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RENDER

render

## Purpose

Render a rectangular projection map to a sphere.

## Description

The most confusing aspect of this program is by far the image orientation.
I can't make the conventions natural for everyone (not even myself), but
here's what this program does:
In the output image there is a natural coordinate system, (x,y). Each
row, ie., image[*,i] corresponds to a fixed value of y. image[*,0]
is the row with the LOWEST value of y. This may seem strange, but it
permits a "normal" orientation of the image if displayed with !order=0
(the usual IDL default). The x direction (image[i,*]) works in the
obvious way, image[0,*] is the column with the LOWEST value of x. So,
viewed with !ORDER=0, this is an image that has up at the top. The
top is also considered NORTH when dealing with images that one sees in
the sky (or relative to your point of view).
The position angle of the pole sets the rotation of the sphere in the
plane of the sky (image). North is to the top (+y) and East is to the
left (-x). The position angle (POLE) is the angle of the apparent
North pole of the sphere relative to up (North) in the image, measured
From up (North) counter-clockwise (also known as eastward from North).
Visualizing the indexing of the input map is equally confusing. In
the coordinate system containing the map, North is +y, East is -x, as
before. These coordinates are plane-of-sky on the object. The map
has its own coordinates, latitude and longitude. The first index into
the map is treated like x but is actually East Longitude. The left edge
of image[0,*] is precisely at 0 degrees longitude. As the first index
increases (increasing x?), the longitude increases. The right edge of
the last column in the map is 360 degrees.
Ok, here is the weird part. The first row in the map is the NORTHERN-most
set of pixels. The last row is the SOUTHERN-most set. So, map[0,0]
touches the prime meridian and the north pole.
Thus map[i,j]:
longitude = (i+0.5)/nl * 360.0
latitude = 90.0 - (j+0.5)/nt * 180.0
where nl is the width of map and nt is the height of the map.
These formulas give the lat,lon of the CENTER of the pixel in degrees.
Now, understanding the sub-"earth" and sub-solar longitudes becomes
easy. The sub-"earth" point is the lat,lon of the map that is in the
center of the projected disk. The sub-solar point is the lat,lon of
the map that is nearest to the sun (normal solar illumination). Note,
that as the object rotates, the sub-earth longitude will decrease, not
increase.

Image display

## Inputs

map - Array containing a full map of surface
scale - Scale of image (eg., km/pixel)
pole - Position angle of pole, east from north (degrees)
selat - Sub-earth latitude (degrees)
selon - Sub-earth longitude (degrees)
sslat - Sub-solar latitude (degrees). Only used for Hapke functions.
sslon - Sub-solar longitude (degrees). Only used for Hapke functions.
nx - X size of output image in pixels.
ny - Y xize of output image in pixels.

## Keyword Input Parameters

SILENT - Flag, if set suppresses all printed output
NODISPLAY - Flag, if set suppresses graphical output
GEOM - Undefined (default), no special action.
If defined but not a structure, then upon return geom will contain
all the geometric information needed to render the image with a
new map.
If defined and is a structure, then the contents are taken to be
that needed to do the final image calculation without redoing
all the geometric computation.
XOFFSET - x offset, of object from center of image (in pixels) default=0
YOFFSET - y offset, of object from center of image (in pixels) default=0
Limb darkening model to use (set one of these, at most):

LIN - Linear limb-darkening coeff, map is normal albedo
MIN - Minnaert limb-darkening coeff, map is normal albedo
HAPKE - Hapke scattering model, map is single scattern albedo
HAPKE[0] = h (old style, circa 1981)
HAPKE[1] = P(0)
HAP2 - 2nd generation Hapke scattering model, 1986 and the book,
"Theory of Reflectance and Emittance Spectroscopy"
HAP2[0] = h (new style, circa 1986, p. 226 in book)
HAP2[1:PPARMS] = P(g), or HG function parameters
HAP2[PPARMS+1] = B0, Emperical backscatter factor (p. 228)
HAP2[PPARMS+2] = Theta(bar), surface roughness
PPARMS is deduced from the length of this vector. The minimum
length is 4, for which PPARMS=1. Only PPARMS=1 is allowed
if you are not using a single-particle scattering function.
H93 - When used with HAP2, will select which approximation to the
H-function is used. Default is the simplest (and fastest)
formula from the 1981 Hapke paper. H93, when set, will
force the use of eqn. 8.57 from the Hapke book (from 1993).
Pfn - Specify function to use for P(g) instead of the default constant.
The function must be a procedure taking arguments g,a,F,/radians
a an array of Pparms parameters
F phase function evaluated at phase angles g
Use "fn_hg3.pro" as a model.
The default is to use the scalar value in HAP2 for the value of
the phase function. This is ignored if HAP2 not being used.

## Outputs

image - Rendered image of object. Return is a traditional I/F value.

## Keyword Output Parameters

XARR - Optional return of the array of plane-of-sky x positions for each
pixel in the image. These values are in units of the object
YARR - Optional return of the array of plane-of-sky y positions for each
pixel in the image. These values are in units of the object

## Modification History

95/07/24, Written by Marc W. Buie, Lowell Observatory
96/04/11, MWB, fixed numerous bugs, now works for sun and viewpoint
being different