.nh 4
World Coordinates

    In general, an image may simultaneously have any number of world coordinate
systems associated with it.  It would be quite awkward to try to store an
arbitrary number of WCS descriptors in the image header, so a separate WCS
relation is used instead.  If world coordinates are not used no overhead is
incurred.

Maintenance of the WCS descriptor, transformations of the WCS itself (e.g.,
when an image changes spatially), and coordinate transformations using the WCS
are all managed by the WCS package.  This will be a general purpose package
usable not only in IMIO but also in GIO and other places.  IMIO will be
responsible for copying the WCS records for an image when a new image is
created, as well as for correcting the WCS for the effects of subsampling,
etc. when a section of an image is mapped.

The WCS package will include support for both linear and nonlinear coordinate
systems.  Each WCS is described by a mapping from pixel space to WCS space
consisting of a general nonlinear transformation followed by a linear
transformation.  Either or both of the transformations may be unitary if
desired, e.g., the simple linear transformation is supported as a special case.
.ls 4
.ls 12 image
The name (value of the \fIimage\fR key in the image header) of the image
for which the WCS is defined.
.le
.ls nlnterm
A flag specifying whether the WCS includes a nonlinear term.
.le
.ls invterm
A flag specifying whether the WCS includes an inverse nonlinear term.
If a forward nonlinear transformation is defined but no inverse transformation
is given, coordinate transformations from WCS space to pixel space may be
inefficient or impossible.
.le
.ls linterm
A flag specifying whether the WCS includes a linear term.
.le
.ls fwdtran
The interpreter program for the forward nonlinear transformation.
.le
.ls invtran
The interpreter program for the inverse nonlinear transformation.
.le
.ls lintran
A floating point array describing the linear transformation.
.le
.le


Nonlinear transformations are described by small user supplied \fIprograms\fR
written in a simple RPN language entered as a variable length character string.
The RPN language will include builtin intrinsic functions for all the standard
trigonometric and hyperbolic functions, plus builtin functions for the common
nonlinear transformations as well.  The advantage of this scheme is that the
standard transformations are supported very efficiently without sacrificing
generality.  Even nonstandard nonlinear functions can be computed quite
efficiently since the runtime overhead of an RPN interpreter can be made quite
small compared to the time required to evaluate the trigonometric and other
functions typically used in a nonlinear function.

Implementation of the WCS as a nonlinear function plus a linear function
makes it trivial for IMIO to automatically update the WCS when a linear
transformation is applied to the image (the nonlinear term of the WCS will
not be affected by a linear transformation of the image).
Implementation of the nonlinear term as a program encoded as a character
string permits modification of the nonlinear term by \fIconcatentation\fR
of another nonlinear function, also represented as a character string.
In other words, the final mapping is given by successive application of
a series of nonlinear transformations, followed by the linear transformation.
Hence the WCS may be updated to reflect a subsequent linear or nonlinear
transformation of the image, regardless of the nature of the original WCS.