def testFieldAngleToVector(self):
sp00 = SpherePoint(0, 0, degrees)
degList = (-90, -89.9, -20, 0, 10, 89.9, 90)
for xdeg, ydeg, flipX in itertools.product(degList, degList, (False, True)):
with self.subTest(xdeg=xdeg, ydeg=ydeg, flipX=flipX):
xrad = xdeg * RAD_PER_DEG
signx = -1 if flipX else 1
testOrientation = xdeg != 0 or ydeg != 0
yrad = ydeg * RAD_PER_DEG
fieldAngle = (xrad, yrad)
vector = coordUtils.fieldAngleToVector(fieldAngle, flipX)
self.assertAlmostEqual(np.linalg.norm(vector), 1)
if testOrientation:
# Orientation should match.
orientationFromFieldAngle = math.atan2(yrad, signx*xrad)*radians
# Field angle x = vector y, field angle y = vector z.
orientationFromVector = math.atan2(vector[2], vector[1])*radians
self.assertAnglesAlmostEqual(orientationFromVector, orientationFromFieldAngle)
# Now test as spherical geometry.
sp = SpherePoint(Vector3d(*vector))
separation = sp00.separation(sp)
predictedSeparation = math.hypot(xrad, yrad)*radians
self.assertAnglesAlmostEqual(predictedSeparation, separation)
if testOrientation:
bearing = sp00.bearingTo(sp)
self.assertAnglesAlmostEqual(orientationFromFieldAngle, bearing)
# Test round trip through vectorToFieldAngle.
fieldAngleFromVector = coordUtils.vectorToFieldAngle(vector, flipX)
np.testing.assert_allclose(fieldAngleFromVector, fieldAngle, atol=1e-15)
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 testBearingToValueOnEquator(self):
"""Test if bearingTo() returns the expected value from a point on the equator
"""
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, geom.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 testBearingToValueOnEquator(self):
"""Test if bearingTo() returns the expected value from a point on the equator
"""
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, geom.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 testBearingToFromPole(self):
"""Test if bearingTo() returns the expected value from a point at a pole
"""
for long0Deg in (0, 55, 270):
for atSouthPole in (False, True):
lat0Deg = -90 if atSouthPole else 90
sp0 = SpherePoint(long0Deg, lat0Deg, degrees)
for long1Deg in (0, 55, 270):
for lat1Deg in (-89, 0, 89):
sp1 = SpherePoint(long1Deg, lat1Deg, degrees)
desiredBearing = ((long1Deg - long0Deg) - 90) * degrees
if atSouthPole:
desiredBearing *= -1
measuredBearing = sp0.bearingTo(sp1)
self.assertAnglesAlmostEqual(desiredBearing, measuredBearing)
def testBearingToFromPole(self):
"""Test if bearingTo() returns the expected value from a point at a pole
"""
for long0Deg in (0, 55, 270):
for atSouthPole in (False, True):
lat0Deg = -90 if atSouthPole else 90
sp0 = SpherePoint(long0Deg, lat0Deg, degrees)
for long1Deg in (0, 55, 270):
for lat1Deg in (-89, 0, 89):
sp1 = SpherePoint(long1Deg, lat1Deg, degrees)
desiredBearing = ((long1Deg - long0Deg) - 90) * degrees
if atSouthPole:
desiredBearing *= -1
measuredBearing = sp0.bearingTo(sp1)
self.assertAnglesAlmostEqual(desiredBearing, measuredBearing)
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())