def testSeparationValueGeneric(self):
"""Test if separation() returns the correct value.
"""
# This should cover arcs over the meridian, across the pole, etc.
# Do not use sphgeom as an oracle, in case SpherePoint uses it
# internally.
for lon1, lat1 in self._dataset:
point1 = SpherePoint(lon1, lat1)
x1, y1, z1 = SpherePointTestSuite.toVector(lon1, lat1)
for lon2, lat2 in self._dataset:
point2 = SpherePoint(lon2, lat2)
if lon1 != lon2 or lat1 != lat2:
# Numerically unstable at small angles, but that's ok.
x2, y2, z2 = SpherePointTestSuite.toVector(lon2, lat2)
expected = math.acos(x1 * x2 + y1 * y2 + z1 * z2)
else:
expected = 0.0
sep = point1.separation(point2)
self.assertIsInstance(sep, afwGeom.Angle)
if point1.isFinite() and point2.isFinite():
self.assertGreaterEqual(sep.asDegrees(), 0.0)
self.assertLessEqual(sep.asDegrees(), 180.0)
self.assertAlmostEqual(expected, sep.asRadians())
self.assertAnglesAlmostEqual(sep,
point2.separation(point1))
else:
self.assertTrue(math.isnan(sep.asRadians()))
self.assertTrue(
math.isnan(point2.separation(point1).asRadians()))
def testSeparationPoles(self):
"""White-box test: all representations of a pole should have the same distance to another point.
"""
southPole1 = SpherePoint(-30.0, -90.0, degrees)
southPole2 = SpherePoint(183.0, -90.0, degrees)
regularPoint = SpherePoint(42.0, 45.0, degrees)
expectedSep = (45.0 + 90.0) * degrees
self.assertAnglesAlmostEqual(expectedSep,
southPole1.separation(regularPoint))
self.assertAnglesAlmostEqual(expectedSep,
regularPoint.separation(southPole1))
self.assertAnglesAlmostEqual(expectedSep,
southPole2.separation(regularPoint))
self.assertAnglesAlmostEqual(expectedSep,
regularPoint.separation(southPole2))
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 testBearingToValue(self):
"""Test if bearingTo() returns the expected value.
"""
lon0 = 90.0
lat0 = 0.0 # These tests only work from the equator.
arcLen = 10.0
trials = [
# Along celestial equator
dict(lon=lon0, lat=lat0, bearing=0.0,
lonEnd=lon0+arcLen, latEnd=lat0),
# Along a meridian
dict(lon=lon0, lat=lat0, bearing=90.0,
lonEnd=lon0, latEnd=lat0+arcLen),
# 180 degree arc (should go to antipodal point)
dict(lon=lon0, lat=lat0, bearing=45.0,
lonEnd=lon0+180.0, latEnd=-lat0),
#
dict(lon=lon0, lat=lat0, bearing=45.0,
lonEnd=lon0+90.0, latEnd=lat0 + 45.0),
dict(lon=lon0, lat=lat0, bearing=225.0,
lonEnd=lon0-90.0, latEnd=lat0 - 45.0),
dict(lon=lon0, lat=np.nextafter(-90.0, inf),
bearing=90.0, lonEnd=lon0, latEnd=0.0),
dict(lon=lon0, lat=np.nextafter(-90.0, inf),
bearing=0.0, lonEnd=lon0 + 90.0, latEnd=0.0),
# Argument at a pole should work
dict(lon=lon0, lat=lat0, bearing=270.0, lonEnd=lon0, latEnd=-90.0),
# Support for non-finite values
dict(lon=lon0, lat=nan, bearing=nan, lonEnd=lon0, latEnd=45.0),
dict(lon=lon0, lat=lat0, bearing=nan, lonEnd=nan, latEnd=90.0),
dict(lon=inf, lat=lat0, bearing=nan, lonEnd=lon0, latEnd=42.0),
dict(lon=lon0, lat=lat0, bearing=nan, lonEnd=-inf, latEnd=42.0),
]
for trial in trials:
origin = SpherePoint(trial['lon']*degrees, trial['lat']*degrees)
end = SpherePoint(trial['lonEnd']*degrees, trial['latEnd']*degrees)
bearing = origin.bearingTo(end)
self.assertIsInstance(bearing, afwGeom.Angle)
if origin.isFinite() and end.isFinite():
self.assertGreaterEqual(bearing.asDegrees(), 0.0)
self.assertLess(bearing.asDegrees(), 360.0)
if origin.separation(end).asDegrees() != 180.0:
if not math.isnan(trial['bearing']):
self.assertAlmostEqual(
trial['bearing'], bearing.asDegrees(), 12)
else:
self.assertTrue(math.isnan(bearing.asRadians()))
def testTicket1761(self):
"""Regression test for Ticket 1761.
Checks for math errors caused by unnormalized vectors.
"""
refPoint = SpherePoint(lsst.sphgeom.Vector3d(0, 1, 0))
point1 = SpherePoint(lsst.sphgeom.Vector3d(0.1, 0.1, 0.1))
point2 = SpherePoint(lsst.sphgeom.Vector3d(0.6, 0.6, 0.6))
sep1 = refPoint.separation(point1)
sep2 = refPoint.separation(point2)
sepTrue = 54.735610317245339 * degrees
self.assertAnglesAlmostEqual(sepTrue, sep1)
self.assertAnglesAlmostEqual(sepTrue, sep2)
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()))
