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Патент USA US3094792

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June 25, 1963
A. M. LOSHIN
3,094,783
COORDINATE TRANSFORMATION APPARATUS
Filed Oct. 2, 1957
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INVENTOR.
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June 25, 1963
A. M. LOSHIN
$094,783.
COORDINATE TRANSFORMATION APPARATUS
Filed Oct. 2, 1957
3 Sheeté-Sheet 2
INVENTOR.
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June 25, 1963
A. M. LOSHIN
3,094,783
COORDINATE TRANSFORMATION APPARATUS
Filed Oct. 2, 1957
3 Sheets-Sheet 3
INVENTOR.
United States Patent 0 rice
1
Referring now to FIG. 1, there is shown a curve 12
plotted and drawn on graph paper.
Albert M. Loshin, 8640 Bay Parkway, Brooklyn 14, N.Y.
For the sake of
simplicity assume that the ?gure is of essentially equal
Filed Oct. 2, 1957, Ser. No. 687,844
1 Claim. (Cl. 33-24)
(Granted under Title 35, U.S. Code (1952), sec. 266)
The invention described herein may be manufactured
height and width, that is, the x and y axes are equal.
Then, suppose it is desirable to transform this curve 12
to a curve 14 shown in FIG. 2, where the y or horizontal
dimension is 1.41 times longer than that of the x or ver
and used by or for the United States Government for
governmental purposes without payment to me of any
The invention relates generally to a method and means
3,094,783‘
2
3,094,783
COORDINATE TRANSFORMATION APPARATUS
royalty thereon.
7
Patented June 25, 1963
tical dimension.
To determine the angular inclination of copy plane 18
10 in FIG. 3 with relation to the reference plane 16 in order
for reproducing ?gures such as plots of orthogonal graphs
and at the same time varying the ratio of the horizontal
to accomplish the desired ratio change, it is necessary to
?nd the angle 0. Since the relationship of the two curves
vary as the cosine of this angle then the required angle
and vertical dimensions. More particularly, the inven
tion concerns a simple and direct technique whereby 15 would be the one whose cosine was equal to
?gures including plots of orthogonal graphs can be re
1
produced in such a manner that the relationship of hori—
zontal to vertical dimensions can be changed to a new
1.41
and desired ratio.
or approximately 45°. Then, by inclining the copy plane
‘In the reproduction of graphs for analysis and com
18, 45° in relation to the reference plane 16 and project
parison, a problem arises when the scales and dimensions
ing the curve 12 onto the copy plane, the resulting curve
vary on the graphs or ?gures to be compared. Also in
14 will be increased in the horizontal or y direction by a
the publication of prepared graphs a similar problem is
encountered when it is desired to use .a certain plot in a
particular limited space of a de?nite size and shape in 25
the printed report. The present invention overcomes
these dil?culties by presenting relatively low cost easy
factor of of 1.41, while the vertical or x dimension re
mains the same.
It may be desirable in certain instances to simultane
ously decrease one of the dimensions while increasing
to-use methods for varying the relative dimensions of
plots, graphs, drawings or other ?gures by a process of
the other. In FIG. 4 there is shown an example of this
particular variation. Using the same curve 12 as the
Accordingly, it is a primary object of the invention to
the reference plane 16 but, instead, is on a different plane
20 placed at an angle 0', 30° from the reference plane 16.
Since the cosine of 30° is .866, then the vertical dimen~
reproduction thereby eliminating the necessity of tedious 30 original, the copy plane 18 is inclined at 45° thus the
horizontal dimension is increased the same amount as in
and time-consuming procedure of redrawing or replot
FIG. 3. However, since the original is not mounted on
ting the ?gures in order to obtain the desired size.
provide .a method and means for reproducing graphs and
drawings whereby either the vertical or horizontal dimen 35
sion of the curve 12 would be reduced by this factor
resulting
in a vertical dimension ratio of 1:.866 while the
resulting reproduction is of some desired shape and size
horizontal dimension ratio has increased to 1:1.41. This
or some new and different ratio of height to width.
process may be called doubly oblique projection and re
Another object of the invention is to provide rela
sion or both can be varied independently so that the
sults in a curve 22 which has changed from a horizontal
tively simple and easy-to-use apparatus for accomplishing 40 to
vertical ratio of 1:1 to a ratio of 1.41:.866.
This invention is particularly concerned with the method
The apparatus mechanically, photographically, or other
and means for accomplishing the projection of the original
the desired ratio variation of the ?gure to be reproduced.
wise projects a given ?gure onto an angularly related plane
thus effecting the desired change in dimensions propor—
curve in such a manner as to result in the desired varia
tional to the angular difference between the plane on 45 tion. A mechanical device having a pantograph linkage
system for projecting a curve is shown in FIG. 5 with an
which the original ?gure is mounted and the inclined
exploded detail of some of its parts in FIG. 6.
copy board.
A particular advantage of this method of reproduction
lies in the fact that by determining the angle between the
planes, the new ratio can easily be computed because there
exists the simple relationship of 1: cos 6, where 0 is the
angle between the planes in singly oblique projection. In
The device is supported on a stable base 31 on which
the frame and most of the supports are directly mounted.
The principal frame member 32 serves as a support for
the original-?gure holder 33 which is located some distance
above the base 31. A side frame 35 is employed to support
the varied-?gure holder 37 and since these two holders
must be capable of being rotated or tilted with respect to
double oblique projection where it is desired to vary
both dimensions, the angle 6 is measured from a refer
ence plane which lies perpendicular to the direction of 55 one another, provision is made to make the varied-?gure
holder 37 singly oblique in respect to the original-?gure
projection.
These and other objects, features, and advantages will
become more apparent after considering the following
detailed description taken in connection with the annexed
drawings and appended claim.
‘In the drawings:
FIG. 1 illustrates a typical curve to be varied;
FIG. 2. shows a view of the curve having the desired
holder 33. This is effected by mounting the varied-?gure
holder 37 on the side frame 35 with hinges 36.
Provision is made to lock said holder 37 in any desired
position by a slotted and calibrated support member 39
60 and a position locking knob 40. Additional rigidity of the
varied-?gure holder 37 can be obtained, if necessary, by
adjusting and locking one or more adjustable spot supports
41 which might be included for this purpose.
A ?ange 42 ?xed to the base member 31 supports the
FIG. 3 shows a schematic view of the transformation; 65
principal supporting rod 43 which in turn supports the
FIG. 4 shows schematically an example of doubly
entire tracing apparatus. Two clamps 44 locked in place
oblique projection;
by suitable bolts, serve to mount the tracing apparatus on
FIGS. 5 and 6 depict a mechanical device for producing
the principal supporting rod 43. These clamps 44 each
the transformation; and
hold
a vertical cylindrical bushing 46 shown in detail in
FIGS. 7 and 8 show photographic apparatus for accom
FIG. 6. The swiveling rod 45 is mounted in these bush
plishing this result.
ings and, as its name implies, turns freely around on its
height to width ratio;
3,094,783
4
l
axis thus acting as a pivot forthe remainder of the tracing
apparatus. The pivot-guide rod connector 47, shown in
detail in the FIG. 6, connects the substantially horizontal
guide rods 48 to the swiveling rod 45 and also restrains
them from moving up and down when the clamps 44 are
properly spaced. The guide rod connectors 47 should
ride on the ends of the cylindrical bushings 46 with sliding
contact, lubricated to reduce friction and wear.
to advantage in framing the unexposed paper 69 so that
unwanted distortion will be avoided. The light source
60 is kept lighted for a time adequate to permit proper
exposure.
In FIG. 8, which is an example of doubly oblique pro
j'ection, a remote source of parallel light is speci?ed. Since
two transformations are possible in this case, the parallel
source of light is not necessarily perpendicular to the
plane on which the original film is held. It is, however,
The guide rods 48 rotate in one plane only and restrain
with the plane of 'base 75 and perpendicular to
the styli riders 50 and 54 to a single degree of freedom, 10 parallel
the
common
edge between 75 and plane 76, said planes
namely along the axis of said guide rods 48. The sub
being attached at their common edges by hinges 77. Since
stantially horizontal guide rods 48 are given rigidity by
the parallel beam is quite remote only a portion of it is
joining their ends with two substantially vertical connect
utilized, hence, would be less critical as to evenness of
ing rods 49, thus forming a complete structure loop. The
tracing stylus rider 50 is free to move in a plane to permit 15 intensity.
The device as shown in FIG. 8 consists of a base 75
tracing a curve. The writing stylus rider 54 identically
onto which a front frame 76 is attached by means of
follows the movement of the tracing stylus rider S0 in a
hinges ‘77. An angular scale 78 is provided to hold said
different plane. This will permit the tracing of any point
frame 76 at the desired angle and to indicate said angle
on the ?gure, and locates such point by what is tanta
in relation to the base 75 or calibrated directly in accord
mount to its polar coordinates with respect to the pivot. 20 ance with the corresponding transformation ratio. Clamps
The two riders 50 and 54 are to have the same identical
79 are provided to hold the original ?lm or plate 80 in
motion. In order ‘for the writing stylus rider 54 to be
its proper position. The rear frame 81 is attached by
laterally displaced along the guide rods as the tracing
means of binge 82 to upright member 83 which in turn
stylus rider 50 is moved, these two riders must be rigidly
is ?rmly attached to the base 75. The angular scale 84
connected. This is accomplished by the use of control 25 is provided so that the angular displacement of the rear
rods 51, control-follower plate 52, and the follower rods
frame 81 can be determined and also to hold said frame
53. The control-follower plate 52 also rides on the guide
at this desired angle. Clamps (not shown) are provided
rods 48 to give the structure greater rigidity.
to hold the photosensitive paper or ?lm 85 in place for
To effect the actual projection, vertical movement must
exposure. This device can simultaneously reduce the axis
be allowed so that the vertical writing stem 56 will con 30 perpendicular to the base and increase the axis parallel
tact, at all times, the oblique plane of the varied-?gure
with the base. Such a ‘double transformation is seldom
holder 37. This is accomplished by letting the rider 54
warranted except for extending the possible range of ratio
also act as a bushing for the vertical writing stem 56.
changes, particularly Where the ?lm grain would be the
This stem 56, which is free to move up and down, is
limiting
factor.
35
terminated with a writing stylus holder 57, whose writing
Although the invention has been described with refer
point is kept against the varied ?gure by gravity. A
ence to particular embodiments, it will be understood
weight 55 is added to the upper end of the writing stem
to those skilled in the art that various changes and modi‘
56 to insure that the Writing stylus will follow the oblique
?cations can be made therein without departing from the
converted-?gure plane, and to supply suf?cient writing
pressure. A partially completed converted ?gure 38, and 40
invention.
its associated original ?gure 34 are shown mounted on
their respective holders 37 and 33. In actual use, the
new and desire to secure by Letters Patent of the United
.
Having thus described my invention, what I ‘claim as
States is:
.
stylus rider 50 would be moved manually keeping the
A mechanical transformation apparatus for reproduc
tracing stylus along the original ?gure 34 and simultane
ing plane ?gures by tracing while concurrently varying
ously the writing stylus 54 by means of its Writing point 45 the ratio of the height-to-width ‘dimensions thereof, said
will form the converted ?gure comparable to the original
apparatus comprising:
?gure except that one of its orthogonal components is
(a) an elongated member,
elongated.
The results as outlined above may also be obtained by
the use of photographic means. FIG. 7 depicts appara 50
tus for accomplishing the projection where the light source
is immediate or close to the original ?gure.
Using the photographic method it is necessary to obtain
a parallel beam of light. This may be accomplished as
shown in FIG. 7 by providing a point source of light 60 55
located at the focus of parabolic re?ector 61. A non
re?ective shield 62 may be used to prevent a photographic
“hot-spot” or high intensity spot of light from existing,
and to eliminate direct radiation which would be radial
.rather than parallel. The parabolic reflector 61 has a 60
?anged non-reflecting rim 63 which is padded with felt
64 or some other material so as not to harm the ?lm 65.
Ordinarily said ?lm 65 would be a negative of the origi
nal ?gure to be transformed.
A ?at transparent plate of glass66 can be used to sup 65
.port the original ?lm 65. Another ?at plate of glass (not
shown) may be placed on top to protect and/or ?atten
the ?lm 65. The source of parallel light may be scanned
,or moved in the plane of the original ?lm if it is not
sufficiently large or uniform in intensity to cover the en 70
tire ?lm. The original ?gure on ?lm 65 is projected on to
an oblique plane 68 located on the other side of the origi
nal ?lm, producing a latent image on the unexposed photo
sensitive paper or ?lm v69 which lies on the oblique plane
68. A frame 70 with ?at cover glass 67 might be used
(b) means mounting said member for rotation about
a ?rst axis transverse to the longitudinal axis of said
member so that said member is arranged to experi
ence angular motion about said ?rst axis,
(0) a pair of riders located at different positions rela
tive to the length of the ?rst axis and mounted on
said member to slide lengthwise along the member,
said riders being coupled to one another for joint
lengthwise movement along said member to
maintain them at equal radial distances from the
?rst axis so that both riders are arranged to ex
perience in two parallel planes identical polar
motions about said ?rst axis,
V
(d) a tracing stylus carried ‘by one rider,
(:2) a writing stylus carried by the other rider,
(1‘) means mounting at least one stylus on its rider for
free movement relative thereto along an axis parallel
to the ?rst axis,
1
(g) a ?rst plane support for an original ?gure to be
traced,
(h) a second plane support for the traced ?gure,
(i) one of said plane supports being located below and
in operational association with the tracing stylus and
the other of said plane supports being located below
and in operational association with the-writing stylus,
(j) and means mounting said supports in planes trans
verse to said ?rst axis and including
3,094,783
means to selectively adjustably change relative to
said ?rst axis the angular position of at least the
plane of the support operatively associated with
the stylus that is freely movable parallel to the
?rst axis,
‘1
(k) said last-named stylus being biased toward its asso
ciated plane support,
(I) whereby the height-to-width of the reproduced ?g
References Cited in the ?le of this patent
UNITED STATES PATENTS
2,031,358
2,072,286
2,215,462
2,338,729
2,409,603
2,419,078
width ratio of the original ?gure by varying the angu- 10 2,643,576
‘13.1" position of the plane of the adjustable support.
2,746,152
me can be selectively di?ered from the height-to
Bartholowsky ________ __ Feb. 18,
Wellington ___________ __ Mar. 2,
Davidson et a1. _______ __ Sept. 24,
McQuaid _____________ __ Jan. 11,
Wood _______________ __ Oct. 15,
1936
1937
1940
1944
1946
Ivy _________________ __ Apr. 15, 1947
Merriam _____________ __ June 30, 1953
Deak'in ______________ __ May 22, 1956
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