def testOffset(self):
"""Test offset, angularSeparation and orientationTo for offsets over a wide range of angles
"""
for fromPolarAng in (-87.1, -25.5, 0.43, 36.7, 87.0):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-89.9, -45.0, 0.01, 12.5, 89.0, 90.0):
for dist in (0.0001, 0.01, 0.13, 5.73):
sideA = 90.0 - fromPolarAng
angB = 90.0 - fromOrient
sideC = dist
unknownAng, angA, sideB, angC = angSideAng(sideA, angB, sideC)
self.assertFalse(unknownAng)
predEquatAng = fromEquatAng + angC
predPolarAng = 90 - sideB
predAng = angA - 90
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
places = 7
self.assertAlmostEqual(toEquatAng, predEquatAng, places=places)
self.assertAlmostEqual(toPolarAng, predPolarAng, places=places)
self.assertAlmostEqual(toOrient, predAng, places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(dist, fromCoord.angularSeparation(toCoord))
self.assertAlmostEqual(fromOrient, fromCoord.orientationTo(toCoord))
self.assertAlmostEqual(toOrient, wrapNear(180 + toCoord.orientationTo(fromCoord), toOrient))
def testOffsetSmall(self):
"""Test offset, angularSeparation and orientationTo for small offsets not too near the pole
In this regime delta-long = dist along long / cos(lat) is a reasonable approximation
but I have no simple way to compute toOrient, except if dist very small then toOrient = fromOrient
"""
for fromPolarAng in (-40.0, 0.43, 36.7):
cosPolarAng = cosd(fromPolarAng)
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 12.5, 31, 47,
56, 68, 89):
cosFromOrient = cosd(fromOrient)
sinFromOrient = sind(fromOrient)
for dist in (0, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7,
1e-5, 0.001, 0.01, 0.13):
predEquatAng = fromEquatAng + (dist * cosFromOrient /
cosPolarAng)
predPolarAng = fromPolarAng + (dist * sinFromOrient)
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
if abs(dist) > 0.1:
places = 3
else:
places = 5
if abs(dist) < 0.0001:
orientPlaces = 4
else:
orientPlaces = 7
self.assertAlmostEqual(toEquatAng,
predEquatAng,
places=places)
self.assertAlmostEqual(toPolarAng,
predPolarAng,
places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(
dist, fromCoord.angularSeparation(toCoord))
predFromOrient = fromCoord.orientationTo(toCoord)
if numpy.isfinite(predFromOrient):
self.assertAlmostEqual(fromOrient,
predFromOrient,
places=orientPlaces)
self.assertAlmostEqual(
toOrient,
wrapNear(
180 + toCoord.orientationTo(fromCoord),
toOrient),
places=orientPlaces)
else:
self.assertLess(dist, 1e-7)
self.assertAlmostEqual(fromEquatAng, toEquatAng)
self.assertAlmostEqual(fromPolarAng, toPolarAng)
self.assertAlmostEqual(fromOrient, toOrient)
def testOffsetSmall(self):
"""Test offset, angularSeparation and orientationTo for small offsets not too near the pole
In this regime delta-long = dist along long / cos(lat) is a reasonable approximation
but I have no simple way to compute toOrient, except if dist very small then toOrient = fromOrient
"""
for fromPolarAng in (-40.0, 0.43, 36.7):
cosPolarAng = cosd(fromPolarAng)
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 12.5, 31, 47, 56, 68, 89):
cosFromOrient = cosd(fromOrient)
sinFromOrient = sind(fromOrient)
for dist in (0, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-5, 0.001, 0.01, 0.13):
predEquatAng = fromEquatAng + (dist * cosFromOrient / cosPolarAng)
predPolarAng = fromPolarAng + (dist * sinFromOrient)
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
if abs(dist) > 0.1:
places = 3
else:
places = 5
if abs(dist) < 0.0001:
orientPlaces = 4
else:
orientPlaces = 7
self.assertAlmostEqual(toEquatAng, predEquatAng, places=places)
self.assertAlmostEqual(toPolarAng, predPolarAng, places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(dist, fromCoord.angularSeparation(toCoord))
predFromOrient = fromCoord.orientationTo(toCoord)
if numpy.isfinite(predFromOrient):
self.assertAlmostEqual(fromOrient, predFromOrient, places=orientPlaces)
self.assertAlmostEqual(toOrient, wrapNear(180 + toCoord.orientationTo(fromCoord), toOrient), places=orientPlaces)
else:
self.assertLess(dist, 1e-7)
self.assertAlmostEqual(fromEquatAng, toEquatAng)
self.assertAlmostEqual(fromPolarAng, toPolarAng)
self.assertAlmostEqual(fromOrient, toOrient)
def testOffset(self):
"""Test offset, angularSeparation and orientationTo for offsets over a wide range of angles
"""
for fromPolarAng in (-87.1, -25.5, 0.43, 36.7, 87.0):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-89.9, -45.0, 0.01, 12.5, 89.0, 90.0):
for dist in (0.0001, 0.01, 0.13, 5.73):
sideA = 90.0 - fromPolarAng
angB = 90.0 - fromOrient
sideC = dist
unknownAng, angA, sideB, angC = angSideAng(
sideA, angB, sideC)
self.assertFalse(unknownAng)
predEquatAng = fromEquatAng + angC
predPolarAng = 90 - sideB
predAng = angA - 90
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
places = 7
self.assertAlmostEqual(toEquatAng,
predEquatAng,
places=places)
self.assertAlmostEqual(toPolarAng,
predPolarAng,
places=places)
self.assertAlmostEqual(toOrient,
predAng,
places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(
dist, fromCoord.angularSeparation(toCoord))
self.assertAlmostEqual(
fromOrient, fromCoord.orientationTo(toCoord))
self.assertAlmostEqual(
toOrient,
wrapNear(180 + toCoord.orientationTo(fromCoord),
toOrient))
