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ASTTERMS

astterms

Purpose

Evaulate the independent vectors to match an astrometric polynomial function.

Description

This function is a support routine to ASTROM and handles part of the
transformation between pixel (x,y) coordinates and the tangent plane
coordinates (xi,eta). The transformation from (ra,dec) to (xi,eta)
is not handled in this routine. The premise is that the transformation
from the tangent plane to pixel coordinates can be done with a polynominal.
I have implemented all of the common terms found in typical astrometric
solutions. In practice, the high order terms are probably not needed
except for very large fields or for highly distorted fields caused by
excessive optics. Most CCD fields can be accurately modeled using just
the linear terms.
This function does NOT actually evaluate the transformation. Instead,
the independent values for the polynominal are computed. The result is
an array with (nterms,nvals) elements where nterms is the number of
non-zero terms and nvals is the number of input x and y values (which must
be of the same length. The table below lists the contents of the i^th
column in the output array.

Astrometry

Calling Sequence

val=astterms(x,y,terms)

Inputs

x - X - coordinate (scalar or vector)
y - Y - coordinate (scalar or vector)
terms - Which terms are to be built, if this input is a 10-element
integer array, then a 1 means use the term,
0 means don't use it.
0 - const (always use this)
1 - x (always use this)
2 - y (always use this)
3 - r
4 - x^2
5 - y^2
6 - x^3
7 - y^3
8 - xy^2
9 - yx^2
Another input option is provide where terms is an string array
that contains the name of the term. The terms can appear in
any order and any subset can be used. There is NO error
checking to prevent duplicating a term (to save time). The
terms that are supported are (the names must match, case is
ignored):
CONST, X, Y, XX, YY, XY, R (sqrt(x^2+y^2)), XXX, YYY, XYY, XXY,
XXXX, YYYY, XYYY, XXYY, XXXY, XXXXX, YYYYY, XYYYY, XXYYY, XXXYY,
XXXXY, T1, T2, T3, T4, T5, U1, U2, U3, U4, U5
The terms labeled 'T' and 'U' are Chebyshev polynomials, with order
begin given by the repetition of X or Y, (ie., TXX is second order
of degree 1; TXYYY is 1st order in X times 3rd order in Y for
degree 1.
Complete list: (CONST applied to all forms)
degree 1
TX, TY, TXX, TXY,TYY, TXXX, TXXY, TXYY, TYYY,
TXXXX, TXYYY, TXXYY, TXXXY, TYYYY,
TXXXXX, TXYYYY, TXXYYY, TXXXYY, TXXXXY, TYYYYY
degree 2
UX, UY, UXX, UXY, UYY, UXXX, UXXY, UXYY, UYYY,
UXXXX, UXYYY, UXXYY, UXXXY, UYYYY,
UXXXXX, UXYYYY, UXXYYY, UXXXYY, UXXXXY, UYYYYY
The terms labeled L are Legendre polynomials with M=0
PX, PY, PXX, PXY, PYY, PXXX, PXXY, PXYY, PYYY,
PXXXX, PXYYY, PXXYY, PXXXY, PYYYY,
PXXXXX, PXYYYY, PXXYYY, PXXXYY, PXXXXY, PYYYYY

Outputs

return value - Dependent value(s), if x,y was 1-d then this will be scalar.

Modification History

1997/06/17, Written by Marc W. Buie, Lowell Observatory
2009/10/25, MWB, added string input option for terms
2009/12/10, MWB, added 4th order terms (names option only)
2010/02/24, Chris Sauro, added Chebyshev terms
2010/02/28, MWB, filled out Chebyshev and added Legendre
2010/03/31, MWB, added 6th order Legendre

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