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#include <u.h>
#include <libc.h>
#include <bio.h>
#include "sky.h"
void
amdinv(Header *h, Angle ra, Angle dec, float mag, float col)
{
int i, max_iterations;
float tolerance;
float object_x, object_y, delta_x, delta_y, f, fx, fy, g, gx, gy;
float x1, x2, x3, x4;
float y1, y2, y3, y4;
/*
* Initialize
*/
max_iterations = 50;
tolerance = 0.0000005;
/*
* Convert RA and Dec to St.coords
*/
traneqstd(h, ra, dec);
/*
* Set initial value for x,y
*/
object_x = h->xi/h->param[Ppltscale];
object_y = h->eta/h->param[Ppltscale];
/*
* Iterate by Newtons method
*/
for(i = 0; i < max_iterations; i++) {
/*
* X plate model
*/
x1 = object_x;
x2 = x1 * object_x;
x3 = x1 * object_x;
x4 = x1 * object_x;
y1 = object_y;
y2 = y1 * object_y;
y3 = y1 * object_y;
y4 = y1 * object_y;
f =
h->param[Pamdx1] * x1 +
h->param[Pamdx2] * y1 +
h->param[Pamdx3] +
h->param[Pamdx4] * x2 +
h->param[Pamdx5] * x1*y1 +
h->param[Pamdx6] * y2 +
h->param[Pamdx7] * (x2+y2) +
h->param[Pamdx8] * x2*x1 +
h->param[Pamdx9] * x2*y1 +
h->param[Pamdx10] * x1*y2 +
h->param[Pamdx11] * y3 +
h->param[Pamdx12] * x1* (x2+y2) +
h->param[Pamdx13] * x1 * (x2+y2) * (x2+y2) +
h->param[Pamdx14] * mag +
h->param[Pamdx15] * mag*mag +
h->param[Pamdx16] * mag*mag*mag +
h->param[Pamdx17] * mag*x1 +
h->param[Pamdx18] * mag * (x2+y2) +
h->param[Pamdx19] * mag*x1 * (x2+y2) +
h->param[Pamdx20] * col;
/*
* Derivative of X model wrt x
*/
fx =
h->param[Pamdx1] +
h->param[Pamdx4] * 2*x1 +
h->param[Pamdx5] * y1 +
h->param[Pamdx7] * 2*x1 +
h->param[Pamdx8] * 3*x2 +
h->param[Pamdx9] * 2*x1*y1 +
h->param[Pamdx10] * y2 +
h->param[Pamdx12] * (3*x2+y2) +
h->param[Pamdx13] * (5*x4 + 6*x2*y2 + y4) +
h->param[Pamdx17] * mag +
h->param[Pamdx18] * mag*2*x1 +
h->param[Pamdx19] * mag*(3*x2+y2);
/*
* Derivative of X model wrt y
*/
fy =
h->param[Pamdx2] +
h->param[Pamdx5] * x1 +
h->param[Pamdx6] * 2*y1 +
h->param[Pamdx7] * 2*y1 +
h->param[Pamdx9] * x2 +
h->param[Pamdx10] * x1*2*y1 +
h->param[Pamdx11] * 3*y2 +
h->param[Pamdx12] * 2*x1*y1 +
h->param[Pamdx13] * 4*x1*y1* (x2+y2) +
h->param[Pamdx18] * mag*2*y1 +
h->param[Pamdx19] * mag*2*x1*y1;
/*
* Y plate model
*/
g =
h->param[Pamdy1] * y1 +
h->param[Pamdy2] * x1 +
h->param[Pamdy3] +
h->param[Pamdy4] * y2 +
h->param[Pamdy5] * y1*x1 +
h->param[Pamdy6] * x2 +
h->param[Pamdy7] * (x2+y2) +
h->param[Pamdy8] * y3 +
h->param[Pamdy9] * y2*x1 +
h->param[Pamdy10] * y1*x3 +
h->param[Pamdy11] * x3 +
h->param[Pamdy12] * y1 * (x2+y2) +
h->param[Pamdy13] * y1 * (x2+y2) * (x2+y2) +
h->param[Pamdy14] * mag +
h->param[Pamdy15] * mag*mag +
h->param[Pamdy16] * mag*mag*mag +
h->param[Pamdy17] * mag*y1 +
h->param[Pamdy18] * mag * (x2+y2) +
h->param[Pamdy19] * mag*y1 * (x2+y2) +
h->param[Pamdy20] * col;
/*
* Derivative of Y model wrt x
*/
gx =
h->param[Pamdy2] +
h->param[Pamdy5] * y1 +
h->param[Pamdy6] * 2*x1 +
h->param[Pamdy7] * 2*x1 +
h->param[Pamdy9] * y2 +
h->param[Pamdy10] * y1*2*x1 +
h->param[Pamdy11] * 3*x2 +
h->param[Pamdy12] * 2*x1*y1 +
h->param[Pamdy13] * 4*x1*y1 * (x2+y2) +
h->param[Pamdy18] * mag*2*x1 +
h->param[Pamdy19] * mag*y1*2*x1;
/*
* Derivative of Y model wrt y
*/
gy =
h->param[Pamdy1] +
h->param[Pamdy4] * 2*y1 +
h->param[Pamdy5] * x1 +
h->param[Pamdy7] * 2*y1 +
h->param[Pamdy8] * 3*y2 +
h->param[Pamdy9] * 2*y1*x1 +
h->param[Pamdy10] * x2 +
h->param[Pamdy12] * 3*y2 +
h->param[Pamdy13] * (5*y4 + 6*x2*y2 + x4) +
h->param[Pamdy17] * mag +
h->param[Pamdy18] * mag*2*y1 +
h->param[Pamdy19] * mag*(x2 + 3*y2);
f = f - h->xi;
g = g - h->eta;
delta_x = (-f*gy+g*fy) / (fx*gy-fy*gx);
delta_y = (-g*fx+f*gx) / (fx*gy-fy*gx);
object_x = object_x + delta_x;
object_y = object_y + delta_y;
if((fabs(delta_x) < tolerance) && (fabs(delta_y) < tolerance))
break;
}
/*
* Convert mm from plate center to pixels
*/
h->x = (h->param[Pppo3]-object_x*1000.0)/h->param[Pxpixelsz];
h->y = (h->param[Pppo6]+object_y*1000.0)/h->param[Pypixelsz];
}
void
ppoinv(Header *h, Angle ra, Angle dec)
{
/*
* Convert RA and Dec to standard coords.
*/
traneqstd(h, ra, dec);
/*
* Convert st.coords from arcsec to radians
*/
h->xi /= ARCSECONDS_PER_RADIAN;
h->eta /= ARCSECONDS_PER_RADIAN;
/*
* Compute PDS coordinates from solution
*/
h->x =
h->param[Pppo1]*h->xi +
h->param[Pppo2]*h->eta +
h->param[Pppo3];
h->y =
h->param[Pppo4]*h->xi +
h->param[Pppo5]*h->eta +
h->param[Pppo6];
/*
* Convert x,y from microns to pixels
*/
h->x /= h->param[Pxpixelsz];
h->y /= h->param[Pypixelsz];
}
void
traneqstd(Header *h, Angle object_ra, Angle object_dec)
{
float div;
/*
* Find divisor
*/
div =
(sin(object_dec)*sin(h->param[Ppltdec]) +
cos(object_dec)*cos(h->param[Ppltdec]) *
cos(object_ra - h->param[Ppltra]));
/*
* Compute standard coords and convert to arcsec
*/
h->xi = cos(object_dec) *
sin(object_ra - h->param[Ppltra]) *
ARCSECONDS_PER_RADIAN/div;
h->eta = (sin(object_dec)*cos(h->param[Ppltdec])-
cos(object_dec)*sin(h->param[Ppltdec])*
cos(object_ra - h->param[Ppltra]))*
ARCSECONDS_PER_RADIAN/div;
}
void
xypos(Header *h, Angle ra, Angle dec, float mag, float col)
{
if (h->amdflag) {
amdinv(h, ra, dec, mag, col);
} else {
ppoinv(h, ra, dec);
}
}