Display of still images that appear animated to viewers in motion

BACKGROUND OF THE INVENTION

This invention relates to the display of still images that appear animated to a viewer in motion relative to those images. More particularly, this invention relates to the display of still images that can be other than planar and perpendicular to a viewer's line of sight.

Display devices that display still images appearing to be animated to a viewer in motion are known. These devices include a series of graduated images (i.e., adjacent images that differ slightly and progressively from one to the next). The images are arranged in the direction of motion of a viewer (e.g., along a railroad) such that the images are viewed consecutively. As a viewer moves past these images, they appear animated. The effect is similar to that of a flip-book. A flip-book has an image on each page that differs slightly from the one before it and the one after it such that when the pages are flipped, a viewer perceives animation.

A longstanding trend in mass transportation systems has been the development of installations to provide the passengers in subway systems with animated motion pictures. The animation of these motion pictures is effected by the motion of the viewer relative to the installation, which is fixed to the tunnel walls of the subway system. Such installations have obvious value: the moving picture is viewable through the train windows, through which only darkness would otherwise be visible. Possible useful moving picture subjects could be selections of artistic value, or informative messages from the transportation system or from an advertiser.

Each of the known arrangements provides for the presentation of a series of graduated images, or “frames,” to the viewer/rider so that consecutive frames are viewed one after the other. As is well known, the simple presentation of a series of still images to a moving viewer is perceived as nothing more than a blur if displayed too close to the viewer at a fast rate. Alternatively, at a large distance or low speeds, the viewer sees a series of individual images with no animation. In order to achieve a motion picture effect, known arrangements have introduced methods of displaying each image for extremely short periods of time. With display times of sufficiently short duration, the relative motion between viewer and image is effectively arrested, and blurring is negligible. Methods for arresting the motion have been based on stroboscopic illumination of the images. These methods require precise synchronization between the viewer and the installation in order that each image is illuminated at the same position relative to the viewer, even as the viewer moves at high speed.

The requirements of a stroboscopic device are numerous: the flash must be extremely brief for a fast moving viewer, and therefore correspondingly bright in order that enough light reach the viewer. This requirement, in turn, requires extremely precisely timed flashes. This precision requires extremely consistent motion on the part of the viewer, with little or no change in speed. All of the aforementioned requirements result in a high level of mechanical or electrical complexity and cost, or greater consistency in train motion than exists. Other known arrangements have overcome the need for high temporal precision by providing a transponder of some sort on the viewer's vehicle and a receiver on the installation to determine the viewer's position. These arrangements involve considerable mechanical and electrical complexity and cost.

The aforementioned known arrangements generally require the viewer to be in a vehicle. This requirement may be imposed because the vehicle carries equipment for timing, lighting, or signaling; or because of the need to maintain high consistency in speed; or to increase the viewer's speed, for example. The use of a vehicle requires a high level of complexity of the design because of the number of mechanical elements and because one frequently is dealing with existing systems, requiring modification of existing equipment. The harsh environment of being mounted on a moving subway car may limit the mechanical or electrical precision attainable in any unit that requires it, or it may require frequent maintenance for a part where high precision has been attained.

The use of a vehicle also imposes constraints. At the most basic level, it limits the range of possible applications to those where viewers are on vehicles. More specifically, considerations of the vehicle's physical dimensions constrain a stroboscopic device's applicability. The design must take into account such information as the vehicle's height and width, its window size and spacing, and the positions of viewers within the vehicle. For example, close spacing of windows on a high speed train requires that stroboscopic discharges preferably be of high frequency and number in order that the display be visible to all occupants of a train. The dimensions of the environment, such as the physical space available for hardware installation in the subway tunnel and the distances available over which to project images, impose further constraints on the size of elements of any device as well as on the quality and durability of its various parts.

Though in principle a stroboscopic device can work for slowly moving viewers, simply by spacing the projectors more closely, in practice it is difficult. First, closer spacing increases cost and complexity. Also, once the device is installed with a fixed projector-to-projector distance, a minimum speed is imposed on the viewer.

An existing method for the display of animated images involving relative motion between the viewer and the is device is the zootrope. The zootrope is a simple hollow cylindrical device that produces animation by way of the geometrical arrangement of slits cut in the cylinder walls and a series of graduated images placed on the inside of the cylinder, one per slit. When the cylinder is spun on its axis, the animation is visible through the (now quickly moving) slits.

The zootrope is, however, fixed in nearly all its proportions because its cross section must be circular. Since the animation requires a minimum frame rate, and the frame rate depends on the rotational speed, only a very short animation can be viewed using a zootrope. Although there is relative motion between the viewer and the apparatus, in practice the viewer cannot comfortably move in a circle around the zootrope. Therefore only one configuration is practicable with a zootrope: that in which a stationary viewer observes a short animation through a rotating cylinder.

For the reasons of its incapacity to be altered in shape, the short duration of its animation, and the fact that it must be spun, the zootrope has remained a toy or curiosity without practical application. However, at least one known system displays images along an outdoor railroad track in an arrangement that might be referred to as a “linear zootrope” in which the images are mounted behind a wall in which slits are provided. That outdoor environment is essentially unconstrained.

In view of the foregoing, it would be desirable to provide apparatus for use in a spatially-constrained environment that displays still images that appear animated to a viewer in motion.

It would also be desirable to provide such apparatus for use in a spatially-constrained environment in which the side profile of the apparatus can be somewhat conformed to fit better within the spatially-constrained environment.

SUMMARY OF THE INVENTION

It is an object of this invention to provide apparatus for use in a spatially-constrained environment that displays still images that appear animated to a viewer in motion.

It is also an object of this invention to provide such apparatus for use in a spatially-constrained environment in which the side profile of the apparatus can be somewhat conformed to fit better within the spatially-constrained environment.

In accordance with this invention, apparatus is provided that displays still images. The still images form an animated display to a viewer moving substantially at a known velocity relative to the images substantially along a known trajectory substantially parallel to the images. The apparatus includes a backboard having a backboard length along the trajectory. The images are mounted on a surface of the backboard. Each still image has an actual image width and an image center. Image centers are separated by a frame-to-frame distance. A slitboard is positioned substantially parallel to the backboard facing the surface upon which the images are mounted and is separated therefrom by a board-to-board distance. The slitboard is mounted at a viewing distance from the trajectory. The board-to-board distance and the viewing distance total a backboard distance. The slitboard has a slitboard length along the trajectory and has a plurality of slits substantially perpendicular to the slitboard length. Each slit corresponds to a respective image and has a slit width measured along the slitboard length and a slit center. Respective slit centers of adjacent slits are preferably separated by the frame-to-frame distance.

The side profiles of the slitboard and backboard (viewable either cross-sectionally or elevationally in the same direction as the trajectory) can be preferably as follows:

1) parallel to each other, planar, and perpendicular (e.g., vertical) to a viewer's (e.g., horizontal) line of sight;

2) parallel to each other, planar, and non-perpendicular (e.g., slanted) to a viewer's line of sight;

3) parallel to each other, nonplanar (e.g., curved), and non-perpendicular to a viewer's line of sight; and

4) nonparallel, nonplanar, and non-perpendicular.

This advantageously allows the apparatus to be constructed such that its side profile can be conformed to fit better within a spatially-constrained environment, such as, for example, a subway tunnel.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the invention will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which:

FIG. 1

is a perspective view of an illustrative embodiment of apparatus according to the invention;

FIG. 2

is an exploded perspective view of the apparatus of

FIG. 1

;

FIG. 2A

is a perspective view of an alternative illustrative embodiment of the apparatus of

FIGS. 1 and 2

;

FIG. 3

is a schematic plan view diagram of the geometry and optics of the apparatus of

FIGS. 1 and 2

;

FIG. 3A

is a schematic plan view diagram of the geometry of a curved embodiment of the invention;

FIGS. 4A

,

4

B and

4

C (collectively “FIG.

4

”) are schematic plan view representations of a single image and slit with a viewer at three different positions at three different instants of time;

FIGS. 5A

,

5

B and

5

C (collectively “FIG.

5

”) are schematic plan view representations of a pair of images and slits with a viewer at three different positions at three different instants of time;

FIG. 6

is a schematic plan view representation of a single image being viewed by a viewed over time, illustrating the stretching effect;

FIG. 6A

is a schematic plan view representation illustrating the stretching effect where the backboard is not parallel to the direction of motion;

FIG. 7

is a schematic plan view of a second illustrative embodiment of the invention wherein the images are curved;

FIG. 8

is a schematic plan view of a third illustrative embodiment of the invention wherein the images are inclined relative to the backboard;

FIG. 9

is a schematic plan view of a fourth illustrative embodiment of the invention, similar to the embodiment of

FIG. 8

, but wherein the slitboard includes a series of sections parallel to the images and inclined relative to the backboard;

FIG. 10

is a schematic perspective representation of a pair of combination slitboard/backboards from a fifth illustrative embodiment of the invention which is two-sided;

FIG. 11

is a schematic plan view of the embodiment of

FIG. 10

;

FIG. 12

is a schematic plan view of a sixth embodiment having curved images such as in the embodiment of

FIG. 7

, and being two-sided such as in the embodiment of

FIGS. 10 and 11

;

FIG. 13

is a perspective view of a roller-type image holder for use in a seventh illustrative embodiment of the invention;

FIG. 14

is a perspective view of an eighth illustrative embodiment of the invention;

FIG. 15

is a vertical cross-sectional view, taken from line

15

—

15

of

FIG. 14

, of the eighth illustrative embodiment of the invention;

FIG. 16

is a simplified perspective view showing the mounting of a plurality of modular units in a subway tunnel according to the invention;

FIG. 17

is a schematic side view representation of an embodiment of the invention showing the profiles of the slitboard and backboard;

FIG. 18

is a schematic cross-sectional view of a subway tunnel showing the embodiment of the invention shown in

FIG. 17

mounted therein;

FIG. 19

is a schematic cross-sectional view of a subway tunnel showing another embodiment of the invention mounted therein;

FIGS. 20 and 21

are schematic side view representations of the embodiment of the invention shown in

FIG. 19

showing the profiles of the slitboard and backboard;

FIG. 22

is a schematic cross-sectional view of a subway tunnel showing still another embodiment of the invention mounted therein;

FIG. 23

is a schematic side view representation of yet another embodiment of the invention showing the profiles of the slitboard and backboard;

FIG. 24

is a schematic side view representation of a further embodiment of the invention showing the profiles of the slitboard and backboard; and

FIG. 25

is a flow diagram of a process for determining whether selected profiles for the slitboard and backboard result in acceptable animation according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention preferably produces simple apparatus operating on principles of simple geometric optics that displays animation to a viewer in motion relative to it. The apparatus requires substantially only that the viewer move in a substantially predictable path at a substantially predictable speed. There are many common instances that meet this criterion, including, but not limited to, riders on subway trains, pedestrian on walkways or sidewalks, passengers on surface trains, passengers in motor vehicles, passengers in elevators, and so on. For the remainder of this document, for ease of description, reference will primarily be made to a particular exemplary application—an installation in a subway system, viewable by riders on a subway train—but the present invention is not limited to such an application.

Benefits of the present invention include the following:

1. A viewer preferably does not need to be in a vehicle.

2. Complex stroboscopic illumination is preferably not needed.

3. Precise timing or positioning triggers between the apparatus and the viewer are preferably not needed.

4. Moving parts are preferably not needed.

5. Preferably, no shutter is required.

6. Preferably, no special equipment mounted on the viewer or the viewer's vehicle, if the viewer is in a vehicle, is required.

7. Preferably, no transfer of information between the apparatus and the viewer pertaining to the viewer's position, speed, or direction of motion is needed.

8. A very high depth of field of viewability is preferably offered.

9. Operation independent of the direction of a viewer's motion can be designed.

10. It preferably is effective for each member of a closely spaced series of viewers, independent of their spacing or relative motions.

11. Optics no more precise than a simple slit is preferably required (although other optics may be used).

12. No correlation between vehicle window spacing and picture spacing is preferably required.

13. It preferably offers the possibility of effective magnification of the image in the direction of motion.

14. Very low minimum viewer speed is preferably required because the magnification allows very close spacing of graduated images.

15. No particular geometry, be it circular, linear, or any other geometry is preferably required.

16. It preferably has no maximum speed.

The apparatus preferably includes a series of graduated pictures (“images” or “frames”) spaced at preferably regular intervals and, preferably between the pictures and the viewer, an optical arrangement that preferably restricts the viewer's view to a thin strip of each picture. This optical arrangement preferably is an opaque material with a series of thin, transparent slits in it, oriented with the long dimension of the slit perpendicular to the direction of the viewer's motion. The series of pictures will generally be called a “backboard” and the preferred optical arrangement will generally be called a “slitboard.”

Not essential to the invention, but often desirable, is a source of illumination so that the pictures are brighter than the viewer's environment. The illumination can back-light the pictures or can be placed between the slitboard and backboard to front-light the pictures substantially without illuminating the viewer's environment. When lighting is used it preferably should be constant in brightness. Natural or ambient light can be used. If ambient light is sufficient, the apparatus can be operated without any built-in source of illumination.

Also not necessary, but often desirable, is to make the viewer side of the slitboard dark or nonreflecting, or both, in order to maximize the contrast between the pictures viewable through the slitboard and the slitboard itself. However, the slitboard need not necessarily be dark or nonreflective. For example, the viewer face of the slitboard could have a conventional billboard placed on it with slits cut at the desired positions. This configuration is particularly useful in places where some viewers are moving relative to the device and others are stationary. This may occur, for example, at a subway station where an express train passes through without stopping, but passengers waiting for a local train stand on the platform. The moving viewers preferably will see the animation through the imperceptible blur of the conventional billboard on the slitboard front. The stationary viewers preferably will see only the conventional billboard.

The invention will now be described with reference to

FIGS. 1-16

.

The basic construction of a preferred embodiment of a display apparatus

10

according to the invention is shown in

FIGS. 1 and 2

. In this embodiment, apparatus

10

is essentially a rectangular solid formed by housing

20

and lid

21

. The front and rear of apparatus

10

preferably are formed by slitboard

22

and backboard

23

, which are described in more detail below. Slitboard

22

and backboard

23

preferably fit into slots

24

in housing

20

which are provided for that purpose. Lightframe

25

preferably is interposed between housing

20

and lid

21

and preferably encloses light source

26

, which preferably includes two fluorescent tubes

27

, to light images, or “frames”

230

, on backboard

23

. Slitboard

22

preferably includes a plurality of slits

220

as described in more detail below. Preferably, in order to keep foreign matter out of apparatus

10

, particularly if it is to be used in a harsh or dirty environment such as a subway tunnel, each slit

220

is covered by a light-transmissive, preferably transparent cover

221

(only one shown). Alternatively, each slit

220

may be covered by a semicylindrical lens

222

(only one shown), which also improves the resolution of viewed images. Specifically, if the focal length of the lens is approximately equal to the distance between slitboard

22

and backboard

23

, the resolution of the image may be increased. This improvement of the resolution is effected by narrowing the width of the sliver of the actual image visible at a given instant by the viewer. Alternatively, the use of lenses may allow the slit width to be increased without lowering resolution.

In an alternative embodiment

200

, shown in

FIG. 2A

, housing

201

is similar to housing

20

, except that it includes light-transmissive, preferably transparent, front and rear walls

202

,

203

respectively, forming a completely enclosed structure. At least one of walls

202

,

203

(as shown, it is wall

202

) preferably is hinged as at

204

to form a maintenance door

205

which may be opened, e.g., to replace backboard

23

(to change the images

230

thereon) or to change light bulbs

27

). As shown in

FIG. 2A

, light bulbs

27

are provided in a backlight unit

206

instead of lightframe

25

, necessitating that backboard

23

and images

230

be light-transmissive. Of course, embodiment

200

could be used with lightframe

25

instead of backlight unit

206

. Similarly, apparatus

10

could be provided with backlight unit

206

instead of lightframe

25

, in which case backboard

23

and images

230

would be light-transmissive.

FIG. 3

is a schematic plan view of a portion of apparatus

10

being observed by a viewer

30

moving at a substantially constant velocity V

w

along a track

31

substantially parallel to apparatus

10

. Track

31

is drawn as a schematic representation of a railroad track, but may be any known trajectory such as a highway, or a walkway or sidewalk, on which viewers move substantially at a known substantially constant velocity.

The following variables may be defined from FIG.

3

:

D

s

=slit width

D

ff

=frame-to-frame distance

D

bs

=backboard-to-slitboard distance

V

w

=speed of viewer relative to apparatus

D

sb

=thickness of slitboard

D

i

=actual width of a single image frame

D

vs

=distance from viewer to slitboard

Other parameters, which are not labeled, will be described below, including B (brightness), c (contrast), and D

i

′ (apparent or perceived width of a single image frame).

An alternative geometry is shown in

FIG. 3A

, where track

31

′ is curved, and slitboard

22

′ and backboard

23

′ are correspondingly curved, so that all three are substantially “parallel” to one another. Although not labeled in

FIG. 3A

, the other parameters are the same as in

FIG. 3

, except that, depending on the degree of curvature, there may be some adjustment in the amount of stretching or enlargement of the image as discussed below.

One of the most significant departures of the present invention from previously known apparatus designed to be viewed from a moving vehicle is that no attempt is made to arrest the apparent motion of the image. That is, in the present device the image is always in motion relative to the viewer, and some part of the image is always viewable by the viewer. This contrasts with known systems for moving viewers where a stroboscopic flash is designed to be as close as instantaneous as possible in order to achieve an apparent cessation of motion of an individual image frame, despite its true motion relative to the viewer.

As with all animation, the apparatus according to the invention relies on the well known effect of persistence of vision, whereby a viewer perceives a continuous moving image when shown a series of discrete images. The operation of the invention uses two distinct, but simultaneous, manifestations of persistence of vision. The first occurs in the eye reconstructing a full coherent image, apparently entirely visible at once, when actually shown a small sliver of the image that sweeps over the whole image. The second is the usual effect of the flip book, whereby a series of graduated images is perceived to be a continuous animation.

FIG. 4

illustrates the first persistence of vision effect. It shows the position of viewer

30

relative to one image at successive points (

FIGS. 4A

,

4

B,

4

C) in time. In each of

FIGS. 4A

,

4

B and

4

C, double-ended arrow

40

represents the total actual image width, D

i

, while distance

41

represents the portion of the image visible at a given time. This diagram shows that viewer

30

, over a short period of time, gets to see each part of the image. However, at any given instant only a thin sliver of the picture, of width

41

, is visible. Because the period of time over which the sliver is visible is very short, and therefore the motion of the image viewed through the slit in that time is very small, the viewer perceives very little or no blur, even at very high speeds. There is no theoretical upper limit on the speed at which the apparatus works—the faster the viewer moves, the less time a given sliver is visible. That is, the effect that would cause blur—the viewer's increased speed—is canceled by effect that reduces blur—the period of viewability of a given sliver.

In

FIG. 4

the representation of movement of the viewer's eye is purely illustrative. In practice the viewer's gaze is fixed at a screen that is perceived to be stationary, and the entirety of the frame can be seen through peripheral vision, as with a conventional billboard.

FIG. 5

illustrates the second persistence of vision effect. It shows viewer

30

looking in a fixed direction at three successive points in time. In

FIG. 5A

, a thin sliver of a first image n is in the direct line of the viewer's gaze through slit

221

. In

FIG. 5B

, the viewer's direct gaze falls on a blocking part of slitboard

22

. For the duration that the opaque part of slitboard

22

is in the line of the viewer's direct gaze, the viewer continues to perceive the sliver of image n just seen through slit

221

. In

FIG. 5C

, the direct line of the viewer's gaze falls on slit

222

, adjacent to slit

221

, and viewer

30

sees a sliver of adjacent image n+1. Because each slit

221

,

222

preferably is substantially perfectly aligned with its respective image, the slivers visible at a given angle in the two separate slots preferably correspond substantially precisely. That is, at a position, say, three inches from the left edge of the picture, the sliver three inches from the left edge of the picture is viewable from one frame to the next, and never a sliver from any other part of the image. In this way, the alignment between the slit and the image prevents the confusion and blur perceived by the viewer that otherwise would be caused by the fast motion of the images. Because successive frames differ slightly as with successive images in conventional animations, the viewer perceives animation.

The two persistence of vision effects operate simultaneously in practice. Above a minimum threshold speed, viewer

30

perceives neither discrete images nor discrete slivers.

A very useful effect of apparatus

10

is the apparent stretching, or widening, of the image in the direction of motion.

FIG. 6

illustrates the geometrical considerations explaining this stretching effect. Labeled “Position 1” and “Position 2” are the two positions of a given frame

230

where the opposite edges of frame

230

are visible. Because the positions of frame

230

and slit

220

are fixed relative to each other, they precisely determine the angle at which viewer

30

must look in order that slit

220

be aligned with an edge of the image

230

.

At Position 1, the left edge of image

230

is aligned with slit

220

and the viewer's eye. At Position 2, the right edge of image

230

is aligned with slit

220

and the viewer's eye. In fact, the two positions occur at different times, but, as explained above, this is not observed by the viewer

30

. Only one full image is observed.

If x is the distance from the centerpoint between the two positions of slit

220

to either of the individual positions at Position 1 or Position 2, then the perceived width of the image, D

i

′, is 2x. By similar triangles,

D

vs

/x

=(

D

vs

+D

bs

)/(

x+D

i

/2)

x

(

D

vs

+D

bs

)=(

x+D

i

/2)

D

vs

2

x

=(

D

vs

/D

bs

)

D

i

D

i

′=(

D

vs

/D

bs

)

D

i

(1)

Thus the perceived width of the image, D

i

′, is increased over the actual width of the image by a factor of the ratio of the viewer-slitboard distance to the slitboard-backboard distance.

FIG. 6A

shows the magnification effect when the backboard

23

′ is not substantially parallel to the viewer's trajectory. The magnification is found by defining a formula f(x), where x is the distance along the viewer's trajectory, for the shape of the backboard—that is, the distance of the backboard from the axis defined by the viewer's trajectory—around each slit (for example,

FIG. 7

shows a backboard

71

on which each image

730

forms a semicircle around its respective slit

220

). For ease of convention, one can define an x axis along the direction of the viewer's motion and a y axis perpendicular to the x axis and choose the origin at the position of the viewer

30

.

To find the magnification, one determines how an arbitrary picture element

230

′ on the backboard

23

′ will appear to viewer

30

on a projected flat backboard

23

″. In

FIG. 6A

, a section of the true backboard

23

′ is shown between slitboard

22

and the projected backboard

23

″. A length PR of the backboard

23

′ defines a picture element

230

′. This section

230

′ will appear to viewer

30

as if on projected flat backboard

23

″, as indicated.

For ease of presentation, the section of backboard

23

′ shown is a straight line segment, but this linearity is not required. Also, the backboard shape does not need to be perfectly described by a formula y=f(x). In practice one can approximate the backboard's true shape in a number of ways—for example, by treating the backboard as a series of infinitesimal elements, each of which can be approximated by a line segment.

Viewer

30

, at position A, sees the left edge P of picture element

230

′ when slit

220

is at Q. Because the positions of picture element

230

′ and slit

220

are fixed relative to each other, they precisely determine the angle at which viewer

30

must look in order that slit

220

be aligned with an edge of the element

230

′. Therefore, the right edge R of this picture element

230

′ will be visible when the device has moved relative to viewer

30

to a position where a line parallel to QR passes through A.

The left edge of picture element

230

′ will appear on projected backboard

23

″ at position B, a distance Δx from the y axis. The right edge of picture element

230

′ will appear on projected backboard

23

″ at position C. The apparent width of the image, D

i

′, is the distance BC.

Point P is the intersection of backboard

23

′ with the line through A and B.

Point Q is the intersection of slitboard

22

with the line through A and B.

Point R is the intersection of backboard

23

′ with the line through Q and R.

The distance D

i

is the distance from P to R.

The coordinates of the point P, (P

x

, P

y

) are the solution (x,y) to y=f(x) and

y=

(

D

vb

/Δx

)

x,

(A)

where the latter equation is the formula for the line through A and B.

The coordinates of point Q, (Q

x

, Q

y

), are the solution (x,y) to y=(

D

vb

/Δx

)

x

, and

y=D

bs

. (B)

The coordinates of point R, (R

x

, R

y

) are the solution (x,y) to y=f(x) and

y−Q

y

=((Δ

x+D

i

′)/

D

vb

) (

x−Q

x

). (C)

Finally, the size D

i

that picture element

230

′ should have in order that it stretch to size D

i

′ is given by

D

i

=((

R

x

−P

x

)

2

+(

R

y

−P

y

)

2

)

0.5

, (D)

where the variables on the right hand side can all be found in terms of dimensions of the apparatus and Δx.

The above derivations demonstrate practical methods for determining the stretching effect in order to preshrink an image for either substantially parallel or nonparallel backboards. A useful rule of thumb which is true for either backboard configuration comes from the fact that angle BAC is equal to angle BQR—the angular size of the projected image as seen by the viewer is the same as the angular size of the actual image at the position of slit

220

.

In order to preshrink an image, it can be divided into many elements, starting at Δx=0 and moving sequentially in either direction while incrementing Δx appropriately. Then each element can be preshrunk and placed at the appropriate location on the backboard.

In cases where the viewer's trajectory is curved, such as the geometry shown in

FIG. 3A

, neither the slitboard nor the backboard will necessarily be a straight line. A similar derivation can be used to the one for nonparallel backboards, by defining a function g(x) for the path of the slit relative to the viewer and replacing Relation (B) with y=g(x).

In practice, the images may be shrunk in the direction of motion before being mounted on the backboard in order that when projected they are stretched to their proper proportions, allowing a large image to be presented in a relatively smaller space. Curved or inclined surfaces on the backboard can be used to augment the effect. That is, as a nonplanar backboard approaches the slitboard, the magnification increases greatly. However, for simplicity, the discussion that follows will assume a planar backboard unless otherwise indicated.

As shown below, the stretching effect, when adjusted through the relevant variable parameters of apparatus

10

, can be very useful. Also, the relation between the perceived image size, D

i

′, and the viewer distance, D

vs

, is linear—the image gets bigger as the viewer moves farther away. This can be a useful effect in the right environment.

There are some limitations and side effects. Both effects of persistence of vision require minimum speeds that are not necessarily equal. Too slow a speed can result in the appearance of only discrete vertical lines, or flicker, or a lack of observed animation effect. In practice, the appearance of only discrete vertical lines is the dominant limitation. A possibly useful effect of the stretching effect arises from the fact that slivers of multiple frames are visible at the same time. That is, if the perceived image is ten times larger than the true image, slivers of ten different images may be visible at any given time. Because each frame presents a different point in time in the animation, multiple times of the image may be simultaneously viewable. This effect may, for example, be used to interlace images, if desired. Similarly, multiple instances of a single frame can be displayed, in a manner similar to that used in commercial motion picture projection. Alternatively, the effect can also result in confusion or blur perceived by viewer

30

. In practice this confusion is barely noticeable, however, and can be reduced through a higher frame rate or a slower varying subject of animation.

Another possibly useful effect occurs when the image of one frame

230

is visible through the slit

220

corresponding to an adjacent frame

230

. In this case, multiple side-by-side animations may be visible to the viewer. These “second-order” images can be used for graphic effect, if desired. Or, if not desired, they may be removed by increasing slitboard thickness D

sb

or the ratio D

ff

/D

i

, by introducing a light baffle

32

between slitboard

22

and backboard

23

, or by altering the geometry of backboard

23

. All of these techniques are described below.

Still another possibly useful effect arises from the fact that the stretching effect distorts the proportions of image

230

. One can remove this effect, if not desired, by preshrinking the images

230

so that the stretching effect restores the true proportions. Care must be taken, however, in the case where different viewers

30

observe apparatus

10

, each from a different D

vs

. In this case, the exact restoration to perfect dimensions occurs at one D

vs

only. At another D

vs

, the restoration is not exact. In practice, however, for many useful ranges of parameters, the improper proportions have few or no adverse effects.

In general, four parameters are imposed by the environment—V

w

, D

bs

, D

vs

, and D

i

′. V

w

, the viewer's speed, is generally imposed by, e.g., the speed of the vehicle, typical viewer footspeed, or the speed of a moving walkway, escalator, etc. D

bs

, the backboard-to-slitboard distance, is generally limited by the space between a train and the tunnel wall, or the available space of a pedestrian walkway, for example. D

vs

, the distance from viewer to slitboard, is imposed by, for example, the width of a subway car or the width of a pedestrian walkway. Finally, D

i

′, the perceived image width, should be no larger than the area visible to viewer

30

at a given instant—for example, the width of a train window.

Also generally imposed is the well-established minimum frame rate for the successful perception of the animation effect viz., approximately 15-20 frames per second. The frame rate, the frame-to-frame distance, and viewer speed are related by

Frame rate=

V

w

/D

ff

(2)

Because the frame rate must generally be greater than the minimum threshold, and V

w

is generally imposed by the environment, this relation sets a maximum D

ff

.

For example, for a train moving at about 30 miles per hour (about 48 kilometers per hour), given a minimum frame rate of about 20 frames per second, the relation above determines that D

ff

can be as great as about 2 feet (about 67 cm).

Alternatively, the minimum V

w

is determined by the minimum D

ff

allowable by the image, which is constrained by the fact that D

ff

can be no smaller than D

i

. The stretching effect theoretically allows D

i

to be lowered arbitrarily without lowering D

i

′, because D

bs

can, in principle, be lowered arbitrarily. In practice, however, D

bs

cannot be lowered arbitrarily, because very small values result in very different perceived image widths for each viewer

30

at a different D

vs

. That is, at too small a D

bs

, viewers on opposite sides of a train could see too markedly differently proportioned images. Moreover, small D

bs

, resulting in high magnification, requires correspondingly high image quality or printing resolution.

If viewers at different distances D

vs

will observe apparatus

10

, the closest ones (those with the smallest D

vs

) generally determine the limits on D

bs

.

Because images cannot overlap,

D

i

≦D

ff

. (3)

If D

i

=D

ff

and one can view second order images, they will appear to abut the first order image, slightly out of synchronization. The resulting appearance will be like that of multiple television sets next to each other and starting their programs at slightly different times. This effect may be used for graphic intent, or, if not desired, three variations in parameters can remove it.

First, one can decrease the ratio D

i

/D

ff

, effectively putting space between adjacent images. This change will send second order images away from the primary ones.

Second, one may increase slitboard thickness D

sb

so that second order images are obscured by the cutoff angle. That is, for any non-zero thickness of slitboard

22

, there will be an angle through which if one looks one will not be able to see through the slits. As the thickness of slitboard

22

increases, this angle gets smaller, and can be seen to follow the relation

D

sb

/D

s

≦D

bs

/(

D

i

/2) (4)

This relation may alternatively be written

D

sb

/D

s

≦D

vs

/(

D

i

′/2) (5)

by substitution for D

i

′ from Relation 1. This shows the limit on D

sb

imposed by the desired perceived image width.

The same effect as described in the preceding paragraph can be achieved by placing light baffle

32

between slitboard

22

and backboard

23

, thereby obstructing the view of one image

230

through the slit

220

of an adjacent image

230

.

Third, one can change the shape of the backboard, as illustrated in FIG.

7

. In apparatus

70

, backboard

71

bears curved images

730

so that second order images are not observed. The change in backboard shape will result in a slightly altered stretching effect. As before, this stretching effect can be undone by preshrinking the image in the direction of motion.

The embodiment illustrated in

FIG. 7

has the potentially useful property not only of showing no second order images, but also of an arbitrarily wide first order image. This effect is related to, but distinct from, the stretching effect described above, which assumes a flat backboard geometry. The final observed width of the image is limited by the vignetting of the slitboard—the exact relation can be found by solving Relation 5 for D

i

′. It can be observed from

FIG. 7

that as the viewing angle becomes large, the viewer continues to observe through each given slit

220

only the image

730

corresponding to that slit

220

. In the ideal limit of zero slitboard width, the leftmost sliver of the image is viewable when the viewer looks 90° to the left and the rightmost sliver is viewable when the viewer looks 90° to the right. The slivers in between are continuously viewable between these extreme angles. In other words, each image is observed as infinitely wide. (In

FIG. 7

, the curved image

730

does not quite reach the slitboard

22

, in order to illustrate the maximum viewing angle allowed by the vignetting of a non-zero width slitboard. In principle, the curve of image

730

may reach the slitboard.)

A further relation is that the slit width must vary inversely with the light brightness—i.e., D

s

∝1/B. In general, the device has higher resolution and less blur the smaller the slit width (analogously to how a pinhole camera has higher resolution with a smaller pinhole). Since smaller slits transmit less light, the brightness must increase with decreasing slit width in order that the same total amount of light reach viewer

30

.

The width of slit

220

relative to the image width determines the amount of blur perceived by viewer

30

in the direction of motion. More specifically, the size of slit

220

, projected from viewer

30

onto backboard

23

, determines the scale over which the present device does not reduce blur. This length is set because the sliver of the image that can be seen through slit

220

at any given moment is in motion, and therefore blurred in the viewer's perception. The size of slit

220

relative to the image width should thus be as small as practicable if the highest resolution possible is desired. In the parameter ranges of the two examples below, slit widths would likely be under about 0.03125 inch (under about 0.8 mm).

The achievable brightness and resolution, and their relationship, can be quantified.

First, define the following additional parameters:

L

ambient

=the ambient luminance of the viewer's environment

L

device

=the luminance of the backboard on the apparatus

c=the contrast between the image and the ambient environment at the position of the viewer

D

vb

=D

vs

+D

bs

=the distance between the viewer and the backboard

B

ambient

=the brightness of the ambient environment at the position of the viewer

B

device

=the brightness of the image at the position of the viewer

TF=the transmission fraction, or fraction of light that passes through the slitboard

R=the image resolution

L

ambient

describes the luminance of a typical object within the field of view of the viewer while looking at the image projected by the apparatus. This typical object should be representative of the general brightness of the viewer's environment and should characterize the background light level. For example, in a subway or train it might be the wall of the car adjacent to the window through which the apparatus is viewable.

B

ambient

is the brightness of that object as seen by the viewer, and

B

ambient

=L

ambient

/4

πD

ambient

2

, (6)

where D

ambient

is the distance between the viewer and the ambient object. It is sometimes difficult to select a particular object as representative of the ambient. As discussed above, in an embodiment used in a subway tunnel, the ambient object could be the wall of the subway car adjacent the window, in which case D

ambient

is the distance from the viewer to the wall. For ease of calculation, this may be approximated as D

vs

because the additional distance from the window to the apparatus is relatively small.

L

device

describes the luminance of the images on the backboard of the apparatus. Because the backboard is always viewed through the slitboard, which effectively filters the light passing through it, its brightness at the position of the viewer, B

device

, is

B

device

=(

L

device

/4

πD

vb

2

)×

TF.

(7)

TF, the transmission fraction of the slitboard, is the ratio of the length of slitboard transmitting light to the total length—i.e.,

TF=D

s

/D

ff

≦(

D

s

×D

vs

)/(

D

i

′×D

bs

), (8)

where equality holds in the second line when D

ff

=D

i

.

R, the image resolution, is the ratio of the size of the image to the size of the slit projected onto the backboard,

R

=(

D

i

×D

vs

)/(

D

s

×D

bs

)≈

D

i

/D

s

=(

D

i

′×D

bs

)/(

D

s

×D

vs

) (9)

This quantity is called the resolution because the image tends to blur in the direction of motion on the scale of the width of the slit. Because the eye can see the whole area of the image contained within the slit width at the same time, and the image moves in the time it is visible, the eye cannot discern detail in the image much finer than the projected slit width. Therefore D

s

effectively defines the pixel size of the image in the direction of motion. In other words, for example, if the slit width is one-tenth the width of the image, the image effectively has ten pixels in the direction of motion. In practice, the eye resolves the image to slightly better than R, but R determines the scale.

In order that the image meaningfully project a non-blurry image, R preferably is greater than 10, but this may depend on the image to be projected. It should also be noted that R=1/TF when D

i

=D

ff

, so that increasing the resolution decreases the transmitted light.

c is the contrast between the apparatus image and the ambient environment at the position of the viewer. In order that the image be viewable in the environment of the viewer, the apparatus brightness must be above a minimum brightness

B

device

≧B

ambient

×c.

(10)

In order that the device be visible at all, c defines a minimum device brightness that depends on the properties of the human eye: if the device's image is too dim relative to its environment it will be invisible. The brightness of the device may always be brighter than the minimum defined by c. Practically speaking, c ought to be at least about 0.1. For many applications, such as commercial advertising, it may be desirable that c be greater than 1.

The following parameters comprise the smallest set of parameters (which may be referred to as “independent” parameters) that fully describe the apparatus according to the invention D

vs

, D

bs

, V

w

, L

ambient

, D

ambient

, C, L

device

, D

i

, D

s

, and D

ff

. Other parameters, which may be defined as “dependent parameters” are:

D

i

′=D

i

×D

vs

/D

bs

D

vb

=D

vs

+D

bs

R=D

i

/D

s

FR=V

w

/D

ff

TF=D

s

/D

ff

B

ambient

=L

ambient

/4

πD

ambient

2

B

device

=(

L

device

/4

πD

vb

2

)×

TF

Of the independent parameters, the first five are substantially determined by the environment in which the apparatus is installed. In a subway system, for example, these five parameters are determined by the cross sections of the tunnel and train, the train speed, and the lighting in the train. On a pedestrian walkway or building interior, as another example, these parameters are determined by the dimensions of the walkway or hallway, pedestrian foot speed, and the ambient lighting conditions.

c and the dependent parameters R and FR are constrained by properties of human perception, and that the image of the apparatus be meaningful and not overly degraded by blurring. D

i

′ is constrained either by the environment (the width of a subway window, for example) or by the requirements of the image to be displayed by the apparatus (such as aesthetic considerations) or both. The remaining dependent parameters are determined by the independent parameters.

When these parameters are not substantially constrained, much greater leeway is allowed with the remaining four independent parameters, and the specific relationships set forth below need not be followed. Such relaxed conditions occur, for example, in connection with a surface train traveling outdoors in a flat environment when D

vs

is largely unconstrained. Sometimes a substantially unconstrained parameter results in an environment where the apparatus cannot be used at all, such as where the ambient light level varies greatly and randomly or the viewer speed is completely unknown.

The constraints on the remaining independent parameters are best expressed as a series of inequalities and are derived below.

Combining Relations 6, 7 and 10 provides the minimum slit width,

D

s

≧c

×(

B

ambient

/B

device

)(

D

bs

×D

i

′)/

D

vs

≧c

×(

L

ambient

/L

device

)(

D

vb

2

/D

ambient

2

)(

D

bs

×D

i

′)/

D

vs

(11)

Solving Relation 9 for D

s

gives,

D

s

≦(

D

i

′×D

bs

)/(

R×D

vs

). (12)

Combining Relations 11 and 12 constrains the slit width from above and below:

c

×(

L

ambient

/L

device

)(

D

vb

2

/D

ambient

2

)(

D

bs

×D

i

′)/

D

vs

≦D

s

≦(

D

i

′×D

bs

)/(

R×D

vs

) (13)

In this relation, L

ambient

and all the distances except the slit width are substantially constrained by the environment, and R and c are constrained by properties of human visual perception. As discussed above, for ease of calculation, D

ambient

can be approximated by D

vs

; note also that (D

bs

×D

i

′)/D

vs

=D

i

. The inequality between the far left and far right sides of the relation forces a minimum luminance for the apparatus, L

device

. That is, if the luminance of the apparatus is below a minimum threshold, the apparatus image will be too dim to see in the brightness of the viewer's environment.

Once the luminance of the apparatus is sufficiently high, the inequalities between D

s

and the far left and far right of the relation determine the allowable slit width range. A smaller slit width gives higher resolution but less brightness and a greater slit width gives brightness at the expense of resolution. A higher luminance of the apparatus extends the lower end of the allowable slit width range.

Another similar relation for the frame-to-frame spacing may be derived from the relations above. Relation 3 may be written

D

ff

≧D

i

≧(

D

i

×D

bs

)/

D

vs

. (14)

Relation 2, frame rate=V

w

/D

ff

, may be rewritten

D

ff

≦V

w

/FR,

(15)

where FR denotes the frame rate and the equality has changed to an inequality to reflect that FR is a minimum frame rate necessary for the animation effect to work.

Combining Relations 14 and 15 yields,

(

D

i

′×D

bs

)/

D

vs

≦D

ff

≦V

w

/FR.

(16)

V

w

and all the distances except D

ff

are substantially constrained by the environment, and FR is constrained by properties of human visual perception. Therefore the relation defines an allowable range for D

ff

. It also puts a condition on the environments in which the present invention may be applied—i.e., if the inequality does not hold between the far left and far right hand sides of the relation, the present invention will not be useful.

Choosing a lower D

ff

puts second order frames closer to first order frames while improving the frame rate. Decreasing D

ff

also increases the transmission fraction without decreasing the resolution. Choosing a higher D

ff

moves the images farther apart at the expense of a reduced frame rate.

Though in principle apparatus

10

requires no included light source for its operation if ambient light is sufficient, such as outdoors (lid

21

or backboard

23

would have to be light-transmissive), in practice the use of very thin slits does impose such a requirement. That is, when operated under conditions of low ambient light and desiring moderate resolution, bright interior illumination is preferable. The designation “interior” indicates the volume of the apparatus

10

between backboard

23

and slitboard

22

, as opposed to the “exterior,” which is every place else. The interior contains the viewable images

230

, but otherwise may be empty or contain support structure, illumination sources, optical baffles, etc. as described above in connection with

FIGS. 1

,

2

and

2

A.

Moreover, this illumination preferably should not illuminate the exterior of the device, or illuminate the viewer's environment or reach the viewer directly, because greater contrast between the dark exterior and bright interior improves the appearance of the final image. This lighting requirement is less cumbersome than that for stroboscopic devices—in a subway tunnel environment, this illumination need not be brighter than achievable with ordinary residential/commercial type lighting, such as fluorescent tubes. The lighting preferably should be constant, so no timing complications arise. Preferably the interior of apparatus

10

should be physically sealed as well as possible from the exterior subway tunnel environment as discussed above, preferably while permitting dissipation of heat from the light source, if necessary. The enclosure may also be used to aid the illumination of the interior by reflecting light which would otherwise not be directed towards viewable images

230

.

Two examples show in more detail how the various parameters interrelate.

EXAMPLE 1

The first example illustrates how all constraints tend to relax as V

w

increases. For example, in a typical subway system the following parameters may be imposed:

V

w

≈30 mph (train speed)

D

bs

≈6 inches (space between train and wall)

D

vs

≈6 feet (half the width of a train, for the average location of a viewer

30

within the car)

D

i

′≈3 feet (width of train window)

By Relations (3) and (1),

D

ff

≧D

i

≧(

D

i

′×D

bs

)/

D

vs

≧(3 ft×0.5 ft)/6 ft≧0.25 feet. (17)

If the images are abutted so that D

ff

=D

i

, the maximum frame rate is attained. Then, by Relation (2),

Frame rate=30

mph/

0.25

ft=

176 frames per second. (18)

At this rate the parameters can be adjusted a great deal while still maintaining high quality animation. This frame rate is also high enough to support interlacing of images (see above) if desired, despite the reduction in effective frame rate that results from interlacing.

EXAMPLE 2

The second example illustrates how the constraints tighten when near the minimal frame rate. To find the lowest practicable V

w

, assume the following parameters:

frame rate≈20 frames/sec

D

bs

≈6 inch

D

vs

≈6 feet

D

i

′≈2 feet.

By Relation (1),

D

i

=(

D

bs

×D

i

′)/

D

vs

=(0.5

ft×

2

ft)/

6

ft=

2 inches.

For abutted images, D

ff

=D

i

, and,

V

w

=D

ff

×frame rate=2 inches×20 frames/sec=40 inches/sec,

which is approximately pedestrian footspeed.

The implication of this last result—that the device can successfully display quality animations to pedestrian traffic—vastly increases the potential applicability of this device relative to stroboscopically based arrangements.

The following alternative exemplary embodiments are within the spirit and scope of the invention.

FIG. 8

illustrates another exemplary embodiment

80

altering the optimal viewing angle of the animation. In apparatus

80

, backboard

83

bears images

830

that are inclined at an acute angle to backboard

83

, varying the viewing angle from a right angle to that acute angle. This alteration permits more natural viewing for a pedestrian, for example, by not requiring turning of the pedestrian's head far away from the direction of motion. This embodiment may also eliminate second order images.

FIG. 9

illustrates a further exemplary embodiment

90

similar to apparatus

80

, but in which slitboard

92

is also angled. This refinement again provides a more natural viewing position for a pedestrian. The asymmetric triangular design permits natural viewing for viewers moving from left to right. A symmetric design (not shown), in which the plan of the slitboard might more resemble, for example, a series of isosceles triangles, could accommodate viewers moving in both directions.

FIG. 10

illustrates a technique of using one slitboard

101

as the backboard of a different slitboard

102

, while simultaneously using that slitboard

102

as the backboard of the original slitboard

101

. This configuration permits the back-to-back installation of two devices in the space of one. This apparatus

100

may be improved by offsetting one set of slits from the other by D

i

/2, or some fraction of D

i

.

FIG. 11

shows a simple schematic plan view of is apparatus

100

. Slits

220

of one slitboard

101

are centered between slits

220

of the opposite slitboard

102

, which is acting as the former slitboard's backboard. That is, between slits

220

of one slitboard are images

230

viewable through the other slitboard, and vice-versa. Because the slits are very thin, their presence in the backboard creates negligible distraction.

FIG. 12

shows another embodiment

120

similar to apparatus

100

, but having a set of curved images

1230

(as in

FIG. 7

) facing slits

220

of opposite slitboards/backboards

101

,

102

. Apparatus

120

thus has characteristics, and advantages, of both apparatus

70

and apparatus

100

.

FIG. 13

illustrates a roller type of image display mechanism

130

that may be placed at the position of the backboard. The rollers may contain a plurality of sets of images that can be changed by simply rolling from one set of images to another. Such a mechanism allows the changing of images to be greatly simplified. In order to change from one animation to another, instead of manually changing each image, one may roll such rollers to a different set of images. This change could be performed manually or automatically, for instance by a timer. By incorporating slits

220

, mechanism

130

can be used in apparatus

100

or apparatus

120

.

Yet another exemplary embodiment

140

is shown in

FIGS. 14 and 15

. In apparatus

140

, “backboard”

141

, with its images

142

, is placed between viewer

30

and a series of mirrors

143

. Each mirror

143

preferably is substantially the same size and orientation as any slits that would have been used in the aforementioned embodiments. Mirrors

143

preferably are mounted on a board

144

that takes the place of the slitboard, but mirrors

143

could be mounted individually or on any other suitable mounting. The principles of operation of apparatus

140

are substantially the same as those for the aforementioned embodiments. However, because “backboard”

141

would obscure the sight of mirrors

143

by viewer

30

, “backboard”

141

may be placed above or below the line of sight of viewer

30

. As shown in

FIGS. 14 and 15

, “backboard”

141

is above the line of sight of viewer

30

. As drawn in

FIGS. 14 and 15

, moreover, both “backboard”

141

and “mirrorboard”

144

are inclined. However, with proper placement, inclination of boards

141

,

144

may not be necessary. As in the case of a slitboard, “mirrorboard”

144

will work best when its non-mirror portions are dark, to increase the contrast with the images.

A complete animation displayed using the apparatus of the present invention for use in a subway system may be a sizable fraction of a mile (or more) in length. In accordance with another aspect of the invention, such an animation can be implemented by breaking the backboard carrying the images for such an animation into smaller units, providing multiple apparatus according to the invention to match the local design of the subway tunnel structure where feasible. Many subway systems have repeating support structure along the length of a tunnel to which such modular devices may be attached in a mechanically simplified way.

As an example, the New York City subway system has throughout its tunnel network regularly spaced columns of support I-beams between many pairs of tracks. Installation of apparatus according to the present invention may be greatly facilitated by taking advantage of these I-beams, their regular spacing, and the certainty of their placement just alongside, but out of, the path of the trains. However, this single example should not be construed as restricting the applicability to just one subway system.

The modularization technique has many other advantages. It has the potential to facilitate is construction and maintenance, by taking advantage of structures explicitly designed with the engineering of the subway tunnels in mind. The I-beam structure is sturdy and guaranteed not to encroach on track space. The constant size of the I-beams consistently regulates D

bs

, easing design considerations. Additionally, cost and engineering difficulties are reduced insofar as the apparatus may be easily attached to the exterior of the supports without drilling or possibly destructive alterations to existing structure.

FIG. 16

schematically illustrates an example of the modularization possible for the two-sided apparatus of

FIGS. 10 and 11

. As shown, construction of the whole length of two slitboards, which could be a half mile or more in length, is reduced to constructing many identical slitboards

160

, each about as long as the distance between adjacent I-beam columns

161

(e.g., about five feet). Each of the slitboards is then attached to a pair of the existing support I-beams, along with the other parts of the apparatus as described above.

FIG. 17

schematically illustrates the side profile of display apparatus

1700

, which includes slitboard

1722

and backboard

1723

. Slitboard

1722

and backboard

1723

are parallel to each other, planar, and perpendicular to a viewer's line of sight

1701

. Also shown are viewer-to-backboard distance, D

vb

, and backboard-to-slitboard distance, D

bs

. As described above, D

vb

and D

bs

are well defined for any viewer's horizontal line of sight and, accordingly, so is the magnification factor. For a non-horizontal line of sight, D

vb

and D

bs

both increase by a factor of 1/cos θ (where θ is measured from the horizontal), so the magnification factor remains the same. This cancellation allows display apparatus with a vertical slitboard and a vertical backboard to project images whose magnification is constant in the vertical direction.

FIG. 18

shows a subway tunnel

1802

in which display apparatus

1700

is mounted on each side of the tunnel wall. Walkway

1804

and subway car

1806

, with windows

1808

, are also shown. Walkway

1804

is an access catwalk used by maintenance personnel and is typically only wide enough for one person (walkway

1804

is not a subway station platform used by subway passengers). Because subway tunnels are built to accommodate subway trains and not necessarily display apparatus, some subway tunnels have very limited space for installation of such display apparatus. Thus, for example, display apparatuses

1700

leave little clearance for either subway car

1806

or a person on walkway

1804

, as shown in FIG.

18

. Therefore, a less spatially protrusive display apparatus would improve the safety of passing trains

1806

and maintenance personnel on walkway

1804

. Moreover, such apparatus would likely be easier to install and maintain.

Advantageously, an embodiment of a slanted display apparatus

1900

constructed in accordance with the invention is provided. Display apparatus

1900

is shown in

FIG. 19

mounted in subway tunnel

1802

. Both slitboard

1922

and backboard

1923

are slanted outward to conform better to the available space in tunnel

1802

. Display apparatus

1900

accordingly provides increased clearance, and thus safety, for both subway car

1806

and persons walking on walkway

1804

.

In accordance with the invention, determination of the various display apparatus parameters discussed above are advantageously the same for apparatus

1900

as they are, for example, for display apparatus

1700

, which has a slitboard and backboard perpendicular to a viewer's horizontal line of sight. The determination is the same because the magnification effect of slanted display apparatus

1900

is also constant in the vertical direction provided both the slitboard and backboard are slanted by the same angle. In other words, the magnification factor is constant with respect to viewing angle.

Referring to

FIGS. 20 and 21

, this constant magnification effect can be shown via similar triangles. Note that line segment BD is parallel and equal in length to line segment CF. Thus,

\begin{matrix} \frac{AE}{AD} = \frac{CE}{CF} = \frac{CE}{BD} or & (19) \\ \frac{AE}{CE} = \frac{AD}{BD} & (20) \end{matrix}

Substituting display apparatus parameters in accordance with the invention yields:

\begin{matrix} \frac{D_{vb}^{'}}{D_{bs}^{'}} = \frac{D_{vb}}{D_{bs}} & (21) \end{matrix}

Thus, the magnification factor is constant with respect to viewing angle θ.

Note that to obtain substantially the same space-saving advantage of display apparatus

1900

, display apparatus

1700

can be advantageously installed by simply tilting apparatus

1700

inward.

FIG. 22

shows an embodiment of a curved display apparatus

2200

constructed in accordance with the invention mounted in subway tunnel

1802

. Both slitboard

2222

and backboard

2223

are curved outward to conform even better than display apparatus

1900

to the available space in tunnel

1802

. This embodiment, therefore, provides even more clearance and safety than apparatus

1900

.

Advantageously, display apparatus constructed in accordance with the invention can include some arbitrary slitboard and backboard geometries that enable it to conform to a wide range of available spaces. Examples of such arbitrary geometries are shown in

FIGS. 23 and 24

.

FIG. 23

shows an embodiment of nonplanar display apparatus

2300

in accordance with the invention. Apparatus

2300

includes nonplanar slitboard

2322

and nonplanar backboard

2323

, which are non-vertical and have the same profile (i.e., they are parallel).

FIG. 24

shows another embodiment of nonplanar display apparatus

2400

in accordance with the present invention. Apparatus

2400

includes nonplanar slitboard

2422

and nonplanar backboard

2423

, which are non-vertical and do not have the same profile (i.e., they are not parallel). Neither slitboard

2322

and backboard

2323

nor slitboard

2422

and backboard

2423

are perpendicular to a viewer's respective lines of sight

2301

and

2401

. Note that the slitboard and backboard profiles shown in

FIGS. 23 and 24

are merely illustrative and should in no way limit the invention.

Further note that because of the magnification effect, not all slitboard and backboard geometries result in acceptable animation. In theory, display apparatus that provides a constant magnification for more than one viewer position (e.g., the optimal position) is possible for only a few geometries. Viewers at other positions will observe images whose magnification varies up and down the backboard, resulting in a warped looking image—overly magnified at some positions and under-magnified at others. In practice, however, the amount of warping is often within acceptable limits for viewing positions close to the optimal viewing position.

An obstacle to designing display apparatus having arbitrary slitboard and backboard geometries is finding the magnification factor, which varies with position along the backboard. The magnification factor depends on viewer position, which determines both D

vb

and D

bs

. Once a viewer position, designated by coordinates (x

v

, y

v

), is chosen, magnification factor, m, can be found for each position on the backboard, designated by coordinates (x

b

, y

b

). That is, m is a function of x

v

, y

v

, x

b

, and y

b

. Preferably, images of a display apparatus are visible from a range of viewer positions.

Note that the following assumes that the display apparatus is substantially parallel to the viewer's direction of motion (which for

FIGS. 19-24

is into and out of the page, or in the z direction). Thus, reference to a viewer's position, or position along a slitboard or backboard, refers to position in the cross-sectional or side-elevational plane (e.g., with respect to

FIGS. 23 and 24

, the x-direction is horizontal and the y-direction is vertical).

FIG. 25

is a flow diagram of an exemplary process

2500

for determining whether a display apparatus with arbitrary slitboard and backboard geometries results in acceptable animation in accordance with the invention. At

2502

, side profiles of a slitboard and a backboard (as shown, for example, in

FIGS. 23 and 24

) are selected. This selection is preferably in accordance with available installation space. These profiles are preferably smooth with no jumps or sharp corners. Preferably, they monotonically rise, meaning that any horizontal line crossing the profile crosses in at most one point. Should the profiles not meet these preferences, appropriate modifications to process

2500

may be necessary, although much of the process will remain unchanged.

At

2504

, each board profile is represented by a mathematical function (e.g., f

backboard(x,y)

and f

slitboard(x,y)

), which can be an approximation.

At

2506

, an optimal viewer position (x

v,OPT

, y

v,OPT

) is selected. This selection should be made in accordance with the available installation space and most likely or average position of a viewer. For example, in a subway tunnel, this position might be in the center of a subway car at the average height of a person. On a pedestrian walkway, this position might be in the middle of the walkway also at the average height of a person.

At

2508

, a worst case viewer position (x

w

, y

w

) is selected in order to determine whether the chosen profiles will yield acceptable images for viewers away from the optimal position. For example, a worst case position for the subway tunnel installation may be at the seat closest to the window. The worst case position should be the one that results in the most warped observed image. Typically, a worst case position is the farthest from (x

v,OPT

, y

v,OPT

), but not necessarily.

At

2510

, a worst case magnification delta or limit, ML, is selected. Limit ML represents the largest acceptable difference between magnification as observed from the optimal position and magnification as observed from the worst case position. For example, an ML of ±10% may be set as the largest acceptable magnification difference between the two magnifications (i.e., the difference between the worst case position magnification and the optimal position magnification should be no more than ±10%). The selection of ML can be arbitrary and can depend on the degree of tolerable image warpage for a particular display apparatus application.

The magnification factor is preferably determined as a function of position along the height of the backboard (i.e., the y-direction as defined above). Assuming the preferences above, the position on the backboard is referred to as y

b

, which can vary from the bottom of the backboard, y

b,LOW

, to the top of the backboard, y

b,HI

, and for which each y

b

, there is a unique x

b

.

The optimal viewer's line of sight, f

LOS

(x,y),—that is, the line joining (x

v,OPT

, y

v,OPT

) and (x

b

, y

b

)—is now uniquely determined at

2512

. The point where the viewer's line of sight to the backboard crosses the slitboard, (x

s

, y

s

), is the intersection of the two equations for f

LOS

and f

SLITBOARD

.

The magnification for a viewer's position as a function of (x

b

, y

b

) can be determined as follows once the viewer-to-backboard and backboard-to-slitboard distances are known:

D

vb

−{square root over ((

x

b

−x

v,OPT

)

2

+(

y

b

−y

v,OPT

)

2

)} (22)

D

bs

={square root over ((

x

b

−x

s

)

2

+(

y

b

−y

s

)

2

)} (23)

m

OPT

(

x

v,OPT

, y

v,OPT

, x

b

, y

b

)=

D

vb

/D

bs

(24)

Because x

v,OPT

and y

v,OPT

are fixed and x

b

is determined by y

b

, the magnification can be referred to as m

OPT

(Y

b

) without confusion.

At

2514

, the same procedure is followed for determining the magnification factor, m

x

, for the worst viewer position.

At

2516

, m

OPT

(y

b

) and m

w

(y

b

) are compared in view of limit ML. If the difference between the two magnifications is less than or equal to ML, as calculated below:

\begin{matrix} &LeftBracketingBar; \frac{m_{OPT} (y_{b}) - m_{w} (y_{b})}{m_{OPT} (y_{b})} &RightBracketingBar; \leq ML & (25) \end{matrix}

the selected profiles for the slitboard and backboard will result in acceptable observed images. Process

2500

then moves to

2518

, where images are preshrunk as described above in accordance with m

OPT

(y

b

).

If the difference between the two magnifications is greater than ML, indicating unacceptable observed images, process

2500

returns to

2502

where the process repeats with new selected profiles for the slitboard and backboard.

Note that process

2500

can also be used to design display apparatus having curved slitboard and backboard profiles such as display apparatus

2200

.

Thus it is seen that display apparatus for use in spatially-constrained environments is provided that displays still images that appear animated to viewers in motion relative to the apparatus. One skilled in the art will appreciate that the present invention can be practiced by other than the described embodiments, which are presented for purposes of illustration and not of limitation, and the present invention is limited only by the claims which follow.

Number	Name	Date	Kind
742632	Hadden	Oct 1903	A
917587	Good	Apr 1909	A
956857	Jennings	May 1910	A
978854	Czerniewski	Dec 1910	A
1006769	Merrill	Oct 1911	A
2026753	Rosenthal et al.	Jan 1936	A
3463581	Clay	Aug 1969	A
4383742	Brachet et al.	May 1983	A
5108171	Spaulding	Apr 1992	A
5782026	Capie	Jul 1998	A

Number	Date	Country
2053364	Apr 1992	CA
2242807	Jul 1997	CA
2263661	Jan 1998	CA
198 06 556	Aug 1999	DE
298 20 186	Apr 2000	DE
0 393 243	Oct 1990	EP
892874	May 1944	FR
1029300	Jan 1953	FR
1051712	Jan 1954	FR
17677	Mar 1903	GB
6776	Jul 1905	GB
106866	Jun 1917	GB
2 230 104	Oct 1990	GB
2 317 985	Apr 1998	GB
WO 0007059	Feb 2000	WO
WO 0127908	Apr 2001	WO

Display of still images that appear animated to viewers in motion

Information

Patent Number

Date Filed

Date Issued

Inventors

Original Assignees

Examiners

Agents

CPC

US Classifications

Field of Search

US

International Classifications

Abstract

Description

Claims

CROSS REFERENCE TO RELATED APPLICATION

US Referenced Citations (10)

Foreign Referenced Citations (16)

Provisional Applications (1)