6*u^2 + 6*u - 2)^2
# d2x/du2 = -(12*u*(u^5 - 3*u^4 + 2*u^3 + 4*u^2 - 6*u + 2))/(u^3 - 6*u^2 + 6*u - 2)^3
# d3x/du3 = (12*(3*u^8 - 12*u^7 + 10*u^6 + 48*u^5 - 156*u^4 + 176*u^3 - 72*u^2 + 4))/(u^3 - 6*u^2 + 6*u - 2)^4
# dx/dv = 0
controlpoints = [[0, 0, 1], [0, 0, 0], [0, 0, 0], [.5, 0, .5],
[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0],
[0, 0, 0], [0, 0, 0]]
basis = BSplineBasis(4)
surf = Surface(basis, basis, controlpoints, rational=True)
def expect_derivative(u, v):
return (6 * u**2 * (u - 1)**2) / (u**3 - 6 * u**2 + 6 * u - 2)**2
def expect_derivative_2(u, v):
return -(12 * u *
(u**5 - 3 * u**4 + 2 * u**3 + 4 * u**2 - 6 * u + 2)) / (
u**3 - 6 * u**2 + 6 * u - 2)**3
def expect_derivative_3(u, v):
return (12 * (3 * u**8 - 12 * u**7 + 10 * u**6 + 48 * u**5 -
156 * u**4 + 176 * u**3 - 72 * u**2 + 4)) / (
u**3 - 6 * u**2 + 6 * u - 2)**4
# insert a few more knots to spice things up
surf.insert_knot([.3, .51], 0)
surf.insert_knot([.41, .53, .92], 1)
# test first derivatives
self.assertAlmostEqual(
surf.derivative(0.32, 0.22, d=(1, 0))[0],
expect_derivative(0.32, 0.22))
self.assertAlmostEqual(surf.derivative(0.32, 0.22, d=(1, 0))[1], 0)
self.assertAlmostEqual(
surf.derivative(0.71, 0.22, d=(1, 0))[0],
expect_derivative(0.71, 0.22))
self.assertAlmostEqual(
surf.derivative(0.71, 0.62, d=(1, 0))[0],
expect_derivative(0.71, 0.62))
# test second derivatives
self.assertAlmostEqual(
surf.derivative(0.32, 0.22, d=(2, 0))[0],
expect_derivative_2(0.32, 0.22))
self.assertAlmostEqual(
surf.derivative(0.71, 0.22, d=(2, 0))[0],
expect_derivative_2(0.71, 0.22))
self.assertAlmostEqual(
surf.derivative(0.71, 0.62, d=(2, 0))[0],
expect_derivative_2(0.71, 0.62))
# all cross derivatives vanish in this particular example
self.assertAlmostEqual(surf.derivative(0.32, 0.22, d=(1, 1))[0], 0)
self.assertAlmostEqual(surf.derivative(0.32, 0.22, d=(2, 1))[0], 0)
self.assertAlmostEqual(surf.derivative(0.32, 0.22, d=(1, 2))[0], 0)
# test third derivatives
self.assertAlmostEqual(
surf.derivative(0.32, 0.22, d=(3, 0))[0],
expect_derivative_3(0.32, 0.22))
self.assertAlmostEqual(
surf.derivative(0.71, 0.22, d=(3, 0))[0],
expect_derivative_3(0.71, 0.22))
self.assertAlmostEqual(
surf.derivative(0.71, 0.62, d=(3, 0))[0],
expect_derivative_3(0.71, 0.62))
# swapping u for v and symmetric logic
surf.swap()
self.assertAlmostEqual(
surf.derivative(0.22, 0.32, d=(0, 2))[0],
expect_derivative_2(0.32, 0.22))
self.assertAlmostEqual(
surf.derivative(0.22, 0.71, d=(0, 2))[0],
expect_derivative_2(0.71, 0.22))
self.assertAlmostEqual(
surf.derivative(0.62, 0.71, d=(0, 2))[0],
expect_derivative_2(0.71, 0.62))
self.assertAlmostEqual(
surf.derivative(0.22, 0.32, d=(0, 3))[0],
expect_derivative_3(0.32, 0.22))
self.assertAlmostEqual(
surf.derivative(0.22, 0.71, d=(0, 3))[0],
expect_derivative_3(0.71, 0.22))
self.assertAlmostEqual(
surf.derivative(0.62, 0.71, d=(0, 3))[0],
expect_derivative_3(0.71, 0.62))