class TestAzimuthalEquidistantProjection(unittest.TestCase):
def setUp(self):
self.origin = Point(0, 0)
self.p = AzimuthalEquidistantProjection(reference_longitude=0, reference_scale=40)
def test_pole(self):
self.assertEqual(self.p.project(SphericalPoint(0, 90)), self.origin)
def test_latitude(self):
self.assertEqual(self.p.project(SphericalPoint(0, 50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(90, 50)), Point(0, 1))
self.assertEqual(self.p.project(SphericalPoint(180, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(270, 50)), Point(0, -1))
self.p.celestial = True
self.assertEqual(self.p.project(SphericalPoint(0, 50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(90, 50)), Point(0, -1))
self.assertEqual(self.p.project(SphericalPoint(180, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(270, 50)), Point(0, 1))
def test_inverse_project(self):
self.assertEqual(self.p.inverse_project(Point(1, 0)), SphericalPoint(0, 50))
self.assertEqual(self.p.inverse_project(Point(0, 1)), SphericalPoint(90, 50))
self.assertEqual(self.p.inverse_project(Point(-1, 0)), SphericalPoint(180, 50))
self.assertEqual(self.p.inverse_project(Point(0, -1)), SphericalPoint(270, 50))
p = SphericalPoint(225, 76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.inverse_project(Point(1, 0)), SphericalPoint(0, 50))
self.assertEqual(self.p.inverse_project(Point(0, 1)), SphericalPoint(270, 50))
self.assertEqual(self.p.inverse_project(Point(-1, 0)), SphericalPoint(180, 50))
self.assertEqual(self.p.inverse_project(Point(0, -1)), SphericalPoint(90, 50))
p = SphericalPoint(225, 76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
def test_reference_longitude(self):
self.p.reference_longitude = 40
self.assertEqual(self.origin.distance(self.p.project(SphericalPoint(0, 50))), 1.0)
self.assertEqual(self.p.project(SphericalPoint(40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(130, 50)), Point(0, 1))
self.assertEqual(self.p.project(SphericalPoint(220, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(310, 50)), Point(0, -1))
p = SphericalPoint(225, 76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.project(SphericalPoint(40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(130, 50)), Point(0, -1))
self.assertEqual(self.p.project(SphericalPoint(220, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(310, 50)), Point(0, 1))
p = SphericalPoint(225, 76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
self.p.celestial = False
self.p.reference_longitude = -40
self.assertEqual(self.p.project(SphericalPoint(-40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(50, 50)), Point(0, 1))
self.assertEqual(self.p.project(SphericalPoint(140, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(230, 50)), Point(0, -1))
def test_south_pole(self):
self.p = AzimuthalEquidistantProjection(north=False, reference_longitude=0, reference_scale=40)
# Pole
self.assertEqual(self.p.project(SphericalPoint(0, -90)), self.origin)
# Project
self.assertEqual(self.p.project(SphericalPoint(0, -50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(90, -50)), Point(0, -1))
self.assertEqual(self.p.project(SphericalPoint(180, -50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(270, -50)), Point(0, 1))
self.p.celestial = True
self.assertEqual(self.p.project(SphericalPoint(0, -50)), Point(1, 0))
self.assertEqual(self.p.project(SphericalPoint(90, -50)), Point(0, 1))
self.assertEqual(self.p.project(SphericalPoint(180, -50)), Point(-1, 0))
self.assertEqual(self.p.project(SphericalPoint(270, -50)), Point(0, -1))
# Inverse project
self.p.celestial = False
self.assertEqual(self.p.inverse_project(Point(1, 0)), SphericalPoint(0, -50))
self.assertEqual(self.p.inverse_project(Point(0, -1)), SphericalPoint(90, -50))
self.assertEqual(self.p.inverse_project(Point(-1, 0)), SphericalPoint(180, -50))
self.assertEqual(self.p.inverse_project(Point(0, 1)), SphericalPoint(270, -50))
p = SphericalPoint(225, -76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.inverse_project(Point(1, 0)), SphericalPoint(0, -50))
self.assertEqual(self.p.inverse_project(Point(0, 1)), SphericalPoint(90, -50))
self.assertEqual(self.p.inverse_project(Point(-1, 0)), SphericalPoint(180, -50))
self.assertEqual(self.p.inverse_project(Point(0, -1)), SphericalPoint(270, -50))
p = SphericalPoint(225, -76)
pp = self.p.project(p)
ppp = self.p.inverse_project(pp)
self.assertEqual(p, ppp)
def test_other_scale(self):
self.p = AzimuthalEquidistantProjection(reference_longitude=0, reference_scale=80.0/190.0)
self.assertEqual(self.p.project(SphericalPoint(0, 50)), Point(95, 0))
class AzimuthalEquidistantProjection(Projection):
def __init__(
self,
center_longitude=0,
center_latitude=90,
standard_parallel1=None,
standard_parallel2=None,
reference_scale=45,
horizontal_stretch=1.0,
celestial=False,
):
"""Azimuthal equidistant map projection.
Center of projection is the pole, which gets projected to the point (0, 0).
Args:
center_longitude: the longitude that points to the right
center_latitude: the latitude at the center of the map (+ or - 90 degrees)
standard_parallel1: not used
standard_parallel2: not used
reference_scale: degrees of latitude per unit distance
horizontal_stretch: factor with which to expand the horizontal axis
celestial: longitude increases clockwise around north pole
"""
Projection.__init__(
self,
center_longitude,
center_latitude,
standard_parallel1,
standard_parallel2,
reference_scale,
horizontal_stretch,
celestial,
)
self.north = center_latitude > 0
self.origin = Point(0, 0)
if self.north:
if self.reference_scale >= 90:
raise ProjectionError(
f"Invalid reference scale {self.reference_scale} for north pole"
)
else:
self.reference_scale *= -1
if self.reference_scale <= -90:
raise ProjectionError(
f"Invalid reference scale {self.reference_scale} for south pole"
)
@property
def reverse_polar_direction(self):
"""Whether increasing longitude is clockwise or anticlockwise."""
return self.north == self.celestial
def project(self, skycoord):
longitude = self.reduce_longitude(skycoord.ra.degree)
latitude = skycoord.dec.degree
rho = (self.center_latitude - latitude) / self.reference_scale
theta = math.radians(longitude - self.center_longitude)
if self.reverse_polar_direction:
theta *= -1
return Point(self.horizontal_stretch * rho * math.cos(theta),
rho * math.sin(theta))
def backproject(self, point):
rho = self.origin.distance(point)
theta = ensure_angle_range(math.degrees(math.atan2(point.y, point.x)))
if self.reverse_polar_direction:
theta *= -1
longitude = ensure_angle_range(theta + self.center_longitude)
latitude = (-rho * self.reference_scale / self.horizontal_stretch +
self.center_latitude)
return SkyCoordDeg(longitude, latitude)
def parallel(self, latitude, min_longitude, max_longitude):
p = self.project(SkyCoordDeg(0, latitude))
return Circle(self.origin, self.origin.distance(p))
