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 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 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),
geom.HALFPI*geom.radians)
self.assertAnglesAlmostEqual(southPole.bearingTo(northPoleOpposite),
(geom.PI + geom.HALFPI)*geom.radians)
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),
geom.HALFPI*geom.radians)
self.assertAnglesAlmostEqual(southPole.bearingTo(northPoleOpposite),
(geom.PI + geom.HALFPI)*geom.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*geom.arcseconds
spicaPlus = SpherePoint(spica.getLongitude(),
spica.getLatitude() + epsilon)
self.assertAnglesAlmostEqual(epsilon, spicaPlus.separation(spica))
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*geom.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)
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*geom.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())
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*geom.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())
