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 testBearingToValueSameLongitude(self):
"""Test that bearingTo() returns +/- 90 for two points on the same longitude
"""
for longDeg in (0, 55, 270):
for lat0Deg in (-90, -5, 0, 44, 90):
sp0 = SpherePoint(longDeg, lat0Deg, degrees)
for lat1Deg in (-90, -41, 1, 41, 90):
if lat0Deg == lat1Deg:
continue
sp1 = SpherePoint(longDeg, lat1Deg, degrees)
if sp0.atPole() and sp1.atPole():
# the points are at opposite poles; any bearing may be returned
continue
bearing = sp0.bearingTo(sp1)
if lat1Deg > lat0Deg:
self.assertAnglesAlmostEqual(bearing, 90 * degrees)
else:
self.assertAnglesAlmostEqual(bearing, -90 * degrees)
def testBearingToValueSameLongitude(self):
"""Test that bearingTo() returns +/- 90 for two points on the same longitude
"""
for longDeg in (0, 55, 270):
for lat0Deg in (-90, -5, 0, 44, 90):
sp0 = SpherePoint(longDeg, lat0Deg, degrees)
for lat1Deg in (-90, -41, 1, 41, 90):
if lat0Deg == lat1Deg:
continue
sp1 = SpherePoint(longDeg, lat1Deg, degrees)
if sp0.atPole() and sp1.atPole():
# the points are at opposite poles; any bearing may be returned
continue
bearing = sp0.bearingTo(sp1)
if lat1Deg > lat0Deg:
self.assertAnglesAlmostEqual(bearing, 90 * degrees)
else:
self.assertAnglesAlmostEqual(bearing, -90 * degrees)
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 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())