Abstract:
A video projection system employing a concave video screen which provides for enhanced depth cueing. A method of designing a variety of shapes of video screen surfaces by varying certain parameters of a common master equation. Video screen surface shapes providing optimum viewing for specific applications.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to video projection systems. In another aspect, this invention concerns a 3D video screen which provides enhanced depth cueing. In still another aspect, this invention concerns a method for designing and/or constructing a concave 3D video screen surface. 
     2. Description of the Prior Art 
     Video projection systems are useful for a variety of applications. Most conventional video projection systems employ a relatively flat screen surface on which images are displayed. Such conventional flat video screen surfaces provide no depth cueing (i.e., 3D effect) unless multiple projectors and/or 3D stereo glasses are employed. However, the use of multiple projectors and 3D stereo glasses is cost prohibitive for most video projection applications. 
     It has recently been discovered that enhanced depth cueing can be provided without the use of multiple projectors or stereo glasses by employing a specially designed concave video screen. U.S. Pat. No. 6,188,517 (assigned to Phillips Petroleum Company) describes such a concave video screen. The screen described in U.S. Pat. No. 6,188,517 generally comprises a concave semi-dome ceiling section, a flat semi-circular floor section, and a semi-cylindrical wall section edgewise joined between the ceiling section and the floor section. While this configuration provides enhanced depth cueing for certain viewing applications, it has been discovered that other video applications are best viewed on modified concave video screens in order to provide maximum viewing area, minimum distortion, and maximum depth cueing. 
     Because different video applications require different screen designs in order to provide optimum viewing, it is important for the shape of the video screen surface to be tailored for the specific application. However, tailoring the design of a concave video screen surface to a specific application can be an arduous task because, due to its complex shape, the screen surface is difficult to define. Further, once a suitable screen surface has been designed, it can be difficult to accurately manufacture the screen due to the complexity of the screen surface shape. 
     OBJECTS AND SUMMARY OF THE INVENTION 
     It is an object of this invention to provide 3D video projection systems which are optimized for specific applications. 
     Another object of this invention is to provide a simplified system for defining the shape of a complex concave video screen surface. 
     A further object of this invention is to provide a method for designing optimized concave video screens. 
     A still further object of this invention is to provide a method for manufacturing optimized concave video screens. 
     A yet further object of the present invention is to provide optimized 3D video screens which provide enhanced depth cueing, maximum viewing area, and minimum distortion for specific viewing applications. 
     In accordance with one embodiment of the present invention, a method for designing a concave 3D video screen surface is provided. The screen surface extends generally inwardly from a front edge of the screen surface. The screen surface includes an equator dividing the screen surface into a normally upper portion and a normally lower portion. The design method includes the steps of: (a) determining a maximum screen width (X max ); (b) determining a maximum screen height above the equator (Z max ); (c) determining a rounded corner radius (r c ) for the front face; and (d) calculating the location of a plurality of screen surface points by inputting X max , Z max , and r c  into a master equation.                y   =       (       [     1   -     (            x        P       a   P       )       ]     ·     b   P       )       1   P         ,              wherein                 a   =           X   max     2                   if                      z          &lt;     (         X   max     2     -     r   c       )         ,                 a   =         (         X   max     2     -     r   c       )     +             r   c   2     -       (          z        -     (         X   max     2     -     r   c       )       )     2                                    if                      z            ≥     (         X   max     2     -     r   c       )         ,                 b   =         (     1   -       z   2       Z   max   2         )     ·       (       X   max     2     )     2           ,              and                 P   =     2   -     (       k   ·        z            Z   max       )         ,                                
     wherein X max  is in a range of from about 6 inches to about 1200 inches, wherein Z max  is in a range of from about 0.1 X max  to about 0.5 X max , wherein r c  is in a range of from about 0 to about 0.5 X max , wherein k is in a range of from 0.1 to about 0.95, wherein the screen surface extends relative to orthogonal X, Y, and Z axes, wherein x is the orthogonal distance from the Y-Z plane to the display surface, wherein y is the orthogonal distance from the X-Z plane to the display surface, wherein z is the orthogonal distance from the X-Y plane to the surface, and wherein the actual position of each point defining the display surface varies by less than 0.1 X max  from the calculated position of the point as defined by the master equation. 
     In accordance with still another embodiment of the present invention, a 3D video projection system is provided. The video projection system generally comprises a housing, a concave video screen, and a projector. The video screen and projector are positioned within the housing. The projector is operable to project an image on the video screen. The housing has an opening therein through which the video screen can be viewed from outside the housing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING FIGURES 
     FIG. 1 a  is a front perspective view of a concave video screen surface, particularly illustrating the parameters (i.e., X max , Z max , and r c ) which at least partly determine the shape of the screen surface and the position of the screen surface relative to the X, Y, and Z coordinate axes. 
     FIG. 1 b  is a side view of the concave video screen surface of FIG. 1 a , particularly illustrating the position of the screen surface relative to the Y and Z axes. 
     FIG. 1 c  is a top view of the concave video screen surface of FIG. 1 a , particularly illustrating the position of the screen surface relative to the X and Y axes. 
     FIG. 1 d  is an isometric view of the concave video screen surface of FIG. 1 a.    
     FIG. 2 a  is a front perspective view of a prior art concave video screen surface, with the upper domed portion of the screen surface being defined, at least in part, by the parameters set forth in FIG.  1 . 
     FIG. 2 b  is a side view of the concave video screen surface of FIG. 2 a.    
     FIG. 2 c  is a top view of the concave video screen surface of FIG. 2 a.    
     FIG. 2 d  is an isometric view of the concave video screen surface of FIG. 2 a.    
     FIG. 3 a  is a front perspective view of an inventive concave video screen surface, with the upper portion of the screen surface being defined, at least in part, by the parameters set forth in FIG.  1 . 
     FIG. 3 b  is a side view of the concave video screen surface of FIG. 3 a.    
     FIG. 3 c  is a top view of the concave video screen surface of FIG. 3 a.    
     FIG. 3 d  is an isometric view of the concave video screen surface of FIG. 3 a.    
     FIG. 4 a  is a front perspective view of an inventive concave video screen surface, with the entire screen surface being defined, at least in part, by the parameters set forth in FIG.  1 . 
     FIG. 4 b  is a side view of the concave video screen surface of FIG. 4 a.    
     FIG. 4 c  is a top view of the concave video screen surface of FIG. 4 a.    
     FIG. 4 d  is an isometric view of the concave video screen surface of FIG. 4 a.    
     FIG. 5 is a schematic elevation side view of a 3D video projection system constructed in accordance with the principles of the present invention. 
     FIG. 6 is a schematic elevation side view of an alternative 3D video projection system constructed in accordance with the principles of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     One embodiment of the present invention concerns a method for designing and constructing concave video screens. As discussed above, the optimal shape for a concave video screen surface may vary depending on the viewing application for which it is used. 
     It has been discovered that the efficiency of designing and constructing concave video screens can be greatly enhanced by employing a master equation for determining the shape of the screen surface based on certain common parameters. The master equation can be employed in the design of the screen surface to allow the designer to simply change certain parameters and then view the screen surface shape using standard 3D modeling computer software. The master equation can also be employed in the manufacture of concave video screens by using the master equation to calculate a set of 3D coordinates defining the screen surface. These calculated 3D coordinates can be used to create templates for making the screen, or for controlling the machinery (e.g., programmable milling machines) used to make the video screen. 
     Referring now to FIGS. 1 a ,  1   b ,  1   c , and  1   d , a sample concave video screen surface  10  is defined by certain parameters (i.e., X max , Z max , and r c ) which can be employed in the master equation to define its shape. The shape of screen surface  10  is defined relative to orthogonal X, Y, and Z axes. Screen surface  10  has a generally planar front edge  12  which lies in the X-Z plane. Screen surface  10  has a generally planar equator  14  which lies in the X-Y plane. Screen surface  10  has a generally planar central meridian  16  which lies in the Y-Z plane. The maximum width (X max ) of screen surface  10  is the distance between the two sides of front edge  12 , measured along the X axis. The maximum height (Z max ) of screen surface  10  above equator  14  is the distance from the X-Y plane to the upper-most point on front edge  12 , measured along the Z axis. The maximum depth (Y max ) of screen surface  10  is the distance from the X-Z plane to screen surface  10  measured along the Y axis. Front edge  12  can have a rounded corner  18  defined by a rounded corner radius (r c ). The rounded corner radius (r c ) can vary between 0.0 and X max /2. When r c  equals X max /2, front edge  12  has a generally circular or elliptical shape. When r c  equals 0.0, front edge  12  has a generally square or rectangular shape. Each point defining screen surface  10  has a unique x, y, z coordinate measured relative to the X, Y, and Z axes. 
     The master equation of the present invention can be expressed as follows:                y   =       (       [     1   -     (            x        P       a   P       )       ]     ·     b   P       )       1   P         ,              wherein                 a   =           X   max     2                   if                      z          &lt;     (         X   max     2     -     r   c       )         ,                 a   =         (         X   max     2     -     r   c       )     +             r   c   2     -       (          z        -     (         X   max     2     -     r   c       )       )     2                                    if                      z            ≥     (         X   max     2     -     r   c       )         ,                 b   =         (     1   -       z   2       Z   max   2         )     ·       (       X   max     2     )     2           ,              and               P   =     2   -       (       k   ·        z            Z   max       )     .                                    
     In the above master equation, X max , Z max , and r c  are the parameters shown in FIG. 1, while k is an edge transition constant for controlling the angle of screen surface  10  relative to the X-Z plane proximate front edge  12 . The edge transition constant (k) can vary from 0.0 to 1.0. When k equals 0.0, the portion of screen surface  10  immediately adjacent front edge  12  extends from front edge  12  in a direction which is at least substantially perpendicular to the X-Z plane. When k equals 1.0, the portion of screen surface  10  immediately adjacent front edge  12  extends from front edge  12  in a direction which is at least substantially planar and oblique to the X-Z plane. 
     When the values for X max , Z max , r c , and k are entered into the master equation, the master equation can be used to calculate the x, y, z coordinates of the plurality of screen surface points which define the surface of the screen. Prior to calculating the screen surface points, an X axis increment (Δx) and a Z axis increment (Δz) can be determined to control the spacing and number of the screen surface points calculated. Thus, the master equation can be employed to calculate a y coordinate for each Δx increment between −X max/2  and X max/2  and each Δz increment between −Z max  and Z max . Alternatively, when it is desired to only calculate the shape of the screen surface above equator  14 , the master equation can be employed to calculate a y coordinate for each Δx increment between −X max/2  and −X max/2  and each Δz increment between 0.0 and Z max . 
     Although the master equation is expressed herein as calculating y coordinates as a function of x, z, X max , Z max , r c , and k, it is entirely within the ambit of the present invention for the master equation to be rearranged so as to yield x coordinates as a function of y, z, X max , Z max , r c and k, or z coordinates as a function of x, y, X max , Z max , r c , and k. 
     Referring now to FIGS. 2 a ,  2   b ,  2   c , and  2   d , a prior art concave video screen surface  100  is illustrated in relation to orthogonal X, Y, and Z axes. Video screen surface  100  has substantially the same shape as the video screen surface described in U.S. Pat. No. 6,188,517, the entire disclosure of which is incorporated herein by reference. Video screen surface  100  includes a concave semi-dome ceiling  102 , a flat semi-circular floor  104 , and a semi-cylindrical wall  106  edgewise joined between ceiling  102  and floor  104 . The portion of screen surface  100  presented by ceiling  102  can be expressed by the master equation. The shape of ceiling  102  can be defined by the parameters (i.e., X max , Z max , and r c , and k) discussed above with reference to FIG.  1 . As perhaps best illustrated in FIG. 2 a , r c  for ceiling  102  is equal to X max /2. Having r c  equal X max /2 causes the front edge  108  of ceiling  102  to be semi-circular in shape. As perhaps best illustrated in FIG. 2 c , k for ceiling  102  is equal to 0.0, and thus the portion of screen surface  102  immediately adjacent front edge  108  extends perpendicular to the X-Z plane. The exact parameters for the portion of screen surface  100  presented by ceiling  102  in FIG. 2 are as follows: X max =41 inches, Z max =20.5 inches, r c =20.5 inches, and k=0.0. 
     Although screen surface  100  is suitable for certain applications, it has been discovered that different screen shapes present advantages for other applications. FIGS. 3 a ,  3   b ,  3   c  and  3   d  illustrate a screen surface  200  particularly suited for viewing applications such as home cinematography. Screen surface  200  includes an upper portion  202  located above equator  204  and a lower portion  206  located below equator  204 . 
     Upper portion  202  can be defined by the master equation, expressed above, while lower portion  206  has a generally cylindrical, toroidal or even ellipsoidal shape, depending on the requirements of the specific viewing application. As perhaps best illustrated in FIG. 3 a , the rounded corners  208  of front edge  210  of upper portion  202  have a radius of curvature (r c ) which is less than X max /2. This lower r c  value effectively “opens up” the corners of screen surface  200  and allows screen surface  200  to provide more viewing area for watching conventionally formatted media (e.g., movies). The r c  value for upper portion  202  of screen surface  200  is preferably in a range of from about 0.0 to about 0.5 X max , more preferably from about 0.01 X max  to about 0.25 X max , still more preferably of from about 0.025 X max  to about 0.1 X max , and most preferably from 0.04 X max  to 0.06 X max . As perhaps best illustrated in FIG. 3 c , the portion of screen surface  200  immediately adjacent front edge  210  extends at an angle which is less than perpendicular relative to the X-Z plane, thereby effectively “flattening out” the portion of screen surface  200  proximate front edge  210 . This “flattening out” of screen surface  200  proximate front edge  210  reduces image distortion on that portion of screen surface  200 . The “flattening out” of the screen surface is caused by employing a k value in the master equation which is greater than 0.0. Upper portion  202  of screen surface  200  preferably has a k value in a range of from about 0.1 to about 0.95, more preferably from about 0.25 to about 0.75, and most preferably from 0.4 to 0.6. Referring again to FIGS. 3 a ,  3   b ,  3   c  and  3   d , the Z max  value for upper portion  202  of screen surface  200  is preferably in a range of from about 0.1 X max  to 0.5 X max , more preferably from 0.2 X max  to 0.4 X max , and most preferably 0.25 X max  to 0.32 X max . The X max  value for upper portion  202  of screen surface  200  is preferably in a range of from about 6 inches to about 1200 inches, more preferably from about 24 inches to about 96 inches, and most preferably from 36 to 48 inches. 
     FIGS. 4 a ,  4   b ,  4   c , and  4   d  illustrate a screen surface  300  which is particularly suited for viewing applications such as video games. In contrast to the screen surfaces described with reference to FIGS. 2 and 3, both an upper portion  302  and a lower portion  304  of screen surface  300  are defined by the master equation. As perhaps best illustrated in FIG. 4 a , the corners  306  of front edge  308  of screen surface  300  are substantially square. These square corners  306  are provided by employing a small r c  value in the master equation. The r c  value for screen surface  300  is preferably in the range of from about 0.0 to about 0.5 X max , more preferably r c  is less than about 0.1 X max , still more preferably less than about 0.05 X max , and most preferably about 0.0. Screen surface  300  has a k value which causes at least a partial “flattening out” of the portion of screen surface  300  proximate terminal edge  308 . The k value for screen surface  300  is preferably in the range of from about 0.1 to about 0.95, more preferably from about 0.25 to about 0.75, and most preferably from 0.4 to 0.6. The Z max  value for screen surface  300  is preferably in the range of from about 0.1 X max  to about 0.5 X max , more preferably from 0.25 X max  to 0.45 X max , and most preferably from 0.35 X max  to 0.40 X max . The X max  value for screen surface  300  is preferably in a range of from about 6 inches to about 1200 inches, more preferably from about 12 inches to about 60 inches, and most preferably from 16 inches to 36 inches. The aspect ratio, which is the ratio of maximum height (i.e., 2 Z max ) to maximum width (i.e., X max ) of screen surface  300 , is preferably in a range of from about 1:2 to about 1:1, more preferably from about 5:8 to about 7:8, and most preferably about 3:4. The ratio of maximum depth to maximum width for screen surface  300  is preferably in a range of from about 0.1:1 to about 1:1, more preferably from about 0.2:1 to about 0.5:1, and most preferably from 0.3:1 to 0.4:1. 
     As described and shown above, the master equation can be employed to design and manufacture a variety of different screen shapes. The actual shape of the manufactured screen surface should be substantially the same as the calculated shape of the screen surface defined by the master equation. Although minor variations between the actual and calculated screen surface shapes are inevitable, it is preferred for the actual position of each point defining the actual screen surface to vary by less than 0.1 X max  from the calculated position of the point defined by the master equation. More preferably, the actual position of each point defining the actual screen surface varies by less than 0.05 X max  from the calculated position of the point. For example, if X max =20 inches and the calculated y coordinate for the screen surface at x=3.0 inches and z=4.0 inches is 2.0 inches, then the actual y coordinate for the actual screen surface at x=3.0 inches and z=4.0 inches is preferably 2±0.2 inches, more preferably 2±0.1 inches. 
     FIG. 5 illustrates a 3D video projection system  400  which generally comprises a housing  402 , a projector  404 , and a concave video screen  406 . Projector  404  and screen  406  are positioned within housing  402 ., Housing  402  is substantially closed, so as to prevent an excessive amount of light from entering the interior space of housing  402 . However, housing  402  defines an opening  408  which allows screen  406  to be viewed from outside of housing  402 . Video projection system  400  may include a mirror  410  for reflecting the image produced by projector  404  onto screen  406 . Preferably, screen  406  presents a surface similar to that described above with reference to FIG.  4 . 
     FIG. 6 illustrates an alternative 3D video projection system  500  similar to that illustrated in FIG.  5 . However, video projection system  500  is a rear projection system wherein the image is displayed on a backside of the screen  502  and can be viewed from a front side of the screen  502  via the opening  504  in the housing  506 . Screen  502  is preferably vertically spaced from the projector  508 . A plurality of mirrors  510  can be employed to reflect the image emitted by projector  508  onto the backside of screen  502 . Screen  502  preferably presents a surface similar to that described above with reference to FIG.  4 . The configuration of video projection system  508  is ideal for video game applications. 
     Although FIGS. 5 and 6 illustrate projection systems where the projector and video screen are inside a housing, and the image on the screen is viewed from outside the housing, it should be understood that the novel screen surface shapes described herein can also be employed in more conventional theater-style or conference room configurations, as shown in U.S. Pat. No. 6,188,517, for example. 
     The preferred forms of the invention described above are to be used as illustration only, and should not be utilized in a limiting sense in interpreting the scope of the present invention. Obvious modifications to the exemplary embodiments, as hereinabove set forth, could be readily made by those skilled in the art without departing from the spirit of the present invention. 
     The inventors hereby state their intent to rely on the Doctrine of Equivalents to determine and assess the reasonably fair scope of the present invention as pertains to any apparatus not materially departing from but outside the literal scope of the invention as set forth in the following claims.