Abstract:
A cinema sound production device, to be located behind screen, which will produce a phase-coherent spheroidally shaped superimposed wavefront which has an adjustable, determinable radius, thus possessing a stable psycho-acoustic virtual point source, which may move in a continuously variable manner from infinity to within the plane of the device, as well as in any 3 dimensional axis, thereby, with the use of a positioning track and a computer, being able to be keyed in cinematic post production to visual location as displayed on a screen.

Description:
BACKGROUND OF THE INVENTION 
     My invention concerns interaural time delay of a direct sound superimposed wavefront as it is generated by a loudspeaker array and is perceived by the ears and brain to have a distinct spheroidal propagation and thus, a corresponding radius vector and thus, a psychoaccoustic virtual point-source, hereafter referred to as an image, in three dimensional space. 
     Space and source perception of human hearing in nature, as well as with reproduced sound, depend concurrently on at least four different parameters of acoustics which are received by the left and right ears and processed in the hearing center in the brain to identify a sound&#39;s point-source, not only as to direction, but also in rather exacting distance estimation, i.e. to find the radius vector of a given wavefront. 
     These four parameters, as long understood, may be listed as loudness (amplitude of a given soundwave); the acoustic ratio (ratio in amplitude of direct to reflected soundwaves); high frequency roll-off (absorption by the atmosphere of energy of shorter wavelengths); and finally, and most significant for image perception, time delay, or the relative difference in times of arrival of a given wavefront (at the same period of phase) at the two respective ears. 
     In order to explain the physics of creating an image one must note that time delay may be understood to exist in two regions of effect on human hearing. The proportion of the human interaural separation (approximately 15 to 21 cm.), to the audible wavelengths (which vary from approximately 1,720 cm. to 1.72 cm.) may fall into the region referred to as near-field, meaning an interaural phase-shift of time delay which is well within one full cycle of a given wavelength, and which is intelligible by the brain as to degree. On the other hand, this proportion may fall into the region referred to as far field, meaning a phase-shift of time delay which is greater than 360° (one full cycle of a given wavelength), or else very near 0° in the near field which is beyond comprehension to the brain with respect to the oncoming radius vector of a direct wavefront. This far-field proportion is, however, very useful for the spatial reconstruction of reflective walls and other surrounding surfaces in a recorded non-anechoic environment. This use of echo, which may be effective from 10 to 30 ms., is known as the Haas effect and is employed by the recording industry as the primary tool for building a “stereo” as well as “surround” soundstage. 
     On the other hand a direct oncoming wavefront received by the ears in an anechoic condition, i.e., with no reflective surround echo clues, may be subconsciously measured by the brain as to the phase-shift of the arrival times with respect to the tangent of the wavefront at the two ears. Although the difference may be as little as one tenth of a millisecond, in the near field region (which, with an interaural separation of 15-21 cm., lies between approximately 125 HZ (wavelength=275 cm.) and 1500 HZ (wavelength=23 cm.)), this delay may correspond to a comprehensible amount of phase shift (that is greater than 0° and less than 360°), which may be used to triangulate the angle of the oncoming wavefront to the head, using the following relationship:          Sin                 Θ     =     ct   x                            
     where 
     θ is the arriving angle of the radius vector of the oncoming wavefront; 
     c is the speed of sound; 
     t is the time delay; and 
     x is the distance between the ears. 
     Furthermore, by slightly “cocking” the head to the first found angle, the brain may refine this estimation in three-dimensional space, subconsciously and nearly simultaneously, triangulating several aspects of the wavefront, and thus, the curvature or radius, ie., with a flatter wavefront signalling a more distant point-source and more rounded wavefront signalling a nearer point-source. 
     DESCRIPTION OF THE PRIOR ART 
     Prior art (See particularly, U.S. Pat. No. 3,773,984) from Peter Walker of Quad Electroaccoustics Ltd, Huntingdon, England, provides for an arrayed loudspeaker, marketed as the Quad ESL-63 Electrostatic Loudspeaker, which involves a vibrating electrostatically charged thin membrane which is suspended in a plane between two like-dimensioned planar electrode grids which, in turn, are electrically segregated into an array of concentric annular segments surrounding a central circular section. 
     A mono signal drives the central section with no delay and then, in the fashion of a transmission-line loudspeaker (a parallel line of capacitors linked with inductance, which introduces a progressive amount of delay), drives the inner most ring-segment with a given amount of delay and then, each with an additional given amount of delay, drives each additional ring-segment outward from the center until the outer most ring-segment has been activated. 
     Thus, the superimposed wavefront generated by the Walker device propagates in a substantially spherical pattern which has a fixed radius and therefore may be perceived to describe an image which occupies a fixed and stable point in three-dimensional space, approximately two meters behind the loudspeaker device. 
     My invention, with the guidance of data on a positioning track and a computer processor achieves the creation of a stable image at a point in three-dimensional space at an arbitrarily chosen location behind (and including the plane of) the device and then provides means for shifting the location to any other arbitrary location behind the device. 
     SUMMARY OF THE INVENTION 
     A cinema sound reproduction device is described which when fed by an ordinary monaural input will produce a phase coherent spheroidally shaped wavefront which may be perceived by the listener as having a distinct image at an apparent point in three dimensional space, which is positioned some variable distance and direction behind the actual position of said device. 
     The architectural sub-structure of this invention may be implemented in different ways. One such implementation may be an articulated compound spheroidal hinge construction of multiple sixteen-sided polyhedra composed of only equilateral triangles of identical size. Each hinged polyhedron, in turn, may serve as a platform for the mounting of one or more identical lower-midrange conventional loudspeakers. All of the loudspeakers in the array are simultaneously driven in phase, producing wavefront elements which superimpose upon one another to form a combined, or superimposed, wavefront which is heard by an observer to emanate from a source point on the central axis of the array of loudspeakers, such that the distance of the source point is dependent upon the configuration of the articulated spheroidal hinge. The loudspeakers are arrayed in a spheroidal section which has one and only one focal point, and the sound from the loudspeakers in that spheroidal configuration appears to emanate from that focal point. 
     Alternatively the architectural sub-structure of this invention may be a fixed array of identical lower-midrange loudspeakers, sufficient in number to form a single center loudspeaker, plus other surrounding groups of loudspeakers, more or less concentric to the center loudspeaker, utilizing a calculated delay for each individual loudspeaker. 
     In this case, a processor executes mono signals which are fed to the center loudspeaker at minimum delay and then with progressive, calculated delays, successively to each loudspeaker toward and including the outermost ones. 
     In either form of architectural sub-structure, a phase-coherent superimposed spheroidal wavefront produced by said individual loudspeakers may be varied with respect to radius in a continuous way to define a predetermined apparent point in space as the virtual point source, or image, of the wavefront, and then, when the radius is varied, a different apparent point in space becomes the new virtual point source. 
     This is a psychoacoustic image. It may be seen (or heard) to be the radius of the spheroidal wavefront. It may be located anywhere behind said device from infinity to within the plane of the device. 
     The perceived position of the image, whether stationary or in motion, may be made to correspond with the visual spatial location or movements of cinematic characters and/or objects on the cinema screen to be perceived by a viewer to emit a given sound. This may be accomplished in cinematic post production with a synchronized positioning track affixed directly onto the film. 
     Also, the lateral position of an image need not necessarily be centered on said device. In the case of the articulated compound spheroidal hinge variant, the device may be made simply to tilt obliquely with respect to the plane of the screen, and then the image will correspondingly be heard to move laterally, and/or vertically, in accordance with the movement of the central axis of the speaker array. 
     With the fixed-array variant of my invention, the signal may be regulated by a computing processor to choose any predetermined point within the array as the center and consequently to feed surrounding groups of loudspeakers within the array with calculated progressively delayed signals until the outermost group or segment, as needed to emulate the desired sound wavefront. This shifts the apparent source position of the image laterally and/or vertically in accordance with calculations based upon the predetermined source point in three-dimensional space. 
     The actual calculation is fairly straightforward. A sound wavefront emanating from an arbitrarily predetermined point in space expands from that point spherically at the speed of sound. The three-space location of all of the points along the sphere at any instant of time can be calculated given the instant in time at which a sound may be thought to have emanated from the virtual source point, and the elapsed time associated with the desired wavefront. Emulating that sound wavefront from a different point in space with a group of speakers is done by letting each speaker contribute an element to the emulating wavefront at the appropriate time so that the totality of the contributed elements superimpose upon one another to form the desired wavefront. To emulate that hypothetical original sound wavefront from an array of speakers, one calculates the respective delays necessary at each of the individual array speakers for that speaker&#39;s contribution to the emulated wavefront. 
     As may be seen with reference to FIGS. 19 and 19 a,  from some arbitrary point “p” in space behind a planar array of speakers, a line is extended to the nearest point “a” in the plane of an array of speakers (to assume a planar array is convenient for calculation, but not necessary for practice of the invention). It may be seen that a sound wavefront from “p” would pass first at the point “a” in that array. Therefore, the delay for a speaker at “a” would be zero. With respect to the delay “delta t” for activation of a speaker “B” at a point “b” in the planar array, it may be seen that the points “p,” “a,” and “b” form a right triangle such that the distance “pb” is the hypotenuse and “pa” is, with respect to the angle “bpa,” the adjacent side. Thus, the relationship of “pb” to “pa” is the secant of the angle “bpa.” So, if the time taken for the sound originating at “p” to reach the nearest point in the array “a” is one, then secant “bpa” minus one, divided by the speed of sound, gives the delay “delta t” for the speaker at “b.”         δ      t     =       sec      bpa     -     1   c                              
     Thus, to emulate a sound wavefront from “p,” it is only necessary to calculate the respective “delta t”s for each speaker in the array, and activate each at its appointed time. If “p” changes, all the calculations are done again for the new “p” and a different set of activation instructions is dispatched to the respective speakers. 
     Of course, mounting my compound variable-radius hinge speaker device in a universal mount for rotation about both vertical and lateral axes, automatically emulates a sound wavefront from a virtual point on the central axis of the compound variable radius device, located at a distance down that axis which is determined by the degree of curvature, i.e., convexity, of the loudspeaker configuration, when all of the speakers are activated in phase. Using servo motors to control the rotations of the universal mount and the curvature or convexity of the hinge device, allows for automatic operation and swift movement of the device from configuration for emulation of a sound wavefront from a first virtual point to configuration for sound from a second virtual point. 
     Supplying the necessary data for a full system utilizing a device or devices described in this invention may be accomplished by printing the positioning data in a digitized form directly onto the film, or by means of an external device carrying the sound source-point data to drive the loudspeakers by some synchronized means to correspond with the action on the film. From this data, all calculations can be made and activation signals provided to each respective speaker as necessary to emulate each respective wavefront as necessary to follow the visual spatial location as perceived on the screen. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a blank of a sixteen sided polyhedron, with (1-15) being vertices of identical equilateral triangles. 
     FIG. 2 shows how the blank is folded to form the polyhedron unit, with broken lines indicating “valleys” and solid lines forming “ridges.” 
     FIG. 3 shows three successive views (a,b,c) in elevation at 45° intervals of the polyhedron unit as it rotates about the longitudinal axis defined by (4+10), (3+9+15). 
     FIG. 4 shows three views (a,b,c) in plan of the polyhedron unit in FIG.  3 . 
     FIG. 5 shows three successive views (a,b,c) in elevation at 45° intervals of a rigid crossbar structural unit which may be alternatively used in place of the polyhedron unit of FIGS. 3 and 4. 
     FIG. 6 shows three views (a,b,c) in plan of the rigid crossbar structure of FIG.  5 . 
     FIG. 7 shows five plan views of multiple assemblies of the polyhedron units of FIG. 3, in 
     (a) exploded view of 12 polyhedron units, 
     (b) exploded view of four units, 
     (c) exploded view of two assembled hinged groupings of four units each, 
     (d) exploded view of the assembled hinged grouping of eight units seen in (c), with four additional units, and 
     (e) a fully assembled hinged grouping of twelve units, in a substantially planar configuration. 
     FIG. 8 shows the fully hinged grouping of twelve units seen in FIG. 7 ( e ), flexed in a convex configuration toward the viewer. 
     FIG. 9 shows seven successive views (a,b,c,d,e,f,g) in side elevation of the hinge structure in FIG. 7 ( e ) as it flexes from an extreme convex configuration, FIG. 9 ( a ), through a planar state, FIG. 9 ( d ), and on to an extreme concave configuration, FIG. 9 ( g ). 
     FIG. 10 shows hinging detail for joinder of hinging edges of polyhedron units, and how control levers may be connected. 
     FIG. 11 is a frame from a cinematic film. 
     FIG. 11 a  is a diagram of the scene in FIG.  11 . 
     FIG. 12 is a plan diagram of the scene in FIG.  11 . 
     FIG. 13 shows three successive diagrammatic perspective views, respectively, of a virtual point source, the hinged assembly of polyhedron units with loudspeakers mounted thereon, and a superimposed phase-coherent spherical sound wavefront emanating from the loudspeakers. 
     FIG. 14 is a side view, partially cut away, and partially exploded, of a configuration control mechanism for a twelve-unit assembly of polyhedrons, with loudspeakers mounted thereon, with an enlarged section in FIG. 14 a.    
     FIG. 15 is a top view of the configuration control mechanism of FIG. 14, with an enlarged section in FIG. 15 a.    
     FIG. 16 is a loudspeaker array formed from a hinged assembly of 12 polyhedron units. 
     FIG. 17 is a side view diagram of the loudspeaker array of FIG. 16 showing a virtual point source, the array and a superimposed phase coherent wavefront. 
     FIG. 18 shows a front view of a fixed planar array of loudspeakers. 
     FIG. 19 is a diagram showing a virtual source, two loudspeakers from the array of FIG.  18  and control units. FIG. 19 a  shows a triangle formed by two speakers and a virtual point source. 
     FIG. 20 shows a diagrammatic plan of a hypothetical cinema with a loudspeaker array, virtual point sources and means for activating individual speakers in accordance with delay information which is recorded on the cinematic film. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     With respect to FIGS. 1-3, a structural-unit in the form of a sixteen sided polyhedron may be formed from a blank as shown in FIG.  1 . The structural unit is formed by folding the two edges  1 - 3 ,  13 - 15  toward each other along lines  4 - 6  and  10 - 12 , and sealing at  1 + 13 ,  2 + 14 ,  3 + 15 . The blank is now half as wide as when unfolded and still the same length. Now a convex end  6 ,  3 + 9 + 15 ,  12  and a concave end  4 ,  1 + 7 ,  10  are observed, which are sealed such that the convex end  6 ,  3 + 9 + 15 ,  12  seals as it naturally falls in place, and the concave end must be pinched together at points  5 ,  11  so that edges  7 ,  4 + 10 ,  1 + 13  seal at a right angle to sealed edges  6 ,  3 + 9 + 15 ,  12 . 
     A resulting polyhedron as in FIG. 3 has an axis of symmetry referred to as the longitudinal axis 4+10 to 3+9+15 about which there exists at every 180 degree revolution congruity and at every 90 degree revolution there exists congruity which is reversed with respect to the axis 4+10 to 3+9+15. 
     The angle formed by that axis and each of four edges ( 1 + 13  to  4 + 10 ), ( 4 + 10  to  7 ), ( 6  to  3 + 9 + 15 ), and ( 3 + 9 + 15  to  12 ) is substantially 54.27° and the angle between edges ( 1 + 13  to  4 + 10 ) and ( 4 + 10  to  7 ) or ( 6  to  3 + 9 + 15 ) and ( 3 + 9 + 15  to  12 ) is substantially 108.55°. These four edges are used for mounting hinges when the structural unit is assembled into a compound hinge. 
     There are twenty-four edges formed by sixteen facets. Four edges ( 5  to  2 + 14 ), ( 2 + 14  to  11 ), ( 5  to  8 ) and ( 8  to  11 ), are concave, or “valleys.” All other edges are convex or “hills.” 
     One can also form a structural unit of this invention by fastening together 12 equilateral triangles of the same size in the form shown, or such a structural unit could be carved from solid materials, or molded, vacuum-formed, or otherwise created. 
     An alternative structure which is architecturally interchangeable with a polyhedron of FIG. 3, and which is therefore identical for structural purposes when assembling a compound lever, is shown in FIG. 5, which consists of a central longitudinal bar  16  and two pairs of contiguously angled bars  17 ,  18 , and  19 ,  20 . 
     As seen in FIG. 6, each bar pair is offset perpendicular to the other as viewed along said longitudinal bar  16 . The angle within each pair is substantially 108.55°, and the angle of each bar  17 ,  18 ,  19  and  20  with said longitudinal bar is substantially 54.27°. 
     Material used for construction of said crossbar must allow for rigid joining, such as welded steel, as the bars act as hinge edges within a multiplicity of these crossbar structures in order to form my articulated compound spheroidal hinged compound lever, whereas with the polyhedron structure, structural integrity is afforded by its rigid, geometrically structured form. 
     It may be readily observed that it is feasible to construct the polygon structure with a reinforcing crossbar structure, or other skeletal structure, within the polygon, to afford greater flexibility in the choice of materials for fabrication of the polygon and to provide purchase for the mounting of hinges along the hinging surfaces. 
     Assembly of a twelve-unit compound hinge is shown in the several views of FIG.  7 . In FIG. 7 a  all twelve units are shown exploded and separated from one another, but in the correct orientation for joinder along their common hinging edges. The central four units, when fully assembled have vertices  21  which are to be assembled together to a common point  21 . The leftmost two of the central four have vertices h which are to be assembled together to form a common point h. Similarly, the rightmost two of the central four have vertices h′, which are to be assembled together to form a common point h′ on the fully assembled 12-unit device. The points h and h′ are drawn horizontally toward or apart from one another as part of the means for controlling the amount of excursion and configuration change of the 12-unit device. 
     As with the horizontal vertices h and h′, the uppermost two of the central four units have vertices v which are to be assembled together to form a common point v. Also, the lowermost two of the central four units have vertices v′ which are to be assembled together for form a common point v′. The points v and v′ are drawn vertically toward or apart from one another as the other part of the means for controlling the amount of excursion and configuration change of the 12-unit device. 
     FIG. 7 b  shows four units, A,B,C,and D, which are to be hinged together so that A&#39;s edge  17  is hinged to B&#39;s edge  18 . B&#39;s edge  19  is hinged to D&#39;s edge  20 . D&#39;s edge  18  is hinged to C&#39;s edge  17  and to complete the loop, C&#39;s edge  20  is hinged to A&#39;s edge  19 . 
     FIG. 7 c  shows two four-units, ABCD and EFGH, each hinged together as shown in FIG. 7 b,  ready to be hinged together into an eight-unit device, by hinging E 17  to C 18  and F 18  to D 17 , thus bringing the vertices  21  of units C, D, E, and F together to make a central point  21  in the eight-unit assembly. 
     FIG. 7 d  shows four additional single units I, J, K and L ready for hinged assembly to each other and to the eight-unit of FIG. 7 c , such that I&#39;s edge  18  is hinged to J&#39;s edge  17 , then I&#39;s edge  20  is hinged to C&#39;s edge  17  while J&#39;s edge  20  is hinged to E&#39;s edge  19 . Finally K and L are hinged at K  17  and L  18 , and then the 12-unit assembly is completed by hinging K 20  to D 19  and L 20  to F 19 . 
     FIG. 7 e  shows the fully hinged/assembled 12-unit ABCDEFGHIJKL configured in a substantially planar configuration, with the points h and h′ and v and v′ now established by the assembly process. 
     FIG. 8 shows the 12-unit from above, as in FIG. 7 e , but reconfigured into a convex configuration with CDEF closest to the viewer and IJKL farthest away. FIG. 8 may be seen to correspond to FIG. 9 g  if FIG. 9 g  were seen from below. 
     FIG. 9 is a series of seven side views of a 12-unit of my invention as it flexes through a series of configurations, from the fully concave in FIG. 9 a  , stepwise to a substantially flat configuration in FIG. 9 d  , and finally to a fully convex configuration in FIG. 9 g.    
     There are natural limits to the respective degrees of concavity or convexity, which are reached, respectively, when adjacent faces of the four central structural units meet mechanically in the process of being flexed together. 
     The addition of more units to a matrix of twelve, as for example, three groups of twelve units hinged together, may form a more complete spheroidal section, however, due to mechanical interferences, the spheroidal sections of such matrices are limited to the longer radii. 
     A single group of twelve units provides substantially a one-third spheroid section in extreme concave or convex orientation. 
     There are a multitude of potential uses for a compound hinge structure, as described above. Such a structure may act as a platform to mount various devices which radiate or receive energy waves, thereby affording the ability to mechanically “focus” and enhance certain properties of such energy waves. 
     For instance, a device may be constructed which may propagate sound wavefronts by radiating them outward from said device, e.g., convexly. Such a device may also receive soundwaves in a concave orientation, from an external sound source, providing for an adjustable phase-reading microphone device. Thus, a specific point may be physically located in space and be recorded or reproduced through the use of digital processing of discreet phase-coherent, superimposed sphere sections. 
     In FIG. 10 a means for hinging edges of polygons is shown. The hinging edges  17 / 18 / 19 / 20  are bored through end to end with sleeve channels  23 . Fulcrum rods  24  are inserted through the sleeve channels  23  and the respective holes in the eyelets  25  and  26 . The eyelet  25  is part of lever  25 , four of which, as will as will be seen, are used in causing flex movements of the finally assembled variable radius device. The eyelets  25 / 26  are secured to the fulcrum rods  24  by screws  27 . Hinging motion is therefore obtained by rotation of the eyelets  25 / 26  relative to the fulcrum rods  24  so that two adjacent polyhedra are constrained to move relative to one another only through a plane which is orthogonal to the fulcrum rods  24 . 
     FIGS. 11,  11   a  and  12  depict a cinematic film frame with two persons speaking respectively from virtual point sources  28  and  30 . FIG. 11 is a depiction of the cinema screen  32 . In FIG. 11 a  the same scene is related to FIGS. 18,  19  and  20  to show how the virtual point sources  28 / 30  appear in the respective contexts of a coplanar array of speakers (FIG.  18 ), a diagram of the locational relationship of the virtual point sources  28 , 30  to the coplanar array of speakers (FIG.  19 ), and the speaker array in a hypothetical theater (FIG.  20 ). 
     As best seen in FIG. 12, two actors  28 ,  30  appear in the field of view  32  of a camera. Radius vectors  29 / 31 , trace the path between the actors (virtual point sources)  28 / 30  and the camera, and illustrate, in plan, the geometry of the cinematic scene and the sound sources which appear within it. 
     FIG. 13 illustrates 3 successive diagrammatic views of a loudspeaker array  33  and a corresponding sound wave front  34 , as it might appear with a virtual point source  28 / 30  far away, at virtual infinity (FIG. 13 a ), more closely located (FIG. 13 b ) and quite near (FIG. 13 c ). For each one of an infinite number of distances down the central axis of a loudspeaker array mounted on a variable radius hinged mount according to my invention, there is one and only one configuration of the hinged mount, and of the loudspeakers mounted thereon, which will produce individual sound waves from each speaker in the correct combination to be superimposed on one another to form a single resultant sound wavefront which emulates a sound wavefront which would come from that point. The greater the degree of curvature, or convexity, of the hinged mounting structure (typically a 12-unit of my invention), the nearer a listener would perceive the virtual point source to be. Conversely, the more nearly the hinged mount approaches flatness (i.e., the longer the radius of the spheroidal section of the hinged mount), the farther away the sound would appear to an observer standing in front of the mounted loudspeaker array. 
     A mounting and control mechanism for a twelve polygon unit loudspeaker mounting array is shown in FIGS. 14,  14   a,    15  and  15   a.    
     The entire apparatus is mounted by means of a geared main mounting plate  48 , which holds a ball-bearing pivot  47  which is tied to a roller bearing housing  44 . Mounted within the roller bearing housing  44  is servo motor and pinion  49 , the teeth of which are engaged with the main mounting plate gear  48 . It may therefore be seen that azimuthal movement of the device around its vertical axis is achieved by activating the servo-pinion  49  to drive against the stationary geared mounting plate  48 . 
     Also mounted within the roller bearing housing  44  is pinion gear assembly  45  which includes a small pinion engaged with teeth of a curved geared head  43 , and further includes a larger gear which is engaged with the servo worm gear  46 , which is fixed in the housing  44 . Thus it may be seen that activation of the servo worm  46  drives the pinion gear assembly  45  to that the small pinion, in turn, drives the gear head  43  radially guided by roller bearings which are held by the roller bearing housing  44 . 
     The geared head  43  is rigidly attached to the base plate  42  with carries the loudspeaker mounting array and the mechanism by which the array curvature is controlled. Thus activation of the servo worm  46  to drive the pinion gear assembly  45  and the geared head  43 , moves the entire loudspeaker mounting array about its horizontal axis. 
     It may now be seen that movement of the central axis of the loudspeaker mounting array is under the control, in terms of elevation above or below a horizon, of the servo worm  46 , and in terms of azimuth, to the left or right of a straight-ahead centered position, of the servo pinion  49 . As those two servos are activated to drive the mounting array, the central axis of the array may be pointed to any spot, left or right, up or down, behind the array, which includes coverage of any virtual point source of sound which one might wish to emulate. 
     Fixed upon the base plate  42  is the servo-worm assembly  41 . The worm is engaged with teeth of a gear-pinion assembly  40  which is journalled into the housing plates  36 . The teeth of the pinion portion of the gear-pinion assembly  40  are engaged with the sliding geared rack  39 . The rack  39  is attached to guide head  38 . Pins  37  which are fixed in the vertical levers  25  are slidably engaged in slots in the guide head  38 . The vertical levers  25  are pivotably constrained by spindles  35  which are fixed to the housing plates  36 . As previously discussed with reference to FIG. 10, the levers  25  are attached at their outer ends to eyelets  26  at the points of the hinged array designated v and v′. 
     It may therefore be seen that activation of the servo worm assembly  41  drives the gear-pinion  40  to move the rack  39  and the guide head  38  so as to move the levers  25  by their guide pins  37 , to pivot about the spindles  35 , causing movement of the eyelets  26  at points v and v′ to change the curvature of the 12-unit polygon speaker mounting array. 
     As best seen in FIGS. 14 a  and  15   a,  the housing plate  36  and its attendant lever  25 , spindle  35 , etc., extend below the level of the mounting plate  42 , through a cut-out  50  in the mounting plate  42 . 
     Horizontal levers  25 , best seen in FIG. 15, are provided to connect (as shown in FIG. 10) with the points h and h′ of the  12  unit polygonal array. The levers  25  (h/h′) are pivotably held in a bracket and counterforce spring assembly  52 , one end of each lever  25  (h/h′) held by the spring, and the other end of each lever  25  (h/h′) connected by the transverse cables and posts back to the guide head  38 , with consequent opposite forces applied to horizontal levers  25  and vertical levers  25 . 
     Thus the entire process of opening (toward a flatter configuration and a longer radius) and closing (toward a more convex configuration and a shorter radius) is effected by activation of the servo worm  41  which drives the gear-pinion assembly  40  to drive the rack  39  and guide head  38  to cause the near ends of the levers  25  (v/v′) to pivot around the spindles  35  and draw the points v and v′ (1) toward or (2) away from one another, thereby causing the array to (1) close or (2) open, forming a new and different spheroidal section which is of, respectively (1) shorter or (2) longer radius. While control of the curvature of the array is achieved by controlling the points v/v′, it is useful to provide a counterforce spring to hold the points h/h′ stable and secure during changes in the configuration of the array, under control of concurrent, but opposite movements of the vertical levers  25  (v,v′) and, through the transverse cables and posts  51 , the horizontal levers  25  (h/h′) with the bracket and counterforce spring  52 . 
     As may now be seen in FIGS. 16 and 17, a 12-unit, hinged, polygonal array  33  of my invention, having been positioned according to a specific predetermined configuration through the mechanisms described above with respect to FIGS. 10,  14 ,  14   a,    15  and  15   a,  may now, by substantially simultaneous activation of the individual speakers  53 , produce a collection of individual sound wavefronts  54 , which superimpose upon one another to form a new, single wavefront  34  which emulates a wavefront which appears to an observer (generally somewhere in front of the speaker assembly) to have come from a virtual pint source  28 / 30  located on the axis of the array  33  at a point whose distance down that axis (behind the array  33 ) corresponds exactly to the degree of curvature, or convexity, predetermined for the array  33 . 
     It may be further seen that activation of the respective servos  49 ,  46 , and  41 , by appropriate control signals can drive the array  33  into any desired configuration, corresponding to any virtual point source generally behind the array  33 . The physical system for electrical supply and control signals to the servos is entirely conventional and is not further detailed. 
     I have now established means by which, with a variable radius, spheroidal-sectioned array  33  of speakers  53 , as shown in FIG. 17, a superimposed wavefront  34  can be made from the contributions of individual speakers, each providing its contribution according to a predetermined arrangement of azimuth, elevation and array curvature, which corresponds to a particular, virtual-source point in space. 
     Another means by which a superimposed wavefront  34  can be provided from contributions of individual speakers  53 , particularly in a cinematic setting, is shown in FIGS. 18,  11   a,  and  20 . Speakers  33 , seen in FIGS. 18 and 20, are provided, presumably, but not necessarily, in a coplanar array. Sounds emanating, according to the story line of the film, from each of two actors, originate from virtual point sources  28 ,  30 , seen straight-on in FIG. 18, as the actors appear on-screen in FIG. 11 a,  and in plan view of a cinematic theater in FIG.  20 . Each speaker  33  is under centralized control for individual activation at a time appropriate to the making of its individual contribution to the superimposed wavefront  34 . 
     Control of a time-delay delta t which regulates the appropriate time for each speaker, is calculated with reference to FIGS. 19 and 19 a . Speakers  33 , labelled a and b respectively are shown as part of the planar array shown in FIGS. 18 and 20. A virtual point source  28 , labelled p is directly behind the speaker a, so that a sound wavefront emanating from the point p and expanding as a regular sphere, first breaks the plane of the array  33  at the point a. Thus, speaker a should be activated just at the time when an expanding sound wavefront from p, or source point  28 , would reach the point a in array  33 . Activation of b (which is to say, of each other speaker at its time, in the array  33 ) is dependent upon the delay necessary for the expanding sound wavefront from p to pass the speaker plane at the point where b is located. Thus, viewing the points pab as a right triangle, one observes that the time for activation of b corresponds to the hypotenuse bp while the time for activation of a corresponds to the adjacent side (with respect to the angle bpa). If pa equals one, then the delay delta t for activation of b is secant bpa (hypotenuse/adjacent) minus 1, divided by the speed of sound, as noted above. 
     One notes that for convenience I have chosen p directly behind the speaker a, which in practice is unlikely. Thus, there would normally be a point a in the speaker plane orthogonal to the point p, which would not be central to one of the speakers  33 . Hence, while no speaker would be activated at a precise instant of the impingement of the hypothetical sound wavefront  34  on the plane of the array  33 , each speaker&#39;s appointed activation time is calculated with respect to that point a. Hence, all speakers in the array may be thought of as having a nonzero delta t. 
     Thus, activating the sound feed to each individual speaker in array  33  in accordance with its respective delta t delay, may be seen in FIG. 20 to produce first and second superimposed sound wavefronts  34  which correspond respectively to wavefronts which would appear (or be heard) to have originated respectively at virtual source points  28  and  30 . 
     In cinematic practice projectors  59  (FIG. 20) project a scene upon a screen  32  which corresponds to a film frame such as that shown in FIG. 11 a,  which contains two virtual source points  28 ,  30 . Data recorded adjacent to the film frame is relayed to a computer  56 , comprising a positioning data track  57  and a normal sound track  58 . 
     With respect to any particular frame the positioning data track  57  provides to the computer  56  the desired point p information and the beginning and ending times for particular sounds. The computer  56  calculates delta t for each speaker in the array  33  and feeds the soundtrack signals at the appointed time to each speaker in turn, thus providing superimposed wavefronts  34  coordinated with the virtual source points for each sound and each frame in the film. 
     Since the film screen  32  is located directly forward of the array  33 , any psychoaccoustic virtual point source  28 ,  30  may be made to correspond to a visual spatial position as perceived on the screen. 
     The sound track  58  may consist of a plurality of forward channels, i.e. for loudspeakers located behind the screen, each corresponding to a different virtual sound source, i.e. a different point p and each being delivered to its corresponding set of speakers in the array  33  according to the respective delta t delays, as necessary to correspond to complex scenes involving multiple, and simultaneous, sounds and sources. 
     Of course, this system may also be used with a simple mono forward channel, e.g. the center channel in a Digital Dolby System 5.1, or its equivalent.