1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# Aaron LI
# Created: 2015-04-17
# Updated: 2016-06-30
#
"""
Calculate the angles between the given center point to other points
on the sphere.
The following input formats are supported:
longitude latitude => FMT
------------------------------------
??h??m??s ??d??m??s => "radec"
?? ?? ?? ?? ?? ?? => "ra3dec3"
deg deg => "degdeg"
"""
import os
import sys
import re
import getopt
import math
USAGE = """Usage:
%(prog)s [ -b -h ] -r RA -d DEC -i infile -f FMT -u UNIT
Required arguments:
-r, --ra
RA (??h??m??s) of the center
-d, --dec
DEC (??d??m??s) of the center
-i, --infile
input file containing the coordinates data
-f, --format
value: radec | ra3dec3 | degdeg
coordinates format of the input data file
-u, --unit
value: deg | arcmin | arcsec
unit of the output data
Optional arguments:
-b, --brief
brief mode: only output results
-h, --help
""" % {'prog': os.path.basename(sys.argv[0])}
def usage():
print(USAGE, file=sys.stderr)
def ra2deg(h, m, s):
"""
Convert RA (hour, minute, second) to degree.
"""
return h * 15.0 + m * 15.0/60.0 + s * 15.0/3600.0
def dec2deg(d, m, s):
"""
Convert DEC (deg, arcmin, arcsec) to degree.
"""
if (d >= 0):
sign = 1.0
else:
sign = -1.0
return sign * (math.fabs(d) + m/60.0 + s/3600.0)
def s_ra2deg(hms):
"""
Convert RA string ("??h??m??s") to degree.
"""
h, m, s = map(float, re.sub('[hms]', ' ', hms).split())
return ra2deg(h, m, s)
def s_dec2deg(dms):
"""
Convert DEC string ("??d??m??s") to degree.
"""
d, m, s = map(float, re.sub('[dms]', ' ', dms).split())
return dec2deg(d, m, s)
def deg2rad(deg):
"""
Convert unit from deg to rad.
"""
return deg * math.pi / 180.0
def rad2deg(rad):
"""
Convert unit from rad to deg.
"""
return rad * 180.0 / math.pi
def central_angle(p1, p2, unit="deg"):
"""
Calculate the central angle between the two points on the sphere.
Input parameters:
p1, p2: (longitude, latitude), coorindates of the two points
Algorithm:
(radial, azimuthal, polar): (r, theta, phi)
central_angle: alpha
longitude: lambda = theta
latitude: delta = 90 - phi
colatitude: phi
Unit vector:
\hat{r}_1 = (cos(theta1) sin(phi1), sin(theta1) sin(phi1), cos(phi1))
= (cos(lambda1) cos(delta1), sin(lambda1) cos(delta1), sin(delta1))
\hat{r}_2 = (cos(theta2) sin(phi2), sin(theta2) sin(phi2), cos(phi2))
= (cos(lambda2) cos(delta2), sin(lambda2) cos(delta2), sin(delta2))
Therefore the angle (alpha) between \hat{r}_1 and \hat{r}_2:
cos(alpha) = \hat{r}_1 \cdot \hat{r}_2
= cos(delta1) cos(delta2) cos(lambda1-lambda2)
+ sin(delta1) sin(delta2)
References:
[1] Spherical Coordinates - Wolfram MathWorld
http://mathworld.wolfram.com/SphericalCoordinates.html
Equation (19)
[2] Great Circle - Wolfram MathWorld
http://mathworld.wolfram.com/GreatCircle.html
Equation (1), (2), (4)
"""
lbd1, delta1 = map(deg2rad, p1)
lbd2, delta2 = map(deg2rad, p2)
dotvalue = (math.cos(delta1) * math.cos(delta2) * math.cos(lbd1-lbd2) +
math.sin(delta1) * math.sin(delta2))
alpha = math.acos(dotvalue)
if unit == "rad":
return alpha
elif unit == "arcmin":
return rad2deg(alpha) * 60.0
elif unit == "arcsec":
return rad2deg(alpha) * 60.0*60.0
else:
# default: degree
return rad2deg(alpha)
def main():
# Mandatory arguments
center_ra = None
center_dec = None
infile = None
# Default parameters
unit = "arcmin"
fmt = "radec" # default format: "??h??m??s ??d??m??s"
# Process command line arguments
try:
opts, args = getopt.getopt(sys.argv[1:], "bd:f:hi:r:u:",
["brief", "dec=", "format=", "help",
"infile=", "ra=", "unit="])
except getopt.GetoptError as err:
print(err)
usage()
sys.exit(2)
brief = False # brief mode
for opt, arg in opts:
if opt in ("-h", "--help"):
usage()
sys.exit(1)
elif opt in ("-b", "--brief"):
brief = True
elif opt in ("-d", "--dec"):
center_dec = arg
elif opt in ("-r", "--ra"):
center_ra = arg
elif opt in ("-i", "--infile"):
infile = arg
elif opt in ("-f", "--format"):
fmt = arg
elif opt in ("-u", "--unit"):
unit = arg
else:
assert False, "unhandled option"
# Check mandatory arguments
if not center_ra:
print("Error: --ra argument required!", file=sys.stderr)
if not center_dec:
print("Error: --dec argument required!", file=sys.stderr)
if not infile:
print("Error: --infile argument required!", file=sys.stderr)
if fmt == "radec":
center_ra_deg = s_ra2deg(center_ra)
center_dec_deg = s_dec2deg(center_dec)
elif fmt == "ra3dec3":
ra_h, ra_m, ra_s = map(float, center_ra.split())
dec_d, dec_m, dec_s = map(float, center_dec.split())
center_ra_deg = ra2deg(ra_h, ra_m, ra_s)
center_dec_deg = dec2deg(dec_d, dec_m, dec_s)
elif fmt == "degdeg":
center_ra_deg = float(center_ra)
center_dec_deg = float(center_dec)
else:
print("Error: unknown format type: %s" % fmt, file=sys.stderr)
sys.exit(2)
if not brief:
print("# Central_angle (unit: %s)" % unit)
datafile = open(infile, "r")
for line in datafile:
if re.match(r"^\s*#", line):
# skip comments
continue
elif re.match(r"^\s*$", line):
# skip blank line
continue
# coordinate format
if fmt == "radec":
ra, dec = line.split()
ra_deg = s_ra2deg(ra)
dec_deg = s_dec2deg(dec)
elif fmt == "ra3dec3":
ra_h, ra_m, ra_s, dec_d, dec_m, dec_s = map(float, line.split())
ra_deg = ra2deg(ra_h, ra_m, ra_s)
dec_deg = dec2deg(dec_d, dec_m, dec_s)
elif fmt == "degdeg":
ra_deg, dec_deg = map(float, line.split())
else:
print("Error: unknown format type: %s" % fmt, file=sys.stderr)
sys.exit(2)
# calculate angle
angle = central_angle((center_ra_deg, center_dec_deg),
(ra_deg, dec_deg), unit=unit)
print("%.10f" % angle)
datafile.close()
if __name__ == "__main__":
main()
|
