def test_concave_sphere(self):
r3 = 10
s3 = Spherical(r=-r3)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s3_dir = s3.intersect(self.p0, self.dir0, self.eps, self.z_dir)
p0s3_tnp = s3.intersect_tangent_plane(self.p0, self.dir0,
self.eps, self.z_dir)
assert ((p0s3_dir[0], p0s3_dir[1].all()) ==
(p0s3_tnp[0], p0s3_tnp[1].all()))
p0s3 = p0s3_dir
assert ((p0s3[0], p0s3[1].all()) == (p0_truth[0], p0_truth[1].all()))
# test for p1 ray, (0, 1, 0), (0, 0, 1)
sag3 = r3 - sqrt(r3*r3 - 1.0)
p1_truth = 1-sag3, np.array([0., 1., -sag3])
p1s3_tnp = s3.intersect_tangent_plane(self.p1, self.dir0,
self.eps, self.z_dir)
p1s3_dir = s3.intersect(self.p1, self.dir0, self.eps, self.z_dir)
assert ((p1s3_dir[0], p1s3_dir[1].all()) ==
(p1s3_tnp[0], p1s3_tnp[1].all()))
p1s3 = p1s3_dir
assert p1s3[0] == approx(p1_truth[0], rel=1e-14, abs=1e-14)
assert p1s3[1].all() == p1_truth[1].all()
dir_p1s3 = s3.normal(p1s3[1])
dir_p1s3_truth = normalize(p1_truth[1] - np.array([0, 0, -r3]))
assert dir_p1s3.all() == dir_p1s3_truth.all()
def test_dbgauss_s1(self):
r1 = 56.20238
c1 = 1/r1
y0 = 25.0
s1 = Spherical(c=c1)
p1 = np.array([0., y0, 0.])
sag1 = r1 - sqrt(r1*r1 - y0*y0)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s1 = s1.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert ((p0s1[0], p0s1[1].all()) ==
(p0_truth[0], p0_truth[1].all()))
self.assertEqual(p0s1[0], 1.0)
npt.assert_allclose(p0s1[1], np.array([0., 0., 0.]),
rtol=1e-14, atol=1e-14)
# test for p1 ray, (0, 1, 0), (0, 0, 1)
p1_truth = 5.866433424372758, np.array([0., y0, sag1])
p1s1 = s1.intersect(p1, self.dir0, self.eps, self.z_dir)
assert p1s1[0] == approx(p1_truth[0], rel=1e-14, abs=1e-14)
npt.assert_allclose(p1s1[1], p1_truth[1], rtol=1e-14)
dir_p1s1 = s1.normal(p1s1[1])
dir_p1s1_truth = -normalize(p1_truth[1] - np.array([0, 0, r1]))
assert dir_p1s1.all() == dir_p1s1_truth.all()
npt.assert_allclose(dir_p1s1, dir_p1s1_truth, rtol=1e-14)
def test_planar_sphere(self):
s1 = Spherical(c=0.0)
p_truth = 1.0, np.array([0., 0., 0.])
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0s1 = s1.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert (p0s1[0], p0s1[1].all()) == (p_truth[0], p_truth[1].all())
# test for p1 ray, (0, 1, 0), (0, 0, 1)
p1s1 = s1.intersect(self.p1, self.dir0, self.eps, self.z_dir)
assert ((p1s1[0], p1s1[1].all()) ==
(p_truth[0], np.array([0., 1., 0.]).all()))
def test_convex_sphere(self):
r2 = 10
c2 = 1/r2
s2 = Spherical(c=c2)
# test for p0 ray, (0, 0, 0), (0, 0, 1)
p0_truth = 1.0, np.array([0., 0., 0.])
p0s2_dir = s2.intersect(self.p0, self.dir0, self.eps, self.z_dir)
p0s2_tnp = s2.intersect_tangent_plane(self.p0, self.dir0,
self.eps, self.z_dir)
assert ((p0s2_dir[0], p0s2_dir[1].all()) ==
(p0s2_tnp[0], p0s2_tnp[1].all()))
p0s2 = p0s2_dir
assert ((p0s2[0], p0s2[1].all()) == (p0_truth[0], p0_truth[1].all()))
# A spherical EvenPolynomial will use iteration to find the
# intersection. Use this case to further check results
sa2 = EvenPolynomial(c=c2)
p0sa2 = sa2.intersect(self.p0, self.dir0, self.eps, self.z_dir)
assert ((p0sa2[0], p0sa2[1].all()) ==
(p0_truth[0], p0_truth[1].all()))
assert (p0s2_dir[0], p0s2_dir[1].all()) == (p0sa2[0], p0sa2[1].all())
# test for p1 ray, (0, 1, 0), (0, 0, 1)
sag2 = r2 - sqrt(r2*r2 - 1.0)
p1_truth = 1+sag2, np.array([0., 1., sag2])
p1s2_dir = s2.intersect(self.p1, self.dir0, self.eps, self.z_dir)
p1s2_tnp = s2.intersect_tangent_plane(self.p1, self.dir0,
self.eps, self.z_dir)
assert ((p1s2_dir[0], p1s2_dir[1].all()) ==
(p1s2_tnp[0], p1s2_tnp[1].all()))
p1s2 = p1s2_dir
assert ((p1s2[0], p1s2[1].all()) ==
(p1_truth[0], p1_truth[1].all()))
dir_p1s2 = s2.normal(p1s2[1])
dir_p1s2_truth = -normalize(p1_truth[1] - np.array([0, 0, r2]))
assert dir_p1s2.all() == dir_p1s2_truth.all()