def equatorial_meridian(self, tick_interval, frame):
if tick_interval is not None:
for i in range(int(360 / int(tick_interval))):
l = i * tick_interval
sp = SkyCoordDeg(l, 0, frame=frame).icrs
if self.clip_at_border:
p = self.projection.project(sp)
if not self.clipper.point_inside(p):
continue
else:
if not self.inside_coordinate_range(sp):
continue
p = self.projection.project(sp)
v = self.projection.project(
SkyCoordDeg(l + 1, 0, frame=frame).icrs) - p
v = v.rotate(90) / v.norm
tp1 = p + 0.5 * v
tp2 = p - 0.5 * v
lp = p + 0.4 * v
tick = Line(tp1, tp2)
label = Label(
lp,
text=f"\\textit{{{l}\\textdegree}}",
fontsize="miniscule",
angle=tick.angle - 90,
position="below",
fill="white",
)
yield EquatorialMeridian(l, tick, label)
def _calculate_parallel_circle_center(self):
"""Calculates the center of the parallel circles."""
s0 = SkyCoordDeg(self.center_longitude, 0)
s3 = SkyCoordDeg(self.center_longitude,
numpy.sign(self.center_latitude) * 90)
p0 = self.project(s0)
p1 = self.project(
longitude=self.center_longitude,
latitude=math.fabs(math.degrees(self.G)) - 90,
)
p3 = self.project(s3)
delta = numpy.sign(self.center_latitude) * (p1.y - p0.y)
self.parallel_circle_center = Point(0, p3.y + delta)
def ecliptic_to_equatorial(p, epoch=REFERENCE_EPOCH):
"""Returns the equatorial coordinates for the given point in ecliptic coordinates.
Equations taken from:
Practical Astronomy with your Calculator or Spreadsheet
Peter Duffett-Smith and Jonathan Zwart
Cambridge University Press, 2011
Paragraph 27 (page 51)
Only used to draw the ecliptic.
"""
eps = math.radians(obliquity_of_the_ecliptic(REFERENCE_EPOCH))
ceps = math.cos(eps)
seps = math.sin(eps)
l = math.radians(p.ra.degree)
b = math.radians(p.dec.degree)
longitude = math.degrees(
math.atan2(math.sin(l) * ceps - math.tan(b) * seps, math.cos(l)))
latitude = math.degrees(
math.asin(math.sin(b) * ceps + math.cos(b) * seps * math.sin(l)))
# Precess to the current epoch
pc = PrecessionCalculator(REFERENCE_EPOCH, epoch)
longitude, latitude = pc.precess(longitude, latitude)
return SkyCoordDeg(ensure_angle_range(longitude), latitude)
def constellations_in_area(
min_longitude, max_longitude, min_latitude, max_latitude, nsamples=1000
):
"""Generates a list of all constellations that overlap with the given area.
Uses a simple Monte Carlo strategy.
"""
constellations = {}
sum_weight = 0
for i in range(nsamples):
# Generate a random longitude and latitude pair inside the bounding box
longitude = min_longitude + (max_longitude - min_longitude) * random.random()
latitude = min_latitude + (max_latitude - min_latitude) * random.random()
# Retrieve the short name of the constellation for that coordinate
constellation = get_constellation(
SkyCoordDeg(longitude, latitude), short_name=True
)
# Use the cosine of the latitude as weight, so higher latitude areas are not dominating
weight = math.cos(math.radians(latitude))
# Update the constellation dict and sum_weight
if constellation not in constellations:
constellations[constellation] = weight
else:
constellations[constellation] += weight
sum_weight += weight
# Sort the constellation dict by value and return the constellations of decreasing area
res = sorted([(v / sum_weight, k) for k, v in constellations.items()], reverse=True)
return [x[1] for x in res]
def test_latitude(self):
self.assertEqual(self.p.project(SkyCoordDeg(0, 50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(90, 50)), Point(0, 1))
self.assertEqual(self.p.project(SkyCoordDeg(180, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(270, 50)), Point(0, -1))
self.p.celestial = True
self.assertEqual(self.p.project(SkyCoordDeg(0, 50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(90, 50)), Point(0, -1))
self.assertEqual(self.p.project(SkyCoordDeg(180, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(270, 50)), Point(0, 1))
def pole_markers(self, frame):
for latitude in [-90, 90]:
sp = SkyCoordDeg(0, latitude, frame=frame).icrs
p = self.projection.project(sp)
if self.config.rotate_poles:
delta1 = (self.projection.project(
SkyCoordDeg(sp.ra.degree + 1, sp.dec.degree)) - p)
delta2 = (self.projection.project(
SkyCoordDeg(sp.ra.degree, sp.dec.degree + 1)) - p)
else:
delta1 = Point(1, 0)
delta2 = Point(0, 1)
delta1 *= self.config.pole_marker_size / delta1.norm
delta2 *= self.config.pole_marker_size / delta2.norm
if self.clipper.point_inside(p):
yield Line(p + delta1, p - delta1)
yield Line(p + delta2, p - delta2)
def _generate_equator_points(self):
data = [
SkyCoordDeg(longitude, 0, frame=self.frame).icrs
for longitude in numpy.arange(0, 360, 1)
]
longitudes = [x.ra.degree for x in data]
latitudes = [x.dec.degree for x in data]
i = longitudes.index(min(longitudes))
self.LONGITUDES[self.frame] = longitudes[i:] + longitudes[:i]
self.LATITUDES[self.frame] = latitudes[i:] + latitudes[:i]
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 backproject(self, point):
if self.celestial:
x = -point.x
else:
x = point.x
longitude = (self.center_longitude +
self.reference_scale * x / self.horizontal_stretch)
latitude = point.y * self.reference_scale
return SkyCoordDeg(longitude, latitude)
def polar_tick(self):
if not self.config.polar_tick:
return None
latitude = 90
delta = Point(0, 1)
if self.config.center_latitude < 0:
delta = Point(0, -1)
latitude *= -1
p1 = self.projection.project(SkyCoordDeg(0, latitude))
p2 = p1 + self.config.marked_ticksize * delta
return Line(p1, p2)
def get_constellation_boundaries_for_area(
min_longitude, max_longitude, min_latitude, max_latitude, epoch="J2000.0"
):
# Convert longitude to 0-360 values
# TODO: sometimes boundaries cross the map but have no vertices within the map area + margin and are not plotted
min_longitude = ensure_angle_range(min_longitude)
max_longitude = ensure_angle_range(max_longitude)
if max_longitude == min_longitude:
max_longitude += 360
db = SkyMapDatabase()
q = "SELECT * FROM skymap_constellation_boundaries WHERE"
if min_longitude < max_longitude:
q += " ((ra1>={0} AND ra1<={1}".format(min_longitude, max_longitude)
else:
q += " (((ra1>={0} OR ra1<={1})".format(min_longitude, max_longitude)
q += " AND dec1>={0} AND dec1<={1}) OR".format(min_latitude, max_latitude)
if min_longitude < max_longitude:
q += " (ra2>={0} AND ra2<={1}".format(min_longitude, max_longitude)
else:
q += " ((ra2>={0} OR ra2<={1})".format(min_longitude, max_longitude)
q += " AND dec2>={0} AND dec2<={1}))".format(min_latitude, max_latitude)
res = db.query(q)
result = []
for row in res:
p1 = SkyCoordDeg(row["ra1"], row["dec1"])
p2 = SkyCoordDeg(row["ra2"], row["dec2"])
e = ConstellationBoundaryEdge(p1, p2)
e.precess()
result.append(e)
db.close()
return result
def backproject(self, point):
sign_n = numpy.sign(self.n)
rho = (math.radians(self.reference_scale) * sign_n *
math.sqrt(point.x**2 + (self.rho_0 - point.y)**2))
theta = math.degrees(
math.atan2(sign_n * point.x, sign_n * (self.rho_0 - point.y)))
if self.celestial:
theta *= -1
longitude = self.center_longitude + theta / self.n
latitude = math.degrees(self.G - rho)
return SkyCoordDeg(longitude, latitude)
def test_inverse_project(self):
self.assertEqual(self.p.backproject(Point(1, 0)), SkyCoordDeg(0, 50))
self.assertEqual(self.p.backproject(Point(0, 1)), SkyCoordDeg(90, 50))
self.assertEqual(self.p.backproject(Point(-1, 0)),
SkyCoordDeg(180, 50))
self.assertEqual(self.p.backproject(Point(0, -1)),
SkyCoordDeg(270, 50))
p = SkyCoordDeg(225, 76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.backproject(Point(1, 0)), SkyCoordDeg(0, 50))
self.assertEqual(self.p.backproject(Point(0, 1)), SkyCoordDeg(270, 50))
self.assertEqual(self.p.backproject(Point(-1, 0)),
SkyCoordDeg(180, 50))
self.assertEqual(self.p.backproject(Point(0, -1)), SkyCoordDeg(90, 50))
p = SkyCoordDeg(225, 76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
def equator(self, frame):
e = Equator(frame)
points = e.points_inside_area(self.min_longitude, self.max_longitude,
self.min_latitude, self.max_latitude)
points = [
self.projection.project(SkyCoordDeg(p[0], p[1])) for p in points
]
if not points:
return None
polygon = Polygon(points, closed=False)
if self.clip_at_border:
polys, borders = self.clipper.clip(polygon)
if not polys:
return None
polygon = polys[0]
return polygon
def galactic_to_equatorial(p, epoch=REFERENCE_EPOCH):
"""Returns the equatorial coordinates for the given point in galactic coordinates.
Equations taken from:
Practical Astronomy with your Calculator or Spreadsheet
Peter Duffett-Smith and Jonathan Zwart
Cambridge University Press, 2011
Paragraph 30 (page 58)
Only used to draw the galactic equator.
"""
l = math.radians(p.ra.degree)
b = math.radians(p.dec.degree)
# Get the longitude and latitude of the north galactic pole
ngp = galactic_pole(GALACTIC_NORTH_POLE_EPOCH)
pl = math.radians(ngp.ra.degree)
pb = math.radians(ngp.dec.degree)
# Get the galactic longitude offset
l0 = math.radians(GALACTIC_LONGITUDE_NORTH_CELESTIAL_POLE - 90.0)
# Determine the equatorial
longitude = math.degrees(
math.atan2(
math.cos(b) * math.cos(l - l0),
(math.sin(b) * math.cos(pb) -
math.cos(b) * math.sin(pb) * math.sin(l - l0)),
) + pl)
latitude = math.degrees(
math.asin(
math.cos(b) * math.cos(pb) * math.sin(l - l0) +
math.sin(b) * math.sin(pb)))
# Precess to the current epoch
pc = PrecessionCalculator(GALACTIC_NORTH_POLE_EPOCH, epoch)
longitude, latitude = pc.precess(longitude, latitude)
return SkyCoordDeg(ensure_angle_range(longitude), latitude)
def polar_label(self):
if not self.config.polar_tick:
return None
latitude = 90
delta = Point(0, 1)
pos = "above"
text = "+90\\textdegree"
if self.config.center_latitude < 0:
delta = Point(0, -1)
latitude *= -1
pos = "below"
text = "--90\\textdegree"
p1 = self.projection.project(SkyCoordDeg(0, latitude))
p2 = p1 + self.config.label_distance * delta
return Label(
p2,
text=text,
fontsize=self.config.parallel_config.fontsize,
angle=0,
position=pos,
fill="white",
)
def parallel(self, latitude, min_longitude, max_longitude):
p = self.project(SkyCoordDeg(0, latitude))
return Circle(self.origin, self.origin.distance(p))
def galactic_pole(epoch=REFERENCE_EPOCH):
"""Returns the location of the galactic north pole at the given epoch."""
p = PrecessionCalculator(GALACTIC_NORTH_POLE_EPOCH, epoch)
return SkyCoordDeg(*p.precess(GALACTIC_NORTH_POLE.ra.degree,
GALACTIC_NORTH_POLE.dec.degree))
import datetime
import math
from astropy.coordinates import Longitude
from skymap.geometry import SkyCoordDeg, ensure_angle_range
from skymap.coordinates import PrecessionCalculator, REFERENCE_EPOCH
GALACTIC_NORTH_POLE = SkyCoordDeg(Longitude("12h49m").degree, 27.4)
GALACTIC_LONGITUDE_NORTH_CELESTIAL_POLE = 123
GALACTIC_NORTH_POLE_EPOCH = datetime.datetime(1950, 1, 1).date()
# Ecliptic coordinate system
def obliquity_of_the_ecliptic(epoch=REFERENCE_EPOCH):
"""Returns the obliquity of the ecliptic for the given epoch, in degrees.
The calculation is taken from the Astronomical Almanac 2010, as given
on https://en.wikipedia.org/wiki/Axial_tilt#Short_term.
"""
a = 23.0 + 26 / 60.0 + 21.406 / 3600.0
b = -46.836769 / 3600.0
c = -0.0001831 / 3600.0
d = 0.00200340 / 3600.0
e = -0.576e-6 / 3600.0
f = -0.0434e-6 / 3600.0
t = (epoch - REFERENCE_EPOCH).days / 36525.0
return a + b * t + c * t**2 + d * t**3 + e * t**4 + f * t**5
def ecliptic_to_equatorial(p, epoch=REFERENCE_EPOCH):
"""Returns the equatorial coordinates for the given point in ecliptic coordinates.
def inverse_project(self, point):
longitude = (self.center_longitude +
self.reference_scale * point.x / self.horizontal_stretch)
latitude = self.reference_scale * point.y
return SkyCoordDeg(longitude, latitude)
def parallel(self, latitude, min_longitude, max_longitude):
p1 = self.project(SkyCoordDeg(min_longitude - 0.1, latitude))
p2 = self.project(SkyCoordDeg(max_longitude + 0.1, latitude))
return Line(p1, p2)
def meridian(self, longitude, min_latitude, max_latitude):
p1 = self.project(SkyCoordDeg(longitude, min_latitude))
p2 = self.project(SkyCoordDeg(longitude, max_latitude))
return Line(p1, p2)
def parallel(self, latitude, min_longitude, max_longitude):
p = self.project(SkyCoordDeg(self.center_longitude, latitude))
radius = p.distance(self.parallel_circle_center)
return Circle(self.parallel_circle_center, radius)
def test_reference_longitude(self):
self.p.center_longitude = 40
self.assertAlmostEqual(
self.origin.distance(self.p.project(SkyCoordDeg(0, 50))), 1.0)
self.assertEqual(self.p.project(SkyCoordDeg(40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(130, 50)), Point(0, 1))
self.assertEqual(self.p.project(SkyCoordDeg(220, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(310, 50)), Point(0, -1))
p = SkyCoordDeg(225, 76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.project(SkyCoordDeg(40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(130, 50)), Point(0, -1))
self.assertEqual(self.p.project(SkyCoordDeg(220, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(310, 50)), Point(0, 1))
p = SkyCoordDeg(225, 76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
self.p.celestial = False
self.p.center_longitude = -40
self.assertEqual(self.p.project(SkyCoordDeg(-40, 50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(50, 50)), Point(0, 1))
self.assertEqual(self.p.project(SkyCoordDeg(140, 50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(230, 50)), Point(0, -1))
def test_inverse_projection(self):
self.assertEqual(self.p.backproject(Point(0, 0)), SkyCoordDeg(0, 45))
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(15, 45))),
SkyCoordDeg(15, 45))
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(-15, 45))),
SkyCoordDeg(-15, 45),
)
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(29, 32))),
SkyCoordDeg(29, 32))
self.p.celestial = True
self.assertEqual(self.p.backproject(Point(0, 0)), SkyCoordDeg(0, 45))
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(15, 45))),
SkyCoordDeg(15, 45))
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(-15, 45))),
SkyCoordDeg(-15, 45),
)
self.assertEqual(
self.p.backproject(self.p.project(SkyCoordDeg(29, 32))),
SkyCoordDeg(29, 32))
def parallels(self):
config = self.config.parallel_config
interval = config.tick_interval
current_latitude = math.ceil(self.min_latitude / interval) * interval
# Internal ticks and labels
internal_longitude = self.config.center_longitude
if self.config.internal_label_longitude is not None:
internal_longitude = self.config.internal_label_longitude
internal_meridian = self.projection.meridian(internal_longitude,
self.min_latitude,
self.max_latitude)
internal_tickangle = internal_meridian.angle - 90
if internal_tickangle < 0:
internal_tickangle += 180
while current_latitude <= self.max_latitude:
# print(f"Parallel at {current_latitude}")
parallel = self.projection.parallel(current_latitude,
self.min_longitude,
self.max_longitude)
internal_point = self.projection.project(
SkyCoordDeg(internal_longitude, current_latitude))
if not self.clipper.point_inside(internal_point):
internal_point = None
if self.clip_at_border:
parallel_parts, borders = self.clipper.clip(parallel)
for p, b in zip(parallel_parts, borders):
yield Parallel(
current_latitude,
p,
b,
internal_point,
internal_tickangle,
config,
)
else:
if isinstance(parallel, Circle) and ensure_angle_range(
self.min_longitude) != ensure_angle_range(
self.max_longitude):
# Construct the arc from the endpoints
p1 = (self.projection.project(
SkyCoordDeg(self.min_longitude, current_latitude)) -
parallel.center)
p2 = (self.projection.project(
SkyCoordDeg(self.max_longitude, current_latitude)) -
parallel.center)
parallel = Arc(parallel.center, parallel.radius, p1.angle,
p2.angle)
yield Parallel(
current_latitude,
parallel,
["right", "left"],
internal_point,
internal_tickangle,
config,
)
current_latitude += interval
"bottom", "top"
]
mc.coordinate_grid_config.parallel_tick_borders = [
"left", "right"
]
mc.coordinate_grid_config.parallel_internal_labels = False
mc.coordinate_grid_config.meridian_labeltextfunc = meridian_label
mc.coordinate_grid_config.flip_meridian_labels = False
print("Latitude:", mc.min_latitude, mc.max_latitude)
print("Longitude:", mc.min_longitude, mc.max_longitude)
voffset = cc["offset"]
if mc.center_latitude < 0:
# Adjust offset
p1 = mc.projection.project(
SkyCoordDeg(mc.max_longitude, mc.min_latitude))
p2 = mc.projection.project(
SkyCoordDeg(mc.min_longitude, mc.min_latitude))
voffset += abs(p1.y - p2.y)
if left:
mc.llcorner = p.llcorner + Point(0,
LEGEND_HEIGHT + voffset)
mc.origin = mc.llcorner + Point(
LEGEND_WIDTH, 0.5 * mc.latitude_range * MM_PER_DEGREE)
else:
mc.llcorner = p.llcorner + Point(0,
LEGEND_HEIGHT + voffset)
mc.origin = mc.llcorner + Point(
0, 0.5 * mc.latitude_range * MM_PER_DEGREE)
def test_south_pole(self):
self.p = AzimuthalEquidistantProjection(center_longitude=0,
center_latitude=-90,
reference_scale=40)
# Pole
self.assertEqual(self.p.project(SkyCoordDeg(0, -90)), self.origin)
# Project
self.assertEqual(self.p.project(SkyCoordDeg(0, -50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(90, -50)), Point(0, -1))
self.assertEqual(self.p.project(SkyCoordDeg(180, -50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(270, -50)), Point(0, 1))
self.p.celestial = True
self.assertEqual(self.p.project(SkyCoordDeg(0, -50)), Point(1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(90, -50)), Point(0, 1))
self.assertEqual(self.p.project(SkyCoordDeg(180, -50)), Point(-1, 0))
self.assertEqual(self.p.project(SkyCoordDeg(270, -50)), Point(0, -1))
# Inverse project
self.p.celestial = False
self.assertEqual(self.p.backproject(Point(1, 0)), SkyCoordDeg(0, -50))
self.assertEqual(self.p.backproject(Point(0, -1)),
SkyCoordDeg(90, -50))
self.assertEqual(self.p.backproject(Point(-1, 0)),
SkyCoordDeg(180, -50))
self.assertEqual(self.p.backproject(Point(0, 1)),
SkyCoordDeg(270, -50))
p = SkyCoordDeg(225, -76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
self.p.celestial = True
self.assertEqual(self.p.backproject(Point(1, 0)), SkyCoordDeg(0, -50))
self.assertEqual(self.p.backproject(Point(0, 1)), SkyCoordDeg(90, -50))
self.assertEqual(self.p.backproject(Point(-1, 0)),
SkyCoordDeg(180, -50))
self.assertEqual(self.p.backproject(Point(0, -1)),
SkyCoordDeg(270, -50))
p = SkyCoordDeg(225, -76)
pp = self.p.project(p)
ppp = self.p.backproject(pp)
self.assertEqual(p, ppp)
def interpolate_points(self, step=1.0):
if self.epoch != CONST_BOUND_EPOCH:
raise ValueError(
"Interpolations is only allowed for epoch 1875.0 boundaries!"
)
if self.direction == "parallel":
# dec is changing
fixed_value = self.coord1.ra.degree
v1 = self.coord1.dec.degree
v2 = self.coord2.dec.degree
elif self.direction == "meridian":
# ra is changing
fixed_value = self.coord1.dec.degree
v1 = self.coord1.ra.degree
v2 = self.coord2.ra.degree
else:
raise ValueError("Only one coordinate can change in an 1875 edge!")
d = v2 - v1
if abs(d) < 180:
# No zero crossing (assuming edges never exceed 180)
if d > 0:
# Interpolate from v1 to v2 (forward)
new_values = [v1]
new_val = step * math.ceil(v1 / step)
while new_val < v2:
new_values.append(new_val)
new_val += step
new_values.append(v2)
else:
# Interpolate from v2 to v1 (backward)
new_values = [v1]
new_val = step * math.floor(v1 / step)
while new_val > v2:
new_values.append(new_val)
new_val -= step
new_values.append(v2)
else:
# Zero crossing
if d < 0:
# Interpolate from v1 to v2 (forward), with zero crossing
new_values = [v1]
new_val = step * math.ceil(v1 / step)
while new_val < v2 + 360:
new_values.append(new_val)
new_val += step
new_values.append(v2)
else:
# Interpolate from v2 to v2 (backward), with zero crossing
new_values = [v1]
new_val = step * math.floor(v1 / step)
while new_val + 360 >= v2:
new_values.append(new_val)
new_val -= step
new_values.append(v2)
if self.direction == "parallel":
self.interpolated_points = [SkyCoordDeg(v, fixed_value) for v in new_values]
else:
self.interpolated_points = [SkyCoordDeg(fixed_value, v) for v in new_values]
return self.interpolated_points
def test_projection(self):
self.assertEqual(self.p.cone_angle, 45)
self.assertEqual(self.p.project(SkyCoordDeg(0, 45)), Point(0, 0))
self.assertEqual(self.p.project(SkyCoordDeg(0, 50)), Point(0, 0.5))
self.assertEqual(self.p.project(SkyCoordDeg(0, 35)), Point(0, -1))