def testStrValue(self):
"""Test if __str__ produces output consistent with its spec.
This is necessarily a loose test, as the behavior of __str__
is (deliberately) incompletely specified.
"""
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
numbers = re.findall(r'(?:\+|-)?(?:[\d.]+|nan|inf)', str(point))
self.assertEqual(2, len(numbers),
"String '%s' should have exactly two coordinates." % (point,))
# Low precision to allow for only a few digits in string.
if not math.isnan(point.getLongitude().asRadians()):
self.assertAlmostEqual(
point.getLongitude().asDegrees(), float(numbers[0]), delta=1e-6)
else:
self.assertRegexpMatches(numbers[0], r'-?nan')
if not math.isnan(point.getLatitude().asRadians()):
self.assertAlmostEqual(
point.getLatitude().asDegrees(), float(numbers[1]), delta=1e-6)
# Latitude must be signed
self.assertTrue(numbers[1].startswith("+") or
numbers[1].startswith("-"))
else:
# Some C++ compilers will output NaN with a sign, others won't
self.assertRegexpMatches(numbers[1], r'(?:\+|-)?nan')
def testGetLatitudeValue(self):
"""Test if getLatitude() returns the expected value.
"""
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
self.assertIsInstance(point.getLatitude(), afwGeom.Angle)
# Behavior for non-finite points is undefined; depends on internal
# data representation
if point.isFinite():
self.assertGreaterEqual(point.getLatitude().asDegrees(), -90.0)
self.assertLessEqual(point.getLatitude().asDegrees(), 90.0)
self.assertAnglesAlmostEqual(lat, point.getLatitude())
def testIterResult(self):
"""Test if iteration returns the expected values.
"""
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
if point.isFinite():
# Test mechanics directly
it = iter(point)
self.assertEqual(point.getLongitude(), next(it))
self.assertEqual(point.getLatitude(), next(it))
with self.assertRaises(StopIteration):
next(it)
# Intended use case
lon, lat = point
self.assertEqual(point.getLongitude(), lon)
self.assertEqual(point.getLatitude(), lat)
def testVector3dConstructor(self):
# test poles
for z in (-11.3, -1.1, 0.1, 2.5): # arbitrary non-zero values
sp = SpherePoint(lsst.sphgeom.Vector3d(0.0, 0.0, z))
self.assertTrue(sp.atPole())
self.assertEqual(sp.getLongitude().asRadians(), 0.0)
if z < 0:
self.assertAnglesAlmostEqual(sp.getLatitude(), -90 * degrees)
else:
self.assertAnglesAlmostEqual(sp.getLatitude(), 90 * degrees)
spx = SpherePoint(lsst.sphgeom.Vector3d(11.1, 0.0, 0.0))
self.assertAnglesAlmostEqual(spx.getLongitude(), 0.0 * degrees)
self.assertAnglesAlmostEqual(spx.getLatitude(), 0.0 * degrees)
spy = SpherePoint(lsst.sphgeom.Vector3d(0.0, 234234.5, 0.0))
self.assertAnglesAlmostEqual(spy.getLongitude(), 90.0 * degrees)
self.assertAnglesAlmostEqual(spy.getLatitude(), 0.0 * degrees)
spxy = SpherePoint(lsst.sphgeom.Vector3d(7.5, -7.5, 0.0))
self.assertAnglesAlmostEqual(spxy.getLongitude(), -45.0 * degrees)
self.assertAnglesAlmostEqual(spxy.getLatitude(), 0.0 * degrees)
spxz = SpherePoint(lsst.sphgeom.Vector3d(100.0, 0.0, -100.0))
self.assertAnglesAlmostEqual(spxz.getLongitude(), 0.0 * degrees)
self.assertAnglesAlmostEqual(spxz.getLatitude(), -45.0 * degrees)
# Only one singularity: a vector of all zeros
with self.assertRaises(pexEx.InvalidParameterError):
SpherePoint(lsst.sphgeom.Vector3d(0.0, 0.0, 0.0))
def testGetItemValue(self):
"""Test if indexing returns the expected value.
"""
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
self.assertIsInstance(point[-2], afwGeom.Angle)
self.assertIsInstance(point[-1], afwGeom.Angle)
self.assertIsInstance(point[0], afwGeom.Angle)
self.assertIsInstance(point[1], afwGeom.Angle)
if not math.isnan(point.getLongitude().asRadians()):
self.assertEqual(point.getLongitude(), point[-2])
self.assertEqual(point.getLongitude(), point[0])
else:
self.assertTrue(math.isnan(point[-2].asRadians()))
self.assertTrue(math.isnan(point[0].asRadians()))
if not math.isnan(point.getLatitude().asRadians()):
self.assertEqual(point.getLatitude(), point[-1])
self.assertEqual(point.getLatitude(), point[1])
else:
self.assertTrue(math.isnan(point[-1].asRadians()))
self.assertTrue(math.isnan(point[1].asRadians()))
def testReprValue(self):
"""Test if __repr__ is a machine-readable representation.
"""
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
pointRepr = repr(point)
self.assertIn("degrees", pointRepr)
self.assertEqual(2, len(pointRepr.split(",")))
spcopy = eval(pointRepr)
self.assertAnglesAlmostEqual(
point.getLongitude(), spcopy.getLongitude())
self.assertAnglesAlmostEqual(
point.getLatitude(), spcopy.getLatitude())
def testBearingToValueSingular(self):
"""White-box test: bearingTo() may be unstable if points are near opposite poles.
This test is motivated by an error analysis of the `bearingTo`
implementation. It may become irrelevant if the implementation
changes.
"""
southPole = SpherePoint(0.0*degrees, self.nextUp(-90.0*degrees))
northPoleSame = SpherePoint(0.0*degrees, self.nextDown(90.0*degrees))
# Don't let it be on exactly the opposite side.
northPoleOpposite = SpherePoint(
180.0*degrees, self.nextDown(northPoleSame.getLatitude()))
self.assertAnglesAlmostEqual(southPole.bearingTo(northPoleSame),
afwGeom.HALFPI*afwGeom.radians)
self.assertAnglesAlmostEqual(southPole.bearingTo(northPoleOpposite),
(afwGeom.PI + afwGeom.HALFPI)*afwGeom.radians)
def testSeparationValueAbsolute(self):
"""Test if separation() returns specific values.
"""
# Test from "Meeus, p. 110" (test originally written for coord::Coord;
# don't know exact reference)
spica = SpherePoint(201.2983, -11.1614, degrees)
arcturus = SpherePoint(213.9154, 19.1825, degrees)
# Verify to precision of quoted distance and positions.
self.assertAlmostEqual(32.7930,
spica.separation(arcturus).asDegrees(), 4)
# Verify small angles: along a constant ra, add an arcsec to spica dec.
epsilon = 1.0 * afwGeom.arcseconds
spicaPlus = SpherePoint(spica.getLongitude(),
spica.getLatitude() + epsilon)
self.assertAnglesAlmostEqual(epsilon, spicaPlus.separation(spica))
def testOffsetValue(self):
"""Test if offset() returns the expected value.
"""
# This should cover arcs over the meridian, across the pole, etc.
for lon1, lat1 in self._dataset:
point1 = SpherePoint(lon1, lat1)
if point1.atPole():
continue
for lon2, lat2 in self._dataset:
if lon1 == lon2 and lat1 == lat2:
continue
point2 = SpherePoint(lon2, lat2)
bearing = point1.bearingTo(point2)
distance = point1.separation(point2)
newPoint = point1.offset(bearing, distance)
self.assertIsInstance(newPoint, SpherePoint)
if point1.isFinite() and point2.isFinite():
if not point2.atPole():
self.assertAnglesAlmostEqual(
point2.getLongitude(), newPoint.getLongitude())
self.assertAnglesAlmostEqual(
point2.getLatitude(), newPoint.getLatitude())
else:
self.assertTrue(math.isnan(
newPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(
newPoint.getLatitude().asRadians()))
# Test precision near the poles
lon = 123.0*degrees
almostPole = SpherePoint(lon, self.nextDown(90.0*degrees))
goSouth = almostPole.offset(-90.0*degrees, 90.0*degrees)
self.assertAnglesAlmostEqual(lon, goSouth.getLongitude())
self.assertAnglesAlmostEqual(0.0*degrees, goSouth.getLatitude())
goEast = almostPole.offset(0.0*degrees, 90.0*degrees)
self.assertAnglesAlmostEqual(lon + 90.0*degrees, goEast.getLongitude())
self.assertAnglesAlmostEqual(0.0*degrees, goEast.getLatitude())
def testOffsetValue(self):
"""Test if offset() returns the expected value.
"""
# This should cover arcs over the meridian, across the pole, etc.
for lon1, lat1 in self._dataset:
point1 = SpherePoint(lon1, lat1)
for lon2, lat2 in self._dataset:
if lon1 == lon2 and lat1 == lat2:
continue
point2 = SpherePoint(lon2, lat2)
bearing = point1.bearingTo(point2)
distance = point1.separation(point2)
# offsetting point1 by bearing and distance should produce the same result as point2
newPoint = point1.offset(bearing, distance)
self.assertIsInstance(newPoint, SpherePoint)
self.assertSpherePointsAlmostEqual(point2, newPoint)
if newPoint.atPole():
self.assertAnglesAlmostEqual(newPoint.getLongitude(),
0 * degrees)
# measuring the separation and bearing from point1 to the new point
# should produce the requested separation and bearing
measuredDistance = point1.separation(newPoint)
self.assertAnglesAlmostEqual(measuredDistance, distance)
if abs(measuredDistance.asDegrees() - 180) > 1e-5:
# The two points are not opposite each other on the sphere,
# so the bearing has a well defined value
measuredBearing = point1.bearingTo(newPoint)
self.assertAnglesAlmostEqual(measuredBearing, bearing)
# offset by a negative amount in the opposite direction should produce the same result
newPoint2 = point1.offset(bearing + 180 * degrees, -distance)
self.assertIsInstance(newPoint2, SpherePoint)
# check angular separation (longitude is checked below)
self.assertSpherePointsAlmostEqual(newPoint, newPoint2)
if point1.isFinite() and point2.isFinite():
if not point2.atPole():
self.assertAnglesAlmostEqual(point2.getLongitude(),
newPoint.getLongitude())
self.assertAnglesAlmostEqual(point2.getLongitude(),
newPoint2.getLongitude())
self.assertAnglesAlmostEqual(point2.getLatitude(),
newPoint.getLatitude())
self.assertAnglesAlmostEqual(point2.getLatitude(),
newPoint2.getLatitude())
else:
self.assertTrue(
math.isnan(newPoint.getLongitude().asRadians()))
self.assertTrue(
math.isnan(newPoint2.getLongitude().asRadians()))
self.assertTrue(
math.isnan(newPoint.getLatitude().asRadians()))
self.assertTrue(
math.isnan(newPoint2.getLatitude().asRadians()))
# Test precision near the poles
lon = 123.0 * degrees
almostPole = SpherePoint(lon, self.nextDown(90.0 * degrees))
goSouth = almostPole.offset(-90.0 * degrees, 90.0 * degrees)
self.assertAnglesAlmostEqual(lon, goSouth.getLongitude())
self.assertAnglesAlmostEqual(0.0 * degrees, goSouth.getLatitude())
goEast = almostPole.offset(0.0 * degrees, 90.0 * degrees)
self.assertAnglesAlmostEqual(lon + 90.0 * degrees,
goEast.getLongitude())
self.assertAnglesAlmostEqual(0.0 * degrees, goEast.getLatitude())
def testRotatedValue(self):
"""Test if rotated() returns the expected value.
"""
# Try rotating about the equatorial pole (ie. along a parallel).
longitude = 90.0
latitudes = [0.0, 30.0, 60.0]
arcLen = 10.0
pole = SpherePoint(0.0 * degrees, 90.0 * degrees)
for latitude in latitudes:
point = SpherePoint(longitude * degrees, latitude * degrees)
newPoint = point.rotated(pole, arcLen * degrees)
self.assertIsInstance(newPoint, SpherePoint)
self.assertAlmostEqual(longitude + arcLen,
newPoint.getLongitude().asDegrees())
self.assertAlmostEqual(latitude,
newPoint.getLatitude().asDegrees())
# Try with pole = vernal equinox and rotate up the 90 degree meridian.
pole = SpherePoint(0.0 * degrees, 0.0 * degrees)
for latitude in latitudes:
point = SpherePoint(longitude * degrees, latitude * degrees)
newPoint = point.rotated(pole, arcLen * degrees)
self.assertAlmostEqual(longitude,
newPoint.getLongitude().asDegrees())
self.assertAlmostEqual(latitude + arcLen,
newPoint.getLatitude().asDegrees())
# Test accuracy close to coordinate pole
point = SpherePoint(90.0 * degrees, np.nextafter(90.0, -inf) * degrees)
newPoint = point.rotated(pole, 90.0 * degrees)
self.assertAlmostEqual(270.0, newPoint.getLongitude().asDegrees())
self.assertAlmostEqual(90.0 - np.nextafter(90.0, -inf),
newPoint.getLatitude().asDegrees())
# Generic pole; can't predict position, but test for rotation
# invariant.
pole = SpherePoint(283.5 * degrees, -23.6 * degrees)
for lon, lat in self._dataset:
point = SpherePoint(lon, lat)
dist = point.separation(pole)
newPoint = point.rotated(pole, -32.4 * afwGeom.radians)
self.assertNotAlmostEqual(point.getLongitude().asDegrees(),
newPoint.getLongitude().asDegrees())
self.assertNotAlmostEqual(point.getLatitude().asDegrees(),
newPoint.getLatitude().asDegrees())
self.assertAnglesAlmostEqual(dist, newPoint.separation(pole))
# Non-finite values give undefined rotations
for latitude in latitudes:
point = SpherePoint(longitude * degrees, latitude * degrees)
nanPoint = point.rotated(pole, nan * degrees)
infPoint = point.rotated(pole, inf * degrees)
self.assertTrue(math.isnan(nanPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(nanPoint.getLatitude().asRadians()))
self.assertTrue(math.isnan(infPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(infPoint.getLatitude().asRadians()))
# Non-finite points rotate into non-finite points
for point in [
SpherePoint(-inf * degrees, 1.0 * radians),
SpherePoint(32.0 * degrees, nan * radians),
]:
newPoint = point.rotated(pole, arcLen * degrees)
self.assertTrue(math.isnan(nanPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(nanPoint.getLatitude().asRadians()))
self.assertTrue(math.isnan(infPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(infPoint.getLatitude().asRadians()))
# Rotation around non-finite poles undefined
for latitude in latitudes:
point = SpherePoint(longitude * degrees, latitude * degrees)
for pole in [
SpherePoint(-inf * degrees, 1.0 * radians),
SpherePoint(32.0 * degrees, nan * radians),
]:
newPoint = point.rotated(pole, arcLen * degrees)
self.assertTrue(math.isnan(
nanPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(nanPoint.getLatitude().asRadians()))
self.assertTrue(math.isnan(
infPoint.getLongitude().asRadians()))
self.assertTrue(math.isnan(infPoint.getLatitude().asRadians()))
def testDefaultConstructor(self):
sp = SpherePoint()
self.assertTrue(math.isnan(sp.getLongitude()))
self.assertTrue(math.isnan(sp.getLatitude()))
self.assertFalse(sp.isFinite())
