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
|
/* colors2.cpp: functions for color conversions
Copyright (C) 2010, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
int tycho_to_johnson_colors( const double bt_minus_vt, double *results);
double johnson_b_minus_v_from_tycho( double b_v_t);
/* The following function takes a (B-V)T value, i.e., a B-V color in
the Tycho magnitude system, and computes from it V-VT, the difference
between Johnson V and Tycho V; the corresponding B-V in the Johnson
scheme; and V-Hp, the difference between Johnson V and Hp (Hipparcos
"magnitude") for the input color.
I got the raw data for this from Brian Skiff, who posted them on
the Minor Planet Mailing List (MPML) with the following comment:
"...To get standard V and B from Tycho-2, it is probably best to use the
relation shown by Mike Bessell in the July 2000 PASP... Bessell does not give
an algebraic relation, but instead shows a cubic spline fit with a look-up
table... I have copied out Bessell's table below as a flat ASCII list."
In what follows, values for (B-V)T away from the lookup table
points is computed using (again) a cubic spline. The functions vary
with sufficient slowness that this ought to be accurate down to the
.001 mag level. */
#define LOOKUP_SIZE 46
int tycho_to_johnson_colors( const double bt_minus_vt, double *results)
{
int i, table_loc = (int)( (bt_minus_vt + .25) / .05) - 1;
double dx, coeff[4];
static const short lookup_tbl[LOOKUP_SIZE * 3] = {
/* BT-VT V-VT del(B-V) V-Hp */
/* -0.250 */ 38, 31, 66,
/* -0.200 */ 30, 21, 51,
/* -0.150 */ 22, 11, 36,
/* -0.100 */ 15, 5, 21,
/* -0.050 */ 8, 2, 6,
/* -0.000 */ 1, -5, -11,
/* 0.050 */ -5, -10, -25,
/* 0.100 */ -12, -17, -38,
/* 0.150 */ -18, -20, -48,
/* 0.200 */ -24, -21, -58,
/* 0.250 */ -29, -23, -69,
/* 0.300 */ -35, -25, -79,
/* 0.350 */ -40, -25, -87,
/* 0.400 */ -45, -26, -94,
/* 0.450 */ -50, -30, -101,
/* 0.500 */ -54, -35, -108,
/* 0.550 */ -59, -45, -114,
/* 0.600 */ -64, -51, -120,
/* 0.650 */ -68, -60, -127,
/* 0.700 */ -72, -68, -131,
/* 0.750 */ -77, -76, -134,
/* 0.800 */ -81, -85, -137,
/* 0.850 */ -85, -94, -142,
/* 0.900 */ -89, -104, -147,
/* 0.950 */ -93, -113, -151,
/* 1.000 */ -98, -122, -155,
/* 1.050 */ -102, -131, -158,
/* 1.100 */ -106, -142, -157,
/* 1.150 */ -110, -154, -160,
/* 1.200 */ -115, -166, -162,
/* 1.250 */ -119, -178, -164,
/* 1.300 */ -124, -189, -166,
/* 1.350 */ -128, -199, -166,
/* 1.400 */ -133, -210, -165,
/* 1.450 */ -138, -222, -164,
/* 1.500 */ -143, -234, -161,
/* 1.550 */ -148, -245, -157,
/* 1.600 */ -154, -256, -153,
/* 1.650 */ -160, -266, -148,
/* 1.700 */ -165, -277, -143,
/* 1.750 */ -172, -288, -137,
/* 1.800 */ -178, -299, -131,
/* 1.850 */ -185, -309, -125,
/* 1.900 */ -191, -320, -119,
/* 1.950 */ -199, -331, -112,
/* 2.000 */ -206, -342, -106 };
if( bt_minus_vt < -.25 || bt_minus_vt > 2.)
return( -1); /* out of table range */
if( table_loc < 0)
table_loc = 0;
if( table_loc >= LOOKUP_SIZE - 4)
table_loc = LOOKUP_SIZE - 4;
dx = ((bt_minus_vt + .25) / .05) - (double)table_loc;
coeff[0] = (dx - 1.) * (dx - 2.) * (dx - 3.) / -6.;
coeff[1] = dx * (dx - 2.) * (dx - 3.) / 2.;
coeff[2] = dx * (dx - 1.) * (dx - 3.) / -2.;
coeff[3] = dx * (dx - 1.) * (dx - 2.) / 6.;
for( i = 0; i < 3; i++)
{
const short *tptr = lookup_tbl + i + table_loc * 3;
results[i] = .001 * ((double)tptr[0] * coeff[0]
+ (double)tptr[3] * coeff[1]
+ (double)tptr[6] * coeff[2]
+ (double)tptr[9] * coeff[3]);
}
results[1] += bt_minus_vt; /* change a 'delta' into an 'absolute' */
return( 0);
}
#ifdef TEST_FUNC
#include <stdio.h>
#include <stdlib.h>
/* This function derived from data on p 57, _Intro & Guide to the Data_ */
double johnson_b_minus_v_from_tycho( double b_v_t)
{
double delta = 0.;
if( b_v_t < -.2 || b_v_t > 1.8)
return( 99.); /* no reasonable transformation possible */
if( b_v_t < .1)
delta = -.006 + .006 * (b_v_t + .2) / .3;
else if( b_v_t < .5)
delta = .046 * (b_v_t - .1) / .4;
else if( b_v_t < 1.4)
delta = .046 - .054 * (b_v_t - .5) / .9;
else if( b_v_t < 1.8)
delta = -.008 - .024 * (b_v_t - 1.4) / .4;
return( .85 * b_v_t + delta);
}
int main( const int argc, const char **argv)
{
double ovals[3];
if( argc == 2 && !tycho_to_johnson_colors( atof( argv[1]), ovals))
{
printf( "V-VT = %.4f\n", ovals[0]);
printf( "B-V = %.4f\n", ovals[1]);
printf( "B-V = %.4f (from original formula)\n",
johnson_b_minus_v_from_tycho( atof( argv[1])));
printf( "V-Hp = %.4f\n", ovals[2]);
}
}
#endif
|
