```# Test the paraboloid geometry manager.

import unittest
import numpy as N

from tracer.ray_bundle import RayBundle
from tracer.sphere_surface import CutSphereGM
from tracer.boundary_shape import BoundarySphere

class TestInterface(unittest.TestCase):
def setUp(self):
self.num_rays = 10
dir = N.tile(N.c_[[0, 0, -1]], (1, self.num_rays))
theta = N.linspace(0, 2*N.pi, self.num_rays, endpoint=False)
position = N.vstack((N.cos(theta), N.sin(theta), N.ones(self.num_rays)))

self._bund = RayBundle(position, dir)

# The boundary is positioned to create a bottom hemisphere.
boundary = BoundarySphere(radius=4., location=N.r_[0., 0., -4*N.sqrt(3)/2.])
self.gm = CutSphereGM(2., boundary)
self.prm = self.gm.find_intersections(N.eye(4), self._bund)

def test_find_intersections(self):
"""The correct parametric locations are found for cut sphere geometry"""
self.failUnlessEqual(self.prm.shape, (self.num_rays,))
N.testing.assert_array_almost_equal(self.prm, 1 + 2*N.sin(N.pi/3))

def test_get_normals(self):
"""Cut sphere surface returns center-pointing normals"""
self.gm.select_rays(N.arange(self.num_rays))
n = self.gm.get_normals()
N.testing.assert_array_almost_equal(n[-1,0], n[-1,1:])
N.testing.assert_array_almost_equal(self._bund.get_vertices()[:2],
-n[:2]/N.sqrt((n[:2]**2).sum(axis=0)))

def test_inters_points_global(self):
"""Cut sphere returns correct intersections"""
self.gm.select_rays(N.arange(self.num_rays))
pts = self.gm.get_intersection_points_global()
N.testing.assert_array_equal(pts[:2], self._bund.get_vertices()[:2])
N.testing.assert_array_almost_equal(pts[2], -2*N.sin(N.pi/3))

```