def _hcc_hg(self, x, y, z):
"""Converts hcc coordinates to Stonyhurst heliographic.
x - x coordinate in meters
y - y coordinate in meters
z - z coordinate in meters
Calculations taken and shortened
from sunpy.wcs.
"""
cosb = M.cos(M.deg2rad(self.B0))
sinb = M.sin(M.deg2rad(self.B0))
hecr = M.sqrt(x**2 + y**2 + z**2)
hgln = M.arctan2(x, z*cosb - y*sinb) \
+ M.deg2rad(self.L0)
hglt = M.arcsin((y * cosb + z * sinb)/hecr)
return hgln*180/np.pi, hglt*180/np.pi
def eoa(self, *args, array=True):
"""Takes in coordinates and returns the area of pixels on sun.
Each pixel is projected onto the sun, and therefore pixels close to
the limbs have vastly greater areas. This function uses a closed form
solution to a spherical area integral to calulate the area based on
the heliographic coordinate unit vectors of each corner of the pixel.
We use these to calculate a solid angle of a pyramid with its apex
at the center of the sun.
"""
print ("Calculating element of area.")
# Assume coordinate is in center of pixel.
# Information on pixel standard is in this article.
# http://www.aanda.org/component/article?access=bibcode&bibcode=&bibcode=2002A%2526A...395.1061GFUL
if array:
lon, lat = self.heliographic(corners=True)
lon = lon*np.pi/180
lat = lat*np.pi/180
# Calculating unit vectors of pixel corners for solid angle.
r1 = self._spherical_to_cartesian(lon, lat, 0, 0)
r2 = self._spherical_to_cartesian(lon, lat, 1, 0)
r3 = self._spherical_to_cartesian(lon, lat, 1, 1)
r4 = self._spherical_to_cartesian(lon, lat, 0, 1)
else:
x = args[0]
y = args[1]
lonUL, latUL = self.heliographic(x - .5, y - .5)
lonLL, latLL = self.heliographic(x + .5, y - .5)
lonLR, latLR = self.heliographic(x + .5, y + .5)
lonUR, latUR = self.heliographic(x - .5, y + .5)
# Calculating unit vectors of pixel corners for solid angle.
r1 = np.array([np.cos(np.deg2rad(latUL))*np.cos(np.deg2rad(lonUL)),
np.cos(np.deg2rad(latUL))*np.sin(np.deg2rad(lonUL)),
np.sin(np.deg2rad(latUL))])
r2 = np.array([np.cos(np.deg2rad(latLL))*np.cos(np.deg2rad(lonLL)),
np.cos(np.deg2rad(latLL))*np.sin(np.deg2rad(lonLL)),
np.sin(np.deg2rad(latLL))])
r3 = np.array([np.cos(np.deg2rad(latLR))*np.cos(np.deg2rad(lonLR)),
np.cos(np.deg2rad(latLR))*np.sin(np.deg2rad(lonLR)),
np.sin(np.deg2rad(latLR))])
r4 = np.array([np.cos(np.deg2rad(latUR))*np.cos(np.deg2rad(lonUR)),
np.cos(np.deg2rad(latUR))*np.sin(np.deg2rad(lonUR)),
np.sin(np.deg2rad(latUR))])
# Calculate solid angle of pixel based on a pyrimid shaped polygon.
# See http://planetmath.org/solidangleofrectangularpyramid
cross1 = M.cross(r1, r2, axis=0)
cross2 = M.cross(r3, r4, axis=0)
numerator1 = M.dot(cross1, r3)
numerator2 = M.dot(cross2, r1)
solid_angle1 = 2*M.arctan2(numerator1,
(M.dot(r1, r2) + M.dot(r2, r3) + M.dot(r3, r1) + 1))
solid_angle2 = 2*M.arctan2(numerator2,
(M.dot(r3, r4) + M.dot(r4, r1) + M.dot(r3, r1) + 1))
solid_angle = solid_angle1 + solid_angle2
r = self.RSUN_METERS*100 # Convert to centimeters
if array:
self.area = abs((r**2)*solid_angle)
ind = np.where(self.Rg[1:len(self.Rg)-1, 1:len(self.Rg)-1] > self.rsun)
del self.Rg
self.area[ind] = np.nan
return
else:
if self.rg > self.rsun:
return np.nan
else:
return np.abs((r**2)*solid_angle)
