def azAltFromHADec(haDec, lat):
"""Converts HA/Dec position to az/alt.
Inputs:
- haDec (ha, dec) (degrees)
- lat latitude (degrees)
Returns a tuple containing:
(az, alt) (degrees)
atPole true => object near the pole (see Error Conditions)
Error Conditions:
- If converted position is too near the pole, atPole is true and ha is undefined.
Sign convention: azimuth is 0 south and 90 east.
History:
2002-07-23 ROwen Converted from TCC's sph_HADec2AzAlt 1-2.
2003-05-06 ROwen Modified test data to match new scFromCC.
"""
# convert spherical -ha/dec to direction cosines
negHADec = (-haDec[0], haDec[1])
haDecDC = dcFromSC(negHADec)
# convert ha/dec direction cosines to az/alt direction cosines
azAltDC = Cnv.azAltFromHADec(haDecDC, lat)
# convert az/alt direction cosines to spherical az/alt (deg)
return scFromDC(azAltDC)
def azAltFromHADec(haDec, lat):
"""Converts HA/Dec position to az/alt.
Inputs:
- haDec (ha, dec) (degrees)
- lat latitude (degrees)
Returns a tuple containing:
(az, alt) (degrees)
atPole true => object near the pole (see Error Conditions)
Error Conditions:
- If converted position is too near the pole, atPole is true and ha is undefined.
Sign convention: azimuth is 0 south and 90 east.
History:
2002-07-23 ROwen Converted from TCC's sph_HADec2AzAlt 1-2.
2003-05-06 ROwen Modified test data to match new scFromCC.
"""
# convert spherical -ha/dec to direction cosines
negHADec = (-haDec[0], haDec[1])
haDecDC = dcFromSC (negHADec)
# convert ha/dec direction cosines to az/alt direction cosines
azAltDC = Cnv.azAltFromHADec (haDecDC, lat)
# convert az/alt direction cosines to spherical az/alt (deg)
return scFromDC (azAltDC)
def angSep(posA, posB):
"""Computes the angular separation between two points on a sphere.
Inputs:
- posA(2) one spherical coordinate (deg)
longitude (increasing x to y), latitude,
e.g. (RA, Dec), (-HA, Dec) or (Az, Alt)
- posB(2) the other spherical coordinate (deg)
Returns:
- angSep the angular separation between the two points (deg)
Error Conditions:
(none)
Details:
Convert to Cartesian vectors and go from there.
The simplest method is to take the arc cosine of the dot product,
but this works poorly for small angles. To avoid this problem,
construct a triangle from the origin to one of the vectors
to the halfway point between the vectors, then use atan2
to compute the angle at the origin (half the desired angle)
Based on Pat Wallace's SEP routine.
"""
# convert from sherical to Cartesian coordinates
vecA = dcFromSC(posA)
vecB = dcFromSC(posB)
# compute the magnitude squared of half the difference vector
diffMagSqQuarter = numpy.sum((vecA - vecB)**2) * 0.25
# compute the angle
return 2.0 * RO.MathUtil.atan2d (
math.sqrt(diffMagSqQuarter),
math.sqrt(max(0.0, 1.0-diffMagSqQuarter))
)
def angSep(posA, posB):
"""Computes the angular separation between two points on a sphere.
Inputs:
- posA(2) one spherical coordinate (deg)
longitude (increasing x to y), latitude,
e.g. (RA, Dec), (-HA, Dec) or (Az, Alt)
- posB(2) the other spherical coordinate (deg)
Returns:
- angSep the angular separation between the two points (deg)
Error Conditions:
(none)
Details:
Convert to Cartesian vectors and go from there.
The simplest method is to take the arc cosine of the dot product,
but this works poorly for small angles. To avoid this problem,
construct a triangle from the origin to one of the vectors
to the halfway point between the vectors, then use atan2
to compute the angle at the origin (half the desired angle)
Based on Pat Wallace's SEP routine.
"""
# convert from sherical to Cartesian coordinates
vecA = dcFromSC(posA)
vecB = dcFromSC(posB)
# compute the magnitude squared of half the difference vector
diffMagSqQuarter = numpy.sum((vecA - vecB)**2) * 0.25
# compute the angle
return 2.0 * RO.MathUtil.atan2d(
math.sqrt(diffMagSqQuarter), math.sqrt(max(0.0,
1.0 - diffMagSqQuarter)))
def haDecFromAzAlt (azAlt, lat):
"""Converts alt/az position to ha/dec position.
Inputs:
- azAlt (az, alt) (deg)
- lat latitude (degrees);
>0 is north of the equator, <0 is south
Returns a tuple containing:
- haDec (HA, Dec) (deg), a tuple;
HA is in the range (-180, 180]
- atPole true => object near the pole (see Error Conditions)
Error Conditions:
- If converted position is too near the north or south pole,
atPole is set true and HA is some arbitrary value.
Details:
Sign conventions:
- azimuth is 0 south and 90 east
- ha/dec is the usual left-handed coordinate system
History:
3/01 ROwen Converted to Python from TCC's sph_AzAlt2HADec 1-2.
2/02 ROwen Minor tweaks to header.
2002-07-02 ROwen Renamed from azAltToHADec.
2003-05-06 ROwen Changed HA range from [0, 360) to (-180, 180]
"""
# convert spherical az/alt (deg) to direction cosines
azAltDC = dcFromSC (azAlt)
# convert az/alt direction cosines to -ha/dec direction cosines
negHADecDC = Cnv.haDecFromAzAlt (azAltDC, lat)
# convert -ha/dec direction cosines to spherical -ha/dec (deg)
((negHA, dec), atPole) = scFromDC (negHADecDC)
return ((RO.MathUtil.wrapCtr(-negHA), dec), atPole)
def haDecFromAzAlt(azAlt, lat):
"""Converts alt/az position to ha/dec position.
Inputs:
- azAlt (az, alt) (deg)
- lat latitude (degrees);
>0 is north of the equator, <0 is south
Returns a tuple containing:
- haDec (HA, Dec) (deg), a tuple;
HA is in the range (-180, 180]
- atPole true => object near the pole (see Error Conditions)
Error Conditions:
- If converted position is too near the north or south pole,
atPole is set true and HA is some arbitrary value.
Details:
Sign conventions:
- azimuth is 0 south and 90 east
- ha/dec is the usual left-handed coordinate system
History:
3/01 ROwen Converted to Python from TCC's sph_AzAlt2HADec 1-2.
2/02 ROwen Minor tweaks to header.
2002-07-02 ROwen Renamed from azAltToHADec.
2003-05-06 ROwen Changed HA range from [0, 360) to (-180, 180]
"""
# convert spherical az/alt (deg) to direction cosines
azAltDC = dcFromSC(azAlt)
# convert az/alt direction cosines to -ha/dec direction cosines
negHADecDC = Cnv.haDecFromAzAlt(azAltDC, lat)
# convert -ha/dec direction cosines to spherical -ha/dec (deg)
((negHA, dec), atPole) = scFromDC(negHADecDC)
return ((RO.MathUtil.wrapCtr(-negHA), dec), atPole)
