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colors2.cpp
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colors2.cpp
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/* 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.
References :
https://groups.io/g/mpml/message/771
Bessell 2000, PASP 112, 961 (July), RELATION BETWEEN BT-VT AND
HIPPARCOS/TYCHO DATA FOR B-G MAIN-SEQUENCE STARS AND K-M GIANTS */
#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