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, geom.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 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, geom.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 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 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 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 testComputeAzAltFromPupilBase(self):
"""Test computeAzAltFromBasePupil with general values
"""
# transform the pupil vector back to the base vector
# using the computed internal az/alt position
for vectorPupil, vectorBase, pupilMagFactor, baseMagFactor in itertools.product(
((1, 0, 0), (2, 1, 0), (2, 0, 1), (2, 0.7, -0.8)),
((1, 0, 0), (0, 1, 0), (1, -0.7, 0.8)),
(1, 1000),
(1, 1000),
):
with self.subTest(vectorPupil=vectorPupil, vectorBase=vectorBase, pupilMagFactor=pupilMagFactor,
baseMagFactor=baseMagFactor):
vectorPupilScaled = np.array(vectorPupil, dtype=float) * pupilMagFactor
pupilMag = np.linalg.norm(vectorPupilScaled)
vectorBaseScaled = np.array(vectorBase, dtype=float) * baseMagFactor
pupilAzAlt = coordUtils.computeAzAltFromBasePupil(vectorPupil=vectorPupilScaled,
vectorBase=vectorBaseScaled)
# Check the round trip; note that the magnitude
# of the returned vector will equal
# the magnitude of the input vector.
vectorBaseRoundTrip = coordUtils.convertVectorFromPupilToBase(
vectorPupil=vectorPupilScaled,
pupilAzAlt=pupilAzAlt)
vectorBaseRoundTripMag = np.linalg.norm(vectorBaseRoundTrip)
self.assertAlmostEqual(vectorBaseRoundTripMag, pupilMag, delta=1e-15*pupilMag)
spBase = SpherePoint(Vector3d(*vectorBase))
spBaseRoundTrip = SpherePoint(Vector3d(*vectorBaseRoundTrip))
sep = spBase.separation(spBaseRoundTrip)
self.assertLess(sep.asRadians(), 2e-15)
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 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 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 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 testComputeAzAltFromPupilBaseWithBaseEqualsPupil(self):
"""Test computeAzAltFromBasePupil with baseVector=pupilVector,
so the telescope will to internal az, alt=0
"""
zeroSp = SpherePoint(0, 0, radians)
for vector, pupilMagFactor, baseMagFactor in itertools.product(
((1, 0, 0), (0.1, -1, 0), (0.1, -0.5, 0.5), (0.5, 0, 0.5), (1, 0.7, -0.8)),
(1, 1000),
(1, 1000),
):
with self.subTest(vector=vector, pupilMagFactor=pupilMagFactor, baseMagFactor=baseMagFactor):
vectorPupil = np.array(vector, dtype=float) * pupilMagFactor
vectorBase = np.array(vector, dtype=float) * baseMagFactor
obs = coordUtils.computeAzAltFromBasePupil(vectorPupil=vectorPupil,
vectorBase=vectorBase)
sep = zeroSp.separation(obs).asRadians()
self.assertLess(sep, 1e-14)
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 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 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())