[fitswcs] Status of WCS negotiations

[Mark Calabretta]

Apologies if you receive this twice, I didn't get a return copy.
Mark

------- Forwarded Message


Date: Fri 1998/07/17 12:23:28 +1000
From: Mark Calabretta <mcalabre at grus.atnf.CSIRO.AU>
To:   fitswcs at fits.cv.nrao.edu


On Wed 1998/07/15 14:36:27 -0400, Don Wells wrote
in a message to: fitswcs at fits.cv.nrao.edu

>that we need to implement support for the function widely. I say
>'pixel correction function' because I myself favor perturbing the
>pixel coordinates before applying the linear transformation. I am
>aware that other people prefer polynomial expansions in 'standard
>coordinates' or other functional forms. I hope that we can agree that
>these are mathematically equivalent notations. If any of you believe
>that there is some notational form which is clearly best, please post
>to 'fitswcs' on the subject so that I and others can learn about your
>ideas. If any of you strongly object to some particular notational
>form, please post your objection.  In the end we need to agree on a
>canonical *interchange* notation (we could continue to use private
>conventions in our software, of course).

Plate solutions can be implemented as projection types provided that the
number of projection parameters in G&C is increased.  After the last round of
email discussions on the topic I prepared a note suitable for inclusion in G&C
on how the projection used by the DSS would be handled.  I would also call on
optical astrometrists to specify more general optical plate solutions along
the same lines (or show that this approach is inadequate).  In general, I
view G&C as a framework on which new projection types can be built, either now
or later - better if now since the projection, including the projection codes
assigned, will gain more widespread currency.  Note that plate solution
projection types can co-exist with Pat Wallace's pixel regularization table
(if this is what optical astrometrists want).  The PostScript for the "DSS"
projection is appended.

I have an experimental version of the C incarnation of WCSLIB which handles
100 projection parameters and also the "DSS" projection type.  The change to
the C library for additional projection parameters was isolated to the header
file and should only require a recompile on the part of third-parties.
However, the FORTRAN library would require changing the interfaces and I am
reluctant to do this without general agreement that it would be supported.
If anyone would like to see the C implementation (260 lines of C code appended
to proj.c) I'd be happy to send it.

Mark Calabretta

>>>

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1 0 bop 937 -192 a Fl(1)-54 -93 y Fk(4.4.10)12 b(DSS)h(\(Digitized)h
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y Fg(5)512 1663 y Fj(X)s(Y)20 b Fk(+)9 b Fj(a)656 1669
y Fg(6)675 1663 y Fj(Y)708 1646 y Fg(2)736 1663 y Fk(+)-21
1725 y Fj(a)1 1731 y Fg(7)27 1691 y Ff(\000)46 1725 y
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1767 y Ff(\000)260 1801 y Fj(X)297 1783 y Fg(2)325 1801
y Fk(+)h Fj(Y)400 1783 y Fg(2)419 1767 y Ff(\001)447
1801 y Fk(+)g Fj(a)511 1807 y Fg(13)546 1801 y Fj(X)590
1767 y Ff(\000)609 1801 y Fj(X)646 1783 y Fg(2)675 1801
y Fk(+)f Fj(Y)750 1783 y Fg(2)768 1767 y Ff(\001)787
1775 y Fg(2)813 1801 y Fj(;)45 b Fk(\(3\))-116 1868 y
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Fk(+)10 b Fj(b)118 1874 y Fg(2)136 1868 y Fj(X)j Fk(+)d
Fj(b)243 1874 y Fg(3)270 1868 y Fk(+)g Fj(b)330 1874
y Fg(4)348 1868 y Fj(Y)382 1850 y Fg(2)410 1868 y Fk(+)f
Fj(b)469 1874 y Fg(5)488 1868 y Fj(X)s(Y)19 b Fk(+)9
b Fj(b)627 1874 y Fg(6)646 1868 y Fj(X)683 1850 y Fg(2)711
1868 y Fk(+)-21 1930 y Fj(b)-3 1936 y Fg(7)23 1896 y
Ff(\000)42 1930 y Fj(X)79 1913 y Fg(2)107 1930 y Fk(+)h
Fj(Y)182 1913 y Fg(2)201 1896 y Ff(\001)229 1930 y Fk(+)g
Fj(b)289 1936 y Fg(8)307 1930 y Fj(Y)340 1913 y Fg(3)368
1930 y Fk(+)g Fj(b)428 1936 y Fg(9)446 1930 y Fj(X)s(Y)517
1913 y Fg(2)545 1930 y Fk(+)f Fj(b)604 1936 y Fg(10)639
1930 y Fj(X)676 1913 y Fg(2)696 1930 y Fj(Y)18 b Fk(+)-21
2005 y Fj(b)-3 2011 y Fg(11)32 2005 y Fj(X)69 1988 y
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y Fj(Y)233 1972 y Ff(\000)252 2005 y Fj(X)289 1988 y
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y Ff(\001)439 2005 y Fk(+)f Fj(b)498 2011 y Fg(13)533
2005 y Fj(Y)574 1972 y Ff(\000)593 2005 y Fj(X)630 1988
y Fg(2)658 2005 y Fk(+)h Fj(Y)733 1988 y Fg(2)752 1972
y Ff(\001)771 1980 y Fg(2)796 2005 y Fj(;)62 b Fk(\(4\))-116
2151 y(and)19 b(the)h(J2000)e(righ)o(t)h(ascension)h(and)f(declination)
g(are)g(then)-116 2201 y(giv)o(en)13 b(b)o(y)-116 2347
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2353 y Fi(c)269 2347 y Fk(\))g Fj(=)g Fk(\(1)i Fh(\000)g
Fj(\021)f Fk(tan)f Fj(\016)521 2353 y Fi(c)538 2347 y
Fk(\))q(])h(+)i Fj(\013)644 2353 y Fi(c)660 2347 y Fj(;)198
b Fk(\(5\))-110 2410 y Fj(\016)23 b Fk(=)e(tan)44 2392
y Fe(\000)p Fg(1)89 2410 y Fh(f)p Fk([)o(\()p Fj(\021)10
b Fk(+)g(tan)d Fj(\016)295 2416 y Fi(c)312 2410 y Fk(\))g(cos)h(\()p
Fj(\013)h Fh(\000)g Fj(\013)518 2416 y Fi(c)535 2410
y Fk(\)])d Fj(=)h Fk([1)h Fh(\000)i Fj(\021)e Fk(tan)f
Fj(\016)794 2416 y Fi(c)811 2410 y Fk(])p Fh(g)p Fj(;)14
b Fk(\(6\))-116 2556 y(where)f(\()p Fj(\013)45 2562 y
Fi(c)62 2556 y Fj(;)7 b(\016)99 2562 y Fi(c)116 2556
y Fk(\))12 b(are)h(the)g(plate)f(cen)o(tre)i(J2000.0)d(righ)o(t)h
(ascension)-116 2605 y(and)e(declination.)g(These)j(co)q(e\016cien)o
(ts)f(are)f(enco)q(ded)i(in)d(the)i(DSS)-116 2655 y(FITS)i(header)g
(via)f(the)i(follo)o(wing)c(k)o(eyw)o(ords)1130 -99 y
Fj(X)1164 -93 y Fi(c)1237 -99 y Fd(PP03)1130 -50 y Fj(Y)1154
- -44 y Fi(c)1237 -50 y Fd(PP06)1130 0 y Fj(p)1151 6 y
Fi(x)1237 0 y Fd(XPIXELSZ)1130 50 y Fj(p)1151 56 y Fi(y)1237
50 y Fd(YPIXELSZ)1130 100 y Fj(a)1152 106 y Fg(1)1237
100 y Fd(AMDX1)1130 144 y Fk(.)1130 161 y(.)1130 177
y(.)1237 144 y(.)1237 161 y(.)1237 177 y(.)1130 227 y
Fj(a)1152 233 y Fg(13)1237 227 y Fd(AMDX13)1130 277 y
Fj(b)1148 283 y Fg(1)1237 277 y Fd(AMDY1)1130 321 y Fk(.)1130
338 y(.)1130 354 y(.)1237 321 y(.)1237 338 y(.)1237 354
y(.)1130 404 y Fj(b)1148 410 y Fg(13)1237 404 y Fd(AMDY13)1130
454 y Fj(\013)1157 460 y Fi(c)1237 454 y Fd(PLTRAH,)20
b(PLTRAM,)g(PLTRAS)1130 504 y Fj(\016)1148 510 y Fi(c)1237
504 y Fd(PLTDECSN,)g(PLTDECD,)g(PLTDECM,)1237 554 y(PLTDECS)1032
647 y Fk(In)k(translating)f(the)h(DSS)g(co)q(ordinate)g(system)f(in)o
(to)g(the)970 697 y(presen)o(t)f(formalism)17 b(w)o(e)k(\014rst)g(note)
g(that)g(the)g(DSS)f(transfor-)970 747 y(mation)11 b(is)i(de\014ned)h
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796 y(tion)e(giv)o(en)h(is)f(that)h(for)g(computing)e(celestial)i(co)q
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946 y(of)i(the)i(p)q(olynomial)10 b(equations)k(3)g(and)g(4.)1032
997 y(The)19 b(DSS)f(pixel)g(co)q(ordinates)h(\()p Fj(I)s(;)7
b(J)t Fk(\))19 b(are)g(measured)f(with)970 1047 y(resp)q(ect)g(to)d
(the)g Fc(b)n(ottom)h(left-hand)g(c)n(orner)f Fk(of)g(a)g(pixel)f
(whereas)970 1097 y(the)k(\()p Fj(i;)7 b(j)r Fk(\))18
b(pixel)f(co)q(ordinates)h(used)h(here)f(are)g(measured)g(with)970
1146 y(resp)q(ect)c(to)d(the)h Fc(c)n(entr)n(e)f Fk(of)f(a)h(pixel.)g
(Also,)f(the)i(b)q(ottom)e(left-hand)970 1196 y(corner)i(of)e(the)i
(\014rst)g(pixel)e(in)g(a)h(DSS)f(subimage)g(has)h(co)q(ordinates)970
1246 y(de\014ned)17 b(b)o(y)e(the)h Fd(CNPIX1)e Fk(and)h
Fd(CNPIX2)f Fk(header)i(cards)g(whereas)970 1296 y(the)g(\()p
Fj(i;)7 b(j)r Fk(\))16 b(pixel)f(co)q(ordinates)h(of)f(the)h(cen)o(tre)
h(of)e(the)h(\014rst)g(pixel)970 1346 y(are)e(alw)o(a)o(ys)f(\(1)p
Fj(;)7 b Fk(1\).)13 b(Hence)976 1440 y Fj(I)24 b Fk(=)d
Fj(i)10 b Fk(+)f(\()p Fd(CNPIX1)f Fh(\000)i Fk(0)p Fj(:)p
Fk(5\))c Fj(;)535 b Fk(\(7\))970 1502 y Fj(J)25 b Fk(=)c
Fj(j)12 b Fk(+)d(\()p Fd(CNPIX2)f Fh(\000)i Fk(0)p Fj(:)p
Fk(5\))c Fj(:)530 b Fk(\(8\))1032 1597 y(Substituting)12
b(Eqs.)g(7)f(and)h(8)f(in)o(to)g(1)g(and)h(2)f(to)h(\014nd)g(the)g(\()p
Fj(i;)7 b(j)r Fk(\))970 1647 y(co)q(ordinates)17 b(whic)o(h)f(corresp)q
(ond)h(to)f(\()p Fj(X)q(;)7 b(Y)i Fk(\))16 b(=)f(\(0)p
Fj(;)7 b Fk(0\))15 b(w)o(e)h(ma)o(y)970 1697 y(write)970
1791 y Fd(CRPIX1)k Fk(=)h Fj(x)1199 1797 y Fi(c)1215
1791 y Fj(=p)1257 1797 y Fi(x)1287 1791 y Fh(\000)10
b Fk(\()p Fd(CNPIX1)e Fh(\000)h Fk(0)p Fj(:)p Fk(5\))d
Fj(;)343 b Fk(\(9\))970 1853 y Fd(CRPIX2)20 b Fk(=)h
Fj(y)1195 1859 y Fi(c)1212 1853 y Fj(=p)1254 1859 y Fi(y)1283
1853 y Fh(\000)9 b Fk(\()p Fd(CNPIX2)f Fh(\000)i Fk(0)p
Fj(:)p Fk(5\))c Fj(:)326 b Fk(\(10\))1032 1948 y(The)13
b(co)q(ordinate)f(incremen)o(ts)g(giv)o(en)g(b)o(y)g
Fj(p)1709 1954 y Fi(x)1741 1948 y Fk(and)g Fj(p)1841
1954 y Fi(y)1873 1948 y Fk(in)f(units)970 1998 y(of)18
b(mm/pixel)e(ma)o(y)h(b)q(e)i(con)o(v)o(erted)h(to)f(the)g(required)h
(units)f(of)970 2048 y(degree/pixel)11 b(b)o(y)g(ev)n(aluating)e
Fj(@)r(\030)r(=@)r(X)14 b Fk(and)d Fj(@)r(\021)q(=@)r(Y)20
b Fk(at)10 b(the)i(plate)970 2098 y(cen)o(tre)k(to)d(\014nd)h(the)h
(appropriate)f(scaling)f(factors,)h(whence)970 2192 y
Fd(CDELT1)20 b Fk(=)h Fh(\000)p Fj(a)1229 2198 y Fg(1)1248
2192 y Fj(p)1269 2198 y Fi(x)1289 2192 y Fj(=)p Fk(3600000)p
Fj(;)467 b Fk(\(11\))970 2254 y Fd(CDELT2)20 b Fk(=)h
Fj(b)1193 2260 y Fg(1)1211 2254 y Fj(p)1232 2260 y Fi(y)1252
2254 y Fj(=)p Fk(3600000)p Fj(:)504 b Fk(\(12\))1032
2350 y(F)m(rom)19 b(Eqs.)i(5)f(and)h(6)f(it)h(can)f(b)q(e)i(sho)o(wn)e
(that)h(the)g(stan-)970 2399 y(dard)15 b(co)q(ordinates,)h(\()p
Fj(\030)r(;)7 b(\021)q Fk(\),)14 b(are)i(Cartesian)f(co)q(ordinates)h
(in)f(the)970 2449 y(plane)10 b(of)f(a)h(gnomonic)d(pro)r(jection)k
(with)e(tangen)o(t)h(p)q(oin)o(t)f(\()p Fj(\013)1911
2455 y Fi(c)1928 2449 y Fj(;)e(\016)1965 2455 y Fi(c)1982
2449 y Fk(\).)970 2499 y(Hence)16 b(w)o(e)e(m)o(ust)f(mak)o(e)f(the)i
(asso)q(ciation)970 2593 y Fd(CRVAL1)20 b Fk(=)h Fj(\013)1202
2599 y Fi(c)1218 2593 y Fj(;)706 b Fk(\(13\))970 2655
y Fd(CRVAL2)20 b Fk(=)h Fj(\016)1193 2661 y Fi(c)1210
2655 y Fj(:)714 b Fk(\(14\))p eop
%%Page: 2 2
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256 y(tation)i(of)g(co)q(ordinates)i(is)e(done.)-54 306
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y(L)-106 2639 y Fb(A)-89 2647 y Fl(T)-67 2655 y(E)-47
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eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF

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