Method and system for producing stereographic images of celestial objects

A method and system of producing stereographic images of celestial objects uses distance information to offset one of two images produced on a display device. A digital computer under program control is used in combination with a user input device, such as a keyboard, and a display device, such as a computer monitor and/or a printer.

The computer program implemented by the present invention is set forth in 
Table 1 and the data used in the execution of the program is found in 
Table 2. The source code listings for Borland International's Turbo 
Graphics.TM.Toolbox, version 1, procedures entitled GRAPHIX.SYS, 
KERNEL.SYS, TYPEDEF.SYS, WINDOWS.SYS and 4.times.6. FON are presented in 
Tables 3, 4, 5, 6 and 7 respectively. All tables follow the section 
entitled Best Mode for Carrying Out the Invention. A portion of the 
disclosure of this patent document contains material which is subject to 
copyright protection. The copyright owner has no objection to the 
facsimile reproduction by anyone of the patent document or the patent 
disclosure, as it appears in the Patent and Trademark Office patent file 
or records, but otherwise reserves all copyright rights whatsoever. 
TECHNICAL FIELD 
The present invention relates to generating stereographic images of 
celestial objects such as stars, Messier objects, Halley's comet, and 
meteors through use of dual map projections in which the object's 
astronomical distance from the earth affects its projected image. 
BACKGROUND OF THE INVENTION 
With the advent of computers, and in particular personal computers, a 
number of programs have been developed that map celestial objects from 
their normal spherical coordinates into two-dimensional coordinates using 
well-known map projection techniques commonly used by cartographers. 
Celestial objects such as stars, nebulae, and planets have their positions 
in the sky recorded in a spherical coordinate system similar in concept to 
use of latitude and longitude to record the positions of geographic 
locations on the earth. 
In the terrestial coordinate system, the lines of longitude pass through 
the earth's North and South poles, while the parallel lines of latitude 
intersect these lines of longitude to form a spherical grid. The lines of 
longitude start at zero degrees and extend to 180 degrees east of the 
prime meridian (which passes through Greenwich, England) to encompass one 
hemisphere, and extend another 180 degrees west of the prime meridian to 
encompass the earth's other hemisphere. Thus the lines of longitude extend 
throughout 360 degrees of a sphere. 
Similarly, in celestial coordinates there are lines that pass through the 
North and South poles of the celestial sphere. These lines are known as 
right ascension. Instead of these lines being in units of degrees, they 
are in units of hours, where one hour of right ascension is equal to 15 
degrees. Thus to define all 360 degrees of the celestial sphere, there are 
24 hours of right ascension, ranging from zero hour to twenty-three hours. 
The parallels of latitude on the terrestial sphere are in units of degrees, 
ranging from zero degrees on the equator to 90 degrees at the North and 
South poles. There are thus 90 degrees of latitude north of the equator 
and 90 degrees of latitude south of the equator. 
The corresponding lines that define the celestial sphere are call lines of 
declination. Like the terrestial lines of latitude, these lines of 
declination are in units of degrees both north and south of the celestial 
equator. The lines north of the celestial equator are called positive or 
plus (+) lines of declination while the lines south of the celestial 
equator are called negative or minus (-) lines of declination. 
An excellent discussion of the celestial sphere and its coordinate system 
is presented in Guy Ottewell's The Astronomical Companion, pages 4-11 
(published by G. Ottewell at the Department of Physics, Furman University, 
Greenville, S.C. 
As is well known for terrestial mapping, there are many mathematical 
projection techniques to translate points on a spherical surface into 
points on a planar surface. An in depth review of virtually all the 
well-known mapping techniques is presented in Map Projections--A Working 
Manual, by John P. Snyder (published by the U.S. Geological Survey, 
Professional Paper 1395, dated 1987). One such technique which has also 
found use for projecting the celestial sphere onto a planar surface is 
known as a stereographic projection. According to Snyder, this map 
projection technique has probably been known since the times of the 
ancient Egyptians. The technique projects all points on a hemisphere to a 
plane perpendicular an axis through the sphere, with the lines of 
projection emanating from the axis' pole opposite the plane (see Map 
Projections, above, at pages 154-163, as well as FIG. 1 herein). 
Richard Berry wrote a computer program in the BASIC language called Stars. 
Bas (as published in the August, 1985 issue of Astronomy magazine, pages 
66-71) which performs a stereographic map projection of celestial objects 
onto the planar surface of a computer monitor. The stereographic map 
projection technique used by Berry is used in the preferred embodiment of 
the present invention, although other types of map projection techniques 
can also be used. 
The stereographic map projection technique is used in the present invention 
to achieve a new result; namely, to generate two corresponding but 
different planar projections of the same portion of the celestial sphere. 
One projection is for viewing by the observer's left eye while the other 
projection is for viewing by the observer's right eye. The difference 
between the two projections is a function of the celestial object's 
distance from the earth, so that celestial objects closer to the earth 
than other celestial objects are presented with a greater horizontal 
offset. In this way, when the two images are merged into one by the 
observer's eyes (and brain) the celestial objects will be perceived in 
three dimensions with respect to each other. 
Due to the extreme distances of celestial objects from the earth, the 
horizontal offsets displayed actually represent views of the celestial 
objects as if the viewer's left and right eyes were separated from one 
another by up to trillions of miles, and thus the present invention is 
able to present a view of the heavens heretofore unobservable. 
SUMMARY OF THE INVENTION 
The present invention provides a method to view celestial objects in a 
three-dimensional manner by displaying on a digital computer monitor, or 
other viewing device, two images of the same region of the celestial 
sphere in a manner that causes objects that are closer to the earth than 
others in the same region to appear closer to the viewer. More 
particularly, the two images are displayed side-by-side so that the 
lefthand image is intended for viewing by only the viewer's left eye while 
the right-hand image is intended for viewing by only the viewer's right 
eye. Such side by side images are generally known as stereoscopic pairs or 
stereographs. Similar images of terrestial landscapes and other scenes 
(including some celestial objects with rapid angular movement with respect 
to the earth, such as the moon and some comets--see sky and Telescope, 
April, 1988, pp.366-369) were widely photographed during the latter part 
of the nineteenth century and the early part of the present century. 
The stereographs of terrestial objects are generally made by photographing 
the same scene by two cameras separated by a distance commensurate with a 
person's interocular distance. The two images are generally viewed with a 
stereoscope which contains lenses that provide eye relief to facilitate 
the left eye only focusing on the left photograph and the right eye only 
focusing on the right photograph. 
The stereographic images of the present invention represent two views of 
the celestial sphere from the perspective of such views being separated by 
trillions of miles rather than a few centimeters typical for interocular 
distances. In this way the great distances of the stars and other 
celestial objects can be projected so as to generate a true 
three-dimensional image of the sky. The images can be merged into one 
three-dimensional image by means of a stereoscope or by viewing the 
centerline (actual or apparent) between the two images and mentally 
allowing this centerline to separate, resulting in a three-dimensional 
image in the middle of the viewer's field of view. 
Since the region displayed is user selectable and can vary greatly in size 
and in object distances within the selected area, the projection system 
determines the closest celestial object within the field of view and 
adjusts the apparent spacial separation of the two views so that the 
closest object will appear to the viewer to be some minimum apparent 
distance to the viewer, such as an object which is within several feet 
from the viewer. This adjustment thereby prevents any object from 
appearing so close to the viewer that the viewer's eyes would be unable to 
merge the left and right eye images into one three-dimensional view. 
The present viewing technique also allows generation of a simulated meteor 
shower in either two dimensions or in a stereographic pair representing 
three-dimensions. The apparent closeness of each meteor's path is randomly 
varied from meteor to meteor to more accurately simulate actual meteor 
paths. In addition, the duration, speed and direction of each meteor is 
randomly varied to better simulate an actual meteor shower. 
Another feature of the viewing technique includes the display of the 
Messier objects. These objects were first identified by Charles Messier in 
the mid 1700's and represent many of the brightest star clusters, nebulae 
and extragalatic objects viewable in the northern hemisphere. The objects 
can be displayed with or without display of their corresponding Messier 
Number. 
In addition, the viewing technique can display the coordinates of the 
celestial viewing area as well as the coordinates of the object closest to 
the celestial pole within the field of view. 
A marking arrow can also be displayed to facilitate the use of the display 
as a teaching tool. 
Inverse display of the viewing area is also available whereby the 
background is represented as a bright area and the celestial objects as 
dark objects. 
The relative magnitude of the stars and other celestial objects is 
represented by corresponding increased size of the object. 
A printout of the selected viewing area is also available in both normal 
background and inverse background. 
OBJECTS OF THE INVENTION 
It is a principal object of the present invention to provide a method for 
determining and displaying a three-dimensional projection of any selected 
portion of the celestial sphere, incorporating into the projection 
distance information of the celestial objects within the selected portion. 
Another object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere wherein two side-by-side map projections of the selected 
portion are presented with the celestial objects of one projection offset 
in one dimension inversely proportional to the distance of each object 
from the earth so that when the viewer's left and right eyes merge the two 
projections to form a true three-dimensional image of the displayed 
celestial objects. 
A still further object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere as described above, wherein the apparent spacial 
separation of the viewing positions of the two images is displayed. 
A further object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere as described above, wherein the coordinates of the 
selected portion are displayed. 
Another object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere as described above, further providing display of 
simulated meteor showers in a two or three-dimensional projection. 
A further object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere as described above, with display of Messier objects and 
Halley's comet. 
A still further object of the present invention is to provide a method of 
displaying a three-dimensional projection of a selected portion of the 
celestial sphere as described above, which provides means for printing the 
image displayed. 
Other objects of the present invention will in part be obvious and will in 
part appear hereinafter.

BEST MODE FOR CARRYING OUT THE INVENTION 
The present invention is directed to a method of generating a stereographic 
pair of images of a selected region of the night sky so as to accurately 
depict the relative distances of stars and other celestial objects in a 
three-dimensional manner when the pair is merged by the observer into a 
single image. The stereographic pair is directly analogous to the 
stereographic pairs commonly used in the late 1800's and early 1900's to 
illustrate landscapes and other objects. The same concept is employed 
today in the popular Viewmaster.RTM. displays which allow the observer to 
view two transparencies of the same object in a way that allows the images 
to be merged into one image that contains three-dimensional information. 
The underlying concept employed by such stereographic pairs is quite 
straightforward; namely, take two pictures or photographs of the the same 
scene or object from slightly different locations which are offset from 
each other by approximately the same distance as a person's interocular 
distance (the distance between the pupils of a person's eyes-- 
approximately 3 inches or 7.62 centimeters). In this manner the two images 
if separately seen by the observer's left and right eyes, mimic what the 
observer would "see" if the same scene was directly observed. 
Of course when a person looks at the night sky the stars do not appear in 
three-dimensions since they are so far from the earth that they all appear 
to be infinitely distant. The observer's left and right eyes see no 
angular difference since the person's interocular distance is 
infinitesimal compared to the distance of the star. Indeed, the closest 
star to the earth after the sun is alpha centauri C (also known as Proxima 
Centauri), which is 1.295 parsecs from the earth. A parsec is equal to 
approximately 3.259 light years, where one light year is the distance 
light travels in one year (a parsec corresponds to the distance at which 
an object would have an annual parallax of one arc second--1/3600 of one 
degree-- when observed from two opposite points on the earth's orbit about 
the sun). Since light travels 186,300 miles per second (approximately 
300,000 kilometers per second), a light year is equal to approximately 
5.9.times.10.sup.12 miles (9.47.times.10.sup.12 kilometers). Thus the 
closest star to the earth is approximately 19.2 trillion miles (30.9 
trillion kilometers) away. 
Therefore in order to generate a stereographic pair of the night sky with 
three-dimensional information that the human eye can see, it is necessary 
that the parallax or angles subtended between the two images be comparable 
to the angles that one sees when relatively close objects are seen. For 
instance, if an interocular distance ("s") is assumed to be three inches 
(7.62 cm), then an object four meters away subtends an angle of 0.01905 
radians or 1.09 degrees (based on the equation s=(r).times.(theta)), where 
s is the subtended distance, r is the radius, and theta is the subtended 
angle, see FIG. 3). Similarly for a star 1.295 parsec from the earth 
(corresponding to the value of r) the distance between the left and right 
eye views to appear four meters away is: 
EQU s=1.295.times.0.01905 
or 0.253 parsec, which is equal to approximately 485 billion miles (762 
billion kilometers). It is therefore clear that the two views must 
represent views "seen" apart from each other by very great distances if a 
three-dimensional stereographic pair is to be generated. 
It has been experimentally found that the maximum displacement between the 
left and right views that the human eye can merge into a single image 
without the use of a stereoscope is approximately 3/8 of an inch (0.375 
inch or 9.525 mm). This offset is the same as an object seen at a distance 
of four meters for a typical human eye focal length of 50 millimeters. As 
seen in FIG. 3, s is 0.07624 meter, r is 4 meters, and therefore theta is 
0.01905 radian. If the eye focal length is 50 millimeters, then r' is 0.05 
meter, theta' is equal to theta and thus s' is 
(0.05).times.(0.01905)=9.525 millimeters, or 3/8 inch (0.375 inch). 
From an astronomic perspective such an offset corresponds to a parsec 
spacing between the two views of approximately 0.253 parsec if the object 
is as close to the earth as Proxima Centauri. That is, the 3/8 inch offset 
is proportional to 4 meters in the same ratio as a 0.253 parsec spacing is 
to 1.295 parsecs. 
Although the offset discussed above is with respect to the right eye, an 
equal amount of offset in the opposite direction would result in the same 
stereographic perspective if such an offset is applied to the image seen 
by the left eye and no offset presented in the right eye image. 
Alternatively, if the object shown in FIG. 3 is positioned along the 
midpoint between the left and right eyes, geometry shows that each eye 
would have an offset equal to one-half that obtained in the above 
examples. Such offsets would then be presented to the left eye and right 
eye images with the same end result. 
Overview of the Implementing Computer Program and Hardware 
The computer program for implementing a stereographic pair of astronomic 
images of any selected region of the celestial sphere is presented in 
Table 1 which appears at the end of this specification along with Table 2 
identified below. Copyright is claimed in the computer program but the 
copyright owner hereby authorizes facsimile reproduction of the patent 
document, including the copyrighted computer program. 
The computer program is written in Borland International's Turbo 
Pascal.RTM. ver. 3.0 (Borland International, Inc., 4585 Scotts Valley 
Drive, Scotts Valley, Calif. 95066). The program incorporates graphic 
routines published by Borland International known as Turbo Graphix 
Toolbox.TM.. These routines are specifically implemented in the computer 
program for use in Hercules.TM. graphics, a monochromatic graphic standard 
developed by Hercules Computer Technology Inc., 2550 Ninth Street, 
Berkeley, Calif. 94710. As implemented in the Graphix.TM. routines, this 
monographic display has a horizontal resolution of 720 pixels (points) and 
a vertical resolution of 350 pixels. 
The computer program can be run on IBM PC's or compatible computers, such 
as computer 20 shown in FIG. 2, having an associated monitor 22 and 
keyboard 23 and an optional printer 24 for hardcopy output of the 
celestial images. 
This program projects stars and other celestial objects onto a 
two-dimensional image using the stereographic map projection technique as 
shown in FIG. 1 and as discussed in Map Projections--A Working Manual, by 
John P. Snyder and published by the U.S. Government Printing Office, 
Washington, D.C. (1987). The actual equations used for a non-offset image 
were published in Astronomy Magazine, August, 1985 at pages 66-76 in a 
program written by Richard Berry. 
The data for the celestial objects is stored in a database file called 
allstst.dat (see Table 2). This file is based upon a celestial object 
database file called stars.dat used in conjunction with Berry's program. 
Both database files store the celestial object data in humanly readable 
ASCII (American Standard Code for Information Interchange) form. The 
allstst.dat database file was validated using the data in Sky Catalogue 
2000.0, volume 1, edited by Alan Hirshfeld and Roger W. Sinnott, published 
by Sky Publishing Corp. (1982). Star distance information was obtained 
using the data and formulae from Sky Catalogue 2000.0, while Messier 
object distance information was obtained from The Telescope Handbook and 
Star Atlas, by Neale E. Howard; Thomas Y. Crowell Publishers (1975). 
Distance information concerning the orbital positions of Halley's Comet 
can be obtained from Mankind's Comet, by Guy Ottewell and Fred Schaaf, 
published by the Astronomical Workshop, Furman University, Greenville, 
S.C. (1985), although such data is not currently implemented in the 
allstst.dat database. 
Operation of the Computer Program 
The first step in operating the program is loading data stored in the 
celestial objects database file (allstst.dat) into the computer's random 
access memory (RAM) in such a manner that all pertinent information 
concerning the object's celestial coordinates (right ascension and 
declination), magnitude, and distance from the earth is extracted, 
manipulated, and stored in arrays (see pages 21-23 of Table 1 starting 
with "Main Program"). Messier object number information is also extracted. 
Other information such as the celestial object's name (if any) or 
astronomic identifying information or color information could also be 
extracted if such information is to be used by the program (such as to 
display the object's name or its color-- the latter if using a color 
graphics standard such as the color graphics adapter--CGA-- or the 
enhanced graphics adapter--EGA-- used with IBM and IBM--compatible 
computers). The data read from the database file can be viewed by the user 
(see page 22 of Table 1). The display of such data as read by the program 
is presented in Table 3. 
TABLE 3 
__________________________________________________________________________ 
RA DEC 
No. 
HH:MM:SS.F 
DD.MM.SS 
MAG B-V 
STAR DIST 
CONSTELLATION 
__________________________________________________________________________ 
742 
21:42:42.0 
-18.52'00" 
4.7 0.88 
KAPPA 
CAP 
77 CAPRICORNUS 
__________________________________________________________________________ 
Once the data is read into RAM, the user can select or accept the default 
values for the following parameters from a main menu: stereo viewing, 
right ascension, declination, viewing size, coordinate display, a border 
around the selected image(s)-- only one image is displayed for non-stereo 
viewing--, Messier object display as ellipses, Halley's Comet track 
display, a pointing arrow, and meteor shower display. As shown in FIG. 4, 
the parameter selection is made by choosing the highlighted letter 
embodied in each parameter displayed; such as the highlighted "S" in the 
phrase "Stereo Viewing". 
FIG. 4 shows the complete menu generated by the computer program. The right 
ascension coordinate information is displayed in both angular hours, 
minutes, and seconds, and in hours and decimal remainder. Similarly the 
declination is displayed in both degrees, minutes and seconds, and degrees 
and decimal remainder. 
Once the parameter settings are made, the user instructs the program to 
generate the desired image by selecting the "Go" command. 
A typical stereographic pair of images for the region about the 
constellation Orion, with coordinate information display and a border is 
shown in FIG. 5. The same celestial region without a border and without 
display of coordinate information, but with display of Messier objects is 
shown in FIG. 6. The display of the same region in inverse background and 
with the display of a pointing arrow is shown in FIG. 7. FIG. 8 is a 
similar celestial display in normal background showing both the projection 
of Comet Halley's path during its most recent approach to the sun and the 
stereographic display of a simulated meteor. 
Such images can be merged into a single three-dimensional image by having 
the left eye focus on the lefthand image and the right eye focus on the 
righthand image. This merging can be achieved by use of a stereoscope or 
unaided by focusing both eyes on the centerline (actual or apparent) 
separating the two images and then letting this centerline separate 
farther and farther apart until the three-dimensional image appears in the 
middle portion of the viewer's field of view. A small card having a width 
of approximately 1.75 inches (4.45 cm) and a length of approximately 3.5 
inches (8.89 cm) can also be used as an aid by placing the card on an 
imaginary line bisecting the viewer's eyes and adjusting the card's 
distance from the viewer's eyes so that the left eye can only see the 
lefthand image and the right eye can only see the righthand image; and 
then letting these two images merge into one. 
FIG. 9 is a display of the region about the North celestial pole showing 
the display of the star with the maximum declination value (Polaris) as 
well as other coordinate information. FIG. 10 shows the same region in a 
single non-stereo display. Finally, FIG. 11 shows a stereographic pair 
display about the South celestial pole, including the well-known Southern 
Cross. 
The area viewed can be adjusted by the user through use of the "Viewing 
Size" parameter (see FIG. 4). FIGS. 12 and 13 show two stereographic pair 
images of the famous Seven Sisters (Pleiades) for two different viewing 
sizes. In this manner the user can enlarge any region of the celestial sky 
desired. 
During any display, the user can invoke certain changes to the display 
without the need for reentering display parameters from the main menu. 
Thus inverse background is selected by depressing the "I" key while 
simulated meteor shower display is selected by the "M" key. Arrow 
selection is made with the "A" key and printout of the celestial display 
is selected with the "P" key. It is in this manner that the images 
comprising FIGS. 5 through 13 were obtained. 
All of these keys with the exception of the "P" key act as toggles; that 
is, reselection will toggle the selected item ON or OFF. For example, if 
an arrow is shown it can be removed with reselection of the "A" key. It 
can again be shown by selecting the "A" key. 
An arrow when displayed can be moved about through use of the cursor keys 
and the diagonal keys adjacent the cursor keys found on a standard IBM 
PC.RTM. or IBM PC.RTM. compatible keyboard. 
Program Description 
Table 1 is the complete program listing in Turbo Pascal.RTM. source code. 
The source code of the GRAPHIX.SYS, TYPEDEF.SYS, WINDOWS.SYS and 
4.times.6. FON procedures forming part of Borland International's Turbo 
Graphix.TM. Toolbox, version 1, is presented in Tables 3,4,5,6 and 7 
respectively. These procedures are copyrighted by Borland International. 
The overall program named "allstars.sub.-- stereo" (file ALLSTST.PAS, see 
Table 1) is copyrighted by the applicant (see notice above regarding 
facsimile reproduction of the patent document). FIGS. 14A-14E form an 
overall flow chart of Table 1. 
The first portion of the listing contains the program name and a copyright 
notice. 
The next section contains the compiler directives which lander Turbo 
Pascal.RTM. instructs the compiler to perform or not perform certain 
functions (step 50, FIG. 14A). The V- compiler directive allows passing of 
actual parameters which do not match the length of formal parameters. The 
C+ directive controls control character interpretation, including program 
termination at a Read or Readln statement if a Control-C is encountered. 
The U+ directive prevents user interruption with a Control-C during 
program execution. The R- directive instructs the compiler not to perform 
run-time index checks while the K+ directive instructs the compiler to 
generate a stack check code. Other compiler directives appear in the 
listing. Their functions are explained in the Turbo Pascal.RTM. version 
3.0 Reference Manual. 
The LABEL, CONST, TYPE, and VAR sections (step 52, FIG. 14A) which follow 
the compiler directives define various labels (location in the program), 
constants, user defined types, and variables used in the main portion of 
the program. The types identified as "StarNumType" and "HalleyType" are 
used to define pointer variables named "StarDistance" and "HalleyPresent" 
respectively. These pointer variables are declared in order to use the 
Heap portion of memory for data storage since the 64K (64 thousand byte) 
data storage area allowed under Turbo Pascal.RTM.version 3.0 is 
insufficient for this program. 
Various procedures and functions are then defined in the program (steps 54 
and 55, FIGS. 14A-14B) Each procedure and function performs a specific 
task. Each procedure is invoked from either the main program or by another 
procedure or function. The purpose of each procedure and function is 
presented in comment statements which accompany each procedure and 
function. Thus the procedure "spaceremove" removes leading spaces in a 
variable named "testline" and returns the passed parameter to the calling 
portion of the program without leading spaces. The procedure "Indat" has 
its own "update log". 
Some of these procedures and functions were obtained from other programs 
listed in various Borland International publications or toolkits, such as 
the "Select", "ConstStr", "Say", "IOCheck", and "ErrorMessage". The 
"Title", "MainMenu", and "ArrowDraw" procedures were based upon published 
Borland International listings, but modified to accomplish a particular 
message and format. The "rh.sub.-- display", "dec.sub.-- display", 
"Indat", and "Meteor.sub.-- Show" procedures are new and original. 
The "Main Program" follows (step 56, FIG. 14D). This portion of the program 
directs the entire set of events which are executed by the program. First 
the pointer variables "StarDistance" and "HalleyPresent" are allocated 
(step 56, FIG. 14C), then a message is presented on the screen (step 6D 
FIG. 14C), and then various variables are initialized (step 62, FIG. 14C). 
The program then asks the user if retrieved data is to be displayed as it 
is retrieved (step 64, FIG. 14C), and if it is to be displayed, the data 
is shown in a particular format (see Table 3 and steps 66 and 70 FIG. 
14C). The retrieved data is then extracted from the file called 
"allstst.dat" which contains coordinate information for all the 
displayable celestial objects, their distances from the earth, as well as 
other data including the Messier Number for the Messier Objects (step 68, 
FIG 14C). Other data, such as star names and associated constellations is 
within the database but is not presently used by the program. 
Initial default values for an initial celestial display are then 
defined(step 72, FIG. 14C). The MainMenu procedure is then invoked (step 
74, FIG. 14D) which displays default or selected values for the stereo 
viewing option, right ascension, declination, viewing size, coordinate 
display, border display, Messier object display, Halley's Comet display, 
arrow drawing and simulated meteor shower display. Once the desired values 
are selected (or the defaults accepted) by the user, actual display is 
invoked with the "G" letter, standing for "GO". 
If stereo viewing is selected (step 76, FIG. 14D), then the boolean 
variable "stereo" is true and the horizontal and vertical testing sizes 
for the screen are respectively 360 and 340 so as to be able to display 
two images on a monochromatic display with Hercules.TM. monochrome display 
capability (step 78, FIG. 14D). Otherwise the horizontal testing size is 
720 and a slightly larger vertical size of 348 is selected (step 80, FIG. 
14D). The smaller vertical size for stereo viewing is to allow an upper 
screen window for display of parsec spacing between the two views (see 
FIGS. 5-9, 11). 
The actual plotting of celestial objects is invoked after the comment 
statement "plot star on the screen" step 78-88, FIG. 14D. After several 
variables are defined which are necessary to map celestial coordinates 
into a planar display using the stereographic map projection technique 
(variables lam0, phi0, a and b), a for-- next loop equal to the total 
number of celestial objects in file ailstst.dat (defined by variable 
"num") is executed which determines for each object its planar projection 
as defined by variables "x" and "y" for the horizontal and vertical 
coordinates respectively (step 88 or 86 for mono or stereo viewing, see 
FIG. 14D). If stereo viewing is selected and if the righthand display is 
being generated, then the value of "x" is offset based upon the object's 
distance from the earth (step 86, FIG. 14D). This offset value is 
normalized for all objects within the viewing area by variable (step 82, 
FIG. 14D), which in turn is equal to the maximum horizontal displacement 
defined by variable "MaxDispX" times the value of "SD.sub.-- Near", which 
is in units of parsecs This latter variable is determined by the closest 
object displayed in the lefthand display. Thus the horizontal offset for 
each object displayed in the righthand display is minus the value of 
"MaxDispXNormalized" divided by "StarDistance0". 
If coordinate information is to be displayed, then the "Coordinate" boolean 
variable is true and various branches are invoked to determine the maximum 
and minimum right ascension values displayed as well as the screen 
locations where the objects having these values are positioned (step 90, 
FIG. 14D). Variables "rh.sub.-- high" and "rh.sub.-- high.sub.-- val" 
respectively define the horizontal screen location and the corresponding 
right ascension value for the object with the highest right ascension 
value. Similarly, "rh.sub.-- low" and "rh.sub.-- low.sub.-- val" define 
the corresponding horizontal screen location and right ascension value for 
the object with the lowest right ascension value. 
In addition, the horizontal location and right ascension value for the mid 
right ascension value of the displayed area is calculated and displayed 
(variables "middle.sub.-- val" and "rh.sub.-- middle.sub.-- val" 
respectively). 
Since the displayed region of the celestial sphere may be about a celestial 
pole, the high and low right ascension values may have different values 
for objects displayed above and below the celestial pole. When this 
occasion occurs, a second set of high and low right ascension values are 
determined along with their horizontal screen locations as defined by 
"rh.sub.-- high2" and "rh.sub.-- high.sub.-- val2" (for the screen and 
right ascension high values respectively) and by "rh.sub.-- low2" and 
"rh.sub.-- low.sub.-- val2" (for the screen and right ascension low values 
respectively). These right ascension values are displayed along the top of 
the display. 
For declination display, upper and lower screen declination values are 
determined as well as a maximum (for northern celestial sphere displays) 
or minimum (for southern celestial sphere displays) declination value 
associated with the celestial object closest to the respective northern or 
southern celestial pole(step 90, FIG. 14D). Corresponding vertical screen 
locations for these celestial objects are also stored so as to display the 
declination coordinate information at the proper vertical screen height 
associated with the celestial object. 
Thus a distinction is made between the uppermost and lowermost vertical 
position objects (and their corresponding declination values) and the 
highest and lowest declination value objects. The object with the 
highest-most vertical screen location has screen vertical location 
"dec.sub.-- top" and a declination value "dec.sub.-- top.sub.-- val". 
Similarly, the object with the lowest-most vertical screen location has 
screen vertical location "dec.sub.-- bottom" and a declination value 
"dec.sub.-- bottom.sub.-- val". The object with the highest declination 
value has vertical screen location "dec.sub.-- high" and declination value 
"dec.sub.-- high.sub.-- val" while the object with the lowest declination 
value has vertical screen location "dec.sub.-- low" and declination value 
"dec.sub.-- low.sub.-- val". 
The magnitude of the object determines the number of pixels displayed for 
the object. Variable "ma" represents the object's magnitude. 
If Messier objects are to be uniquely displayed, the objects are shown as 
small ellipses using the "drawcircle" procedure and their Messier number 
is displayed through use of variable, see step 90, FIG. 14D "M.sub.-- 
no[j]" (an array variable). 
After the celestial objects are displayed the user can select inverse 
display (white background with black objects) through use of the "I" key 
(steps 92 and 94, FIG. 14E). This key acts as a toggle so that if it is 
depressed again, normal black background and white objects are displayed. 
The "A" key also acts as a toggle so as to select or deselect the display 
of an arrow on the screen (steps 92 and 94, FIG. 14E). If displayed, the 
arrow can be moved about the screen through use of the cursor keys and the 
adjacent diagonal keys (Home, PgUp, End, and PgDn keys) (see "Arrow" 
procedure in Table 1). 
The "M" key is a toggle for the display of a simulated meteor shower (steps 
92 and 94, FIG. 14E). If stereo viewing is selected, the simulated shower 
contains offset information so as to appear three-dimensional. The 
repetition rate, length, direction, and speed of the simulated meteors are 
randomly selected by the program (see "Meteor.sub.-- Shower" procedure in 
Table 1). 
Selection of the "P" key when the celestial display is present on the 
screen outputs the screen information to a printer (step 92 and 96, FIG. 
14E). The Epson MX, RX and FX series graphic printers by Epson America, 
Inc. of Torrance Calif. (or compatible printers thereto), are supported by 
the "hardcopy" procedure forming part of the Turbo Graphix.TM. toolbox. 
Selection of the "Return", "Esc", or "Q" key returns the user to the 
"MainMenu" procedure. 
The present invention thereby provides a method and system for generating 
stereographic three-dimensional displays of celestial objects. Although 
described in part by a computer program written in Turbo Pascal.RTM. for 
use on an IBM PC.RTM. or compatible personal computer, it is apparent that 
the concepts described can be readily adapted to other computer languages 
and other computer systems. 
From the foregoing description, it is submitted that the objects set forth 
above and those made apparent from the description are efficiently 
attained and, since changes may be made in carrying out the methodology of 
the invention, including the computer program or other instructions used, 
it is intended that all matter contained in the above description or shown 
in the accompanying drawings shall be interpreted as illustrative, and not 
in a limiting sense. 
It is submitted that the following claims are intended to cover all the 
generic and specific features of the invention herein described and all 
statements of the scope of the invention, which as a matter of language, 
might be said to fall therebetween. 
##SPC1##