DEPARTMENT OF COMMERCE
SINCLAIR WEEKS, Secretary
WEATHER BUREAU
F. W. REICHELDERFER, Chief
MONTHLY WEATHER REVIEW
Editor, JAMES E. CASKEY, IR.
Volume 82
Number 4
~ ~~
APRIL 1954 Closed June 15,1954 Issued July 15,1954
METEOROLOGICALCHARTSINTHREEDIMENSIONS
ALBERT V. CARLIN
U. S. Weather Bureau, Washlngton, D. C.
[Manuacript received Aprll23, 19541
ABSTRACT
A method is described by which constant pressurecontourcharta can bedrawn as stereographic pairs. These
charts are then made into photographic slides which may be viewed in a stereoscope or projected on a screen to pro-
ducethree-dimensionalrepresentations of constant pressuresurfaces. Two or morepressure levels can be drawn
on the same chartsandwillappear to be separated in vertical spacewhen viewed. Other types of meteorological
charts and graphical representations are amenable to this treatment.
INTRODUCTION
A review of a few principles of stereoscopic vision will
be necessary as an introduction to make clear the process
by which three-dimensional meteorological charts have
been constructed. The main basis of three-dimensional
vision is the fact of having two eyes, separated by a fixed
distance. Each eye sees a slightly different image-the
left eye sees a bit more of the left side of an object, and
vice versa. In addition to this effect, which allows us to
Bee “roundness,” the angle subtended a t the eyes by a
distant object is smaller than the angle subtended by a
nearer object. In other words, the distant object looks
smaller. This is usually described as the effect of per-
spective.
Perhaps more important than these considerations,
however, at least for stationary objects, is the effect of
parallax which is the result of the fact that the two eyes
we separated by a certain distance. Stereoscopic paral-
lax can best be defined with reference to figure 1.
For simplicity, let us assume we have cameras instead
of eyes, the left camera at Ll and the right one at Lz, the
lenses separated by a distance B. To save space, we
have shown the film plates F1 and F2 in front of the lenses
instead of behind, where they of course would be in order
to take pictures; geometrically, however, the relationships
would remain the same. Letf be the focal length of the
lenses; H and AH are distances as indicated. Now the
FIOUEZ I.-Diagram illustrating the principle of stereoscopic parallax. flee text for
explanation.
stereoscopic parallax, p , is defined by the relationship
p=zz-zl, where values of z1 and z2 are taken positive to
the right of the lens axes, negative to the left. The
parallax difference is Ap= Ap2- Apt.
By simple geometry, it can be seen from figure 1 that
plB=jlH. Further, the difference in elevation A H ,
290735-64 vz
98 MONTHLY W E A T H E R R E V I E W APBIL 1954
betweentwo points a and b is related to the parallax
difference by the following approximate equation:
Thus, the quantity Apt or parallax difference, determines
the apparent height of the two points as measured from
the two photographic plates Fl and F2.
It seems likely that the brain somehow is able to inter-
pret the parallax difference sensed through the images on
the retinas of the two eyes as a height or depth difference.
CONSTRUCTION OF CHARTS
These simple principles of stereoscopic vision axe used
in constructing two views of a contour chart which
together will give the appearance of relative depth to the
chart. In general it may be expected that in the two
separate charts, the total parallax difference between the
two lowest contours would be less than that between the
lowest and the highest contours. Since the contour height
FIGUEE Z.-Method for viewing Egures 3,4, and 6. A little practice may be necessary the
Erst time one tries to view stereoscopic pairs by this method. Hold a small mirror
along the right side of the nose, shiny side to the right. Bend over the page as shown
above, being sure to keep both eyes open. The left eye will see the left picture (L) and
at 5nt the right eye will see different things reflected in the mirror. Tilt the mirror
1.
2.
3.
approximation.
This principle was used in drawing the charts shown in 4. a. If the lowest contour is a t "sealevel,"trace
figures 3, 4, and 5.' The process may be described in a it exactly, with exactly the same width of line. If
step-by-step procedure. the numerical value of the contour is printed on
On a light table, trace the contours from the manu- the original chart, trace this lettering exactly also.
script map on& a blank map. If possible, this b. Next, move the top (or blank) chart one milli-
should be done in ink. meter to t h e r i g h t , keeping t h e c h a r t s in lateral
Remove the manuscript map and attach the copy alignment.
to the light table by means of tape. c. Now trace exactly the next higher contour, and
Place a blank map over the contour map which trace also its height value, if desired.
was attached to the lkht table. and match the v
mapa center On center, and laterally size. Larger displacement exaggerates depth. For smaller charts, use proportional dl
This displacement, or slightly smaller, works well for charts about 28 in. x 32 in. in
and longitudinally. placements. It is obvious, oj course, that in order to show depth adequately in cohstant
pressure contour charts, the:depth:dimension is exaggerated compared to the horizontd
dimensions of the maps.
I
h B I L 1954 MONTHLY W E A T H E R R E V I E W 99
d. Continue this process, moving always one milli-
meter to the right before tracing the next higher
contour.
Note: (a) The displacement may equally well be made to
the lef, but once the direction of displacement has
been decided, it must be continued in that direction
for each higher contour. The direction of displace-
ment merely governs the way in which the final
product is viewed or mounted in slide mounts.
(b) If some of the contours are below “sea level,”
(as on some 1,000-mb. charts) the direction of dis-
placement for these contours should be opposite to
that for those above sea level; i. e., if displacement
for contours above sea level is to the right, then
displacement for those below sea levelshould be
to the left, starting with centers of charts exactly
matched.
(c) Amount of displacement may remain the same
for each contour. This gives negligible distortion
in most cases. The amount of displacement gener-
ally found useful is one millimeter for each succes-
sive contour. Increasing this amount of displace-
ment steepens the appearance of ridges and
troughs. Thus the amount of exaggeration may
be controlled.
5 . If the lowest contour is some height above “sea
level,” the blank map should be moved to the
right a proportional amount (one or more milli-
Rowm 4.-A:5-day mean PWmb. chart in 3.D. The depth dimension is very greatly exaggerated inrthis view in order to demonstrate its three-dimensional charsoteristim. Parallax
difference between contours is 4 millimeters.
FIWRE &-The 1000-mb. and Wmb. contours for September 8,1953. Parallax difference between contours is one millimeter.
100 MONTHLY WEATHER REVIEW hBXL 1954
meters) before the fist contour is traced. Follow- If the “derived” chart is displaced to the right for
ing this, the other contours are traced according consecutively higher contours, then the “derived” chart
to the process described in item 4 above. will be the right-hand component of the stereographic
It is to be noted that the distinctive feature of this pair of views. If the displacement is to the left, then the
process by whichfigures 4 and 5 were drawn, is that all “derived” chart will be the left-hand component of the
of the Stereoscopic parallax is drawn into the second, or two views.
“derived” chart. This greatly simplifies the preparation
of 3-D charta, and the distortion is negligible in most CONCLUDING REMARKS
cams. Figure 3 was drawn so as to give just about the
maximum distortion possible in the bottom cone. The
top cone was drawn by introducing half of the parallax
in each view, so that there is no distortion. This can also
be done on contour maps in the first step. To do this,
instead of tracing the manuscript map exactly, the blank
map should be moved one-half a millimeter to the left for
each successively higher contour. Then, steps 2 through
5 may be followed to complete the process.
After the second, or “derived” chart is drawn, both
charts are photographed, with the proper reduction so as
to fit into a stereoscopic slide binder. EfTort can be
saved if the charts are photographed by means of a
conventional 35 mm. stereoscopic camera, for then the
correct frame size will be obtained automatically, and the
transparencies can be mounted directly in conventional
stereo-mounts for use in currently available stereoscopic
projectors or hand viewers. If black and white photo-
graphic f2m is used, transparent positive slides are made
from the negatives. If color film is used, the slides may
be made directly from it.
This process for constructing stereoscopic pairs can be
utilized for all types of charts which depict surfaces or
solid objects by means of contours. This includes imag-
inary surfaces such as those depicting magnetic fields,
isentropic surfaces, constant pressure surfaces, etc.
In addition, any three variables (such as two inde-
pendent and one dependent variable) which may be
represented by families of lines (contours) can be sub-
jected to this graphic process so as’to appear in three
dimensions. Lettering or printing can also be drawn so
as to appear in three-dimensional space.
ACKNOWLEDGMENTS
The great help of Mr. G. C. Tewinkle of the Coast and
Geodetic Survey, in discussing the principles of stere-
oscopy and in practical suggestions for producing three-
dimensional contour charts, made the success of this
project possible. In addition, thanks are due Mr. D. M.
Little of the Weather Bureau for unfailing moral and ma-
terial support.