METHOD, APPARATUS AND ARTICLE OF MANUFACTURE FOR DETERMINING VISIBLE PARTS OF SURFACES OF THREE-DIMENSIONAL OBJECTS AND THEIR PARAMETERS OF SHADING WHILE ACCOUNTING FOR LIGHT AND SHADOW VOLUMES

Abstract: There is provided in an apparatus for facilitating rendering of a three dimensional image on an image plane for display on a display medium; the image plane having a plurality of pixels; a method comprising the steps of: (a) providing a list of surfaces defining the image; (b) subdividing the image plane into a plurality of tiles; (c) associating with a tile one or more surface(s) contained at least partially within the tile; and (d) for each pixel of a tile; (i) projecting a ray into the image; (ii) determining a ray/surface intersection with the one or more surfaces; (iii) generating a surface depth value for each of the one or more surfaces in dependence on the distance of that surface from the image plane; (iv) determining whether any surface is visible at that pixel; and (v) determining color attributes of that pixel accounting for shadows and light based on the results of the determination in the preceding step. During certain successive clock cycles of the above apparatus, pixel data is processed by simultaneously incrementing tile column and row.

Description: TITLE Method, apparatus and article of manufacture for determining visible parts of surfaces of three-dimensional obj ects and their parameters of shading while accounting for light and shadow volumes CROSS REFERENCE TO RELATED APPLICATION(S)/CLATM OF PRIORITY This application claims the benefit of co-pending Israeli Patent Application Serial No. 136430, filed May 29, 2000, and entitled "Ray-Tracing Method And System For Determining Visible Parts Of Surfaces Of Three- Dimensional Objects And Their Parameters Of Shading Accounting For Light And Shadow Volumes," the entire disclosure of which is also incorporated by reference as if set forth at length herein. Moreover, this application relates to co-pending Israeli Patent Application Serial No. 135465, filed April 4, 2000, and entitled "Method and System for Determining Visible Parts of Transparent and Nontransparent Surfaces of Three-Dimensional Objects," the entire disclosure of which is incorporated by reference as if set forth at length herein. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Not applicable. REFERENCE OF AN APPENDIX The Appendix attached hereto is a table comparing prior art products with that of the present solution. BACKGROUND 1. Field of the Invention The present invention relates generally to computer graphics and more particularly to an improved method, apparatus, and article of manufacture for providing real-time shading of surfaces of three-dimensional objects. 2. Brief Description of Related Art The best-known prior art systems for generating real time 3D images utilize the Z-buffer method. It may be implemented in either software or hardware and is used in systems produced by companies such as Silicon Graphics and Hewlett Packard. The Z-buffer method is used to determine which objects, or parts of objects, are visible and which are hidden behind others. With Z-buffering, the graphics processor stores the z-axis value of each pixel in a special area of memory called the Z-buffer. Different objects can have the same x- and y- coordinate values on the screen, but with different z-coordinate values. The object with the lowest z-coordinate value is in front of the other objects, and therefore that's the one that's displayed. Z-buffer type systems require a high level of integration and performance. Ray-tracing is another well-known method for generating 3D images. Ray-tracing is a global illumination based rendering method/illumination model that accounts for the transport of light energy beyond the direct/local contribution from the light sources. By tracing the path of light rays it is able to integrate the tasks of shading, shadow generation, hidden surface removal, projection and scan conversion into one single computational process. It traces rays of light from the eye back through the screen into the scene. A ray is generated for each one of the points (pixels) defining the screen. Then the rays are tested against all objects in the scene to determine if they intersect any objects. For each ray, the closest surface intersection point is determined. If the ray misses all objects, then that pixel is shaded the background color. Ray-tracing enables a high resolution of image to be created and can handle shadows, specular reflections, and texture mapping in a very easy straightforward manner. However, a large number of calculations have to be performed in order to determine the path (and characteristics) of each light ray, as a result of which a ray-tracing method tends to be very slow. Parallel processing in ray- tracing methods is not effective in the implementations known in prior art. United States Patent 5,729,672 entitled "Ray tracing method and apparatus for projecting rays through an object represented by a set of infinite surfaces" describes a method and system for ray-tracing, however, having several essential limitations. This invention is based on the use of a ray-tracing technique for rendering of three-dimensional images. Arbitrary objects are represented by set of convex objects. Each convex object in turn is represented by a set of infinite surfaces. Each surface of scene is classified as either a forward (front- faced) or reverse (back-faced) surface. The front-faced surface represents the condition where a vector normal to the surface points towards the observer. The reverse (back-faced) surface is the opposite. A ray from the observer's eye passing through a chosen pixel on the screen intersects both front-faced and back-faced surfaces. The method is capable of handling shadow and light volumes. The system of US 5,729,672 is implemented as a parallel processing engine. The technique described in US 5,729,672 has several disadvantages, least of which include the following: 1. The necessity to represent each object including light and shadow volumes as a set of convex objects. 2. Calculating depth values for both front-faced and back-faced surfaces. 3. Sorting surfaces of each object into two sets of front-faced and back- faced surfaces. 4. Slow performance. Thus, a solution is needed which overcomes the deficiencies in the prior art. SUMMARY OF THE INVENTION Among other things, the present solution is an improved ray tracing/rendering engine which is approximately five times faster than the prior art devices thereby overcoming many, if not all, of the aforementioned problems of the prior art. Therefore in accordance with one aspect of the present solution there is provided in an apparatus for facilitating rendering of a three dimensional image on an image plane for display on a display medium; the image plane having a plurality of pixels; a method comprising the steps of: (a) providing a list of surfaces defining the image; (b) subdividing the image plane into a plurality of tiles; (c) associating with a tile one or more surface(s) contained at least partially within the tile; and (d) for each pixel of a tile; (i). projecting a ray into the image; (ii). determining a ray/surface intersection with the one or more surfaces; (iii). generating a surface depth value for each of the one or more surfaces in dependence on the distance of that surface from the image plane; (iv). determining whether any surface is visible at that pixel; and (v). determining color attributes of that pixel accounting for shadows and light based on the results of the determination in the preceding step. In accordance with second aspect of the present solution, during certain successive clock cycles of the above apparatus, pixel data is processed by simultaneously incrementing tile column and row. In accordance with third aspect of the present solution there is provided an apparatus for facilitating rendering of a three dimensional image from a list of surfaces defining the image; the rendering to occur on an image plane for display on a display medium; the image plane having a plurality of elementary areas; the apparatus comprising; a plurality of processing elements for determining depth values for ones of the surfaces in the image for each elementary area of the image plane in dependence on the distance of the one of the surfaces from the image plane; the plurality of processing elements arranged in columns and rows; the plurality of processing elements coupled together wherein data is transferred from some of the processing elements in a first of the columns to both adjacent processing elements in its column and its row and the data from the some of the remaining of the processing elements is transferred to the next adjacent processing element in its row. In accordance with fourth aspect of the present solution the apparatus is provided on a single integrated circuit. These and other aspects, features and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Referring briefly to the drawings, embodiments of the present invention will be described with reference to the accompanying drawings in which: Figure 1 illustrates a shadow or light volume in accordance with conventional techniques; Figure 2 illustrates an exemplary embodiment of a system in accordance with the teachings herein; Figures 3 A and 3B each illustrate different views of a projection on a view plane in accordance with the teachings herein; Figure 3C and 3D each illustrate a scan line interval associated with a projection on a view plane in accordance with the teachings herein; Figure 4A and 4B illustrate block diagrams of exemplary processing elements for evaluation of linear expressions in accordance with the teachings herein; Figure 5 illustrates a block diagram of a processing elements for evaluating a ray/surface intersection interval in accordance with the teachings herein; Figure 6 illustrates a block diagram of a processing elements for depth value storage and comparisons in accordance with the teachings herein; Figure 7 illustrates a block diagram of a pixel processing element in accordance with the teachings herein; Figure 8 demonstrates a sequence of pixel processing elements for processing pixels along a scan line/row of an image plane or a tile in accordance with the teachings herein; Figure 9 illustrates the y value for consecutive scan-lines of a tile in accordance with the teachings herein; Figure 10 illustrates a block diagram of an exemplary initializing processing element in accordance with the teachings herein; Figure 11 A illustrates a block diagram of a processor having a matrix of processing elements for processing a plurality of scan-lines in accordance with the teachings herein; Figure 1 IB is an exemplary timing sequence, which illustrates how the processor of Figure 11 processes a tile, clock cycle by clock cycle, in accordance with the teachings herein; Figure 12 illustrates a block diagram of an exemplary alternative initializing processing element in accordance with the teachings herein; Figure 13 illustrates a block diagram of another exemplary alternative embodiment of a processor having a matrix of pixel processing elements and including a plurality of initializing processing elements of Figure 12 in accordance with the teachings herein; Figure 14A and 14B each illustrate an exemplary tiles having associated therewith a corresponding matrix of pixel processing elements in accordance with the teachings herein; Figure 15 illustrates a block diagram of an exemplary alternative initializing processing element having FIFO memory buffers in accordance with the teachings herein; Figure 16 illustrates a block diagram of an exemplary alternative processing element for depth value storing and comparing in accordance with the teachings herein; Figure 17 illustrates a block diagram of an exemplary alternative processing element for calculating surface depth value of a pixel in accordance with the teachings herein; Figure 18 A illustrates a block diagram of still another exemplary alternative embodiment of a tile processor comprising a matrix of pixel processing elements in accordance with the teachings herein; Figure 18B is an exemplary timing sequence, which illustrates how the processor of Figure 18 processes a tile, clock cycle by clock cycle, in accordance with the teachings herein; DETAILED DESCRIPTION OF THE INVENTION Referring more specifically to the drawings, for illustrative purposes the present invention is embodied in the system configuration, method of operation and article of manufacture or product, generally shown in figures 1 - 31. it will be appreciated that the system, method of operation and article of manufacture may vary as to the details of its configuration and operation without departing from the basic concepts disclosed herein. The following description, which follows with reference to certain embodiments herein is, therefore, not to be taken in a limiting sense. In one embodiment of the present invention a ray-tracing-like technique for rendering three-dimensional scenes is employed. FIGURE 1 In one embodiment of the invention three-dimensional objects are represented by a plurality of surfaces. The present invention can handle arbitrary polygons and curved surfaces. In the following description, for simplicity of explanation, it will be considered that surfaces are approximated by planar triangles. Light and shadow volumes are approximated either by planar triangular surfaces or by parts of infinite planes limited by two or three mutually intersecting straight lines - open surfaces. Realistic light and shadow volumes are constructed around the surfaces 1 (Figure 1). For shadow volumes these surfaces produce shadows and for light volumes light spots. (Reference: James D. Foley and others, "Introduction to Computer Graphics", published by Addison-Wesley Publishing Corp. 1997, ρ.501-509). Boundary edges of surfaces 1 and rays emanating from source of the light S limit open side surfaces 2 and 3. These surfaces form shadow or light spot abcdeg when intersecting with arbitrary surface 4. The present invention utilizes only open side surfaces 2 and 3 for representing realistic light and shadow volumes. These surfaces has front-face (surfaces 2) or back-face (surfaces 3) attributes. Planar triangles with front-face or back- face attribute can also be utilized for representing artificial light and shadow volumes. A screen is comprised of a plurality of elementary areas (pixels). A screen is positioned between an observer and the scene. A ray is assumed to pass from the observer through an elementary area of the screen into the scene to be viewed and will intersect various surfaces, which represent objects and light and shadow volumes in the scene. Analysis of these intersections and their distances from the observer provides the possibility to determine the shading of visible surfaces. FIGURE 2 In Figure 2 shows an exemplary graphics processing system constructed in accordance with the teachings of the present invention for implementing certain aspects of the present solution. In a basic embodiment, the system comprises a plurality of interconnecting components, namely, a geometry processor 5, a memory unit 6, a ray-tracing unit 7, a texture shading unit 8 and a display medium. These functional elements could be implemented by suitably programming a conventional programmable graphics processing system. Alternatively, the functional elements could be provided as separate hardwired circuits. GEOMETRY PROCESSOR 5 Geometry processor 5 performs certain pre-processing activities on the object data, including but not limited to the following techniques, clipping, culling, transformations, shadow/light volume determination, subdivision, associating objects/surfaces with regions, etc. Geometry processor 5 transforms coordinates of all objects of the scene. Side surfaces of light and shadow volumes are constructed based on new coordinates of light sources and three-dimensional objects of the scene. Back-faced surfaces for opaque three-dimensional objects are culled (Reference James D. Foley and others, "Introduction to Computer Graphics", published by Addison-Wesley Publishing Corp. 1997, p.448-449, 459-465). For three-dimensional objects with transparent parts and also for shadow and light volumes special attributes are assigned to back and front faced surfaces. The screen/view plane is subdivided into a finite number of regions - tiles. Furthermore, each surface is associated with a tile in which it appears. Several techniques exist for associating surfaces with tiles. One efficient technique is disclosed in Applicants' co-pending application, entitled "Method, Apparatus, and Article of Manufacture For Associating Objects With Regions In Coordinate Space" and which is incorporated in its entirety herein. Only those surfaces associated with a given tile will be processed in each tile. What now follows is a brief description of the above method of associating objects with regions in which they appear. FIGURES 1 AND 2 - TRANSFORMATIONS Reference is now made to Figures 1 and 2, which illustrate region transformations into two-dimensional and three-dimensional space, respectively. Figure 1 illustrates a transformation of a region 2 into two- dimensional space creating a unit square 5. Figure 2 illustrates a transformation of a region 4 into three-dimensional space creating a unit square cube 6. The methods for determining coordinate transformation of arbitrary region into unit cube are well known in the art. For simplicity, the following sections are directed to manipulating objects in two-dimensional scene space in accordance with the teachings herein. However, it is clear to those skilled in the art that the present solution it is not limited thereby as the present solution can be naturally extended, by applying certain conventional modifications thereto, to process scenes in any n-dimensional space. FIGURE 3 - REGIONS AND OBJECTS Figure 3A illustrates a plurality of polygonal arbitrary shaped objects 10 and 12, which are at least partially located inside a region 14 in two- dimensional space with coordinate system XOY. Object 12 is only partially located inside region 14. Therefore, only the indicated hatched part of object 12 will be further considered. As shown in Figure 3B, region 14 is transformed into unit square 16. The same coordinate transformation is applied to objects 10 in region 14. Objects 10 (Figure 3 A) are transformed into objects 18 in unit square 16 and object 12 is transformed into object 17 in unit square 16. FIGURE 4 - MODE OF SUBDIVISION AND NAMING CONVENTION USED FOR ASSIGNING A NAME TO A REGION In order to more fully explain the unique mode of subdivision/naming convention of the present solution reference will now be made to several Figures, which graphically illustrate a unit square being progressively subdivided according to the teachings herein. A method of mathematically dividing the unit cube or square operative in the preferred embodiment of the present invention is demonstrated in the description provided herein below. Briefly speaking, a unit volume, here a square, is mathematically subdivided according to the following description. In one embodiment, the described mathematical mode of subdivision may be done conceptually and not necessarily physically. Each subdivision is associated with a "name". The name for a subdivision is constracted during each division step of the unit square or cube. Initially the unit square or cube is divided into two equal rectangles. The linear subspace in n-dimensional case corresponds to the straight-line segment in two-dimensions. The direction of this line segment is parallel to any one of the coordinate axes. An "empty" name is assigned to an initial unit cube or square. After division of the initial unit cube or square the nearest of the two resulting subdivisions to the coordinate origin is chosen. The name of rectangular subdivision 22 is constracted from the name of previous subdivision by adding the symbol zero (0) to the right hand side of the name of initial subdivision (Figure 4A). The name of rectangular subdivision 24 is constructed from the name of previous subdivision 20 by adding unit symbol (1) to the right hand side of the name of initial subdivision. The general procedure for constracting the name of arbitrary subdivision of unit cube is executed in the following steps: a) For initial rectangular subdivision name is empty (i.e. has no symbols). b) Dividing of subdivision results in appearance of two new rectangular subdivisions. For each new rectangular subdivision symbol 0 or 1 is added to the name on the right hand side. Symbol zero is added to the name of rectangular subdivision nearest to coordinate origin and 1 to the farthest. The names of the subdivisions are stored in memory for subsequent processing. To further illustrate the forgoing points, reference is now made to collectively to Figures 4A, 4B, 4C, 4D in which the results, including the naming convention, of progressively subdividing a unit square in two- dimensional space in accordance with the teachings herein are shown. As shown in Figure 4A, the initial area corresponding to the dimensions of a unit square 20 is assigned to EMPTY. Figure 4B, illustrates the results of subdividing the unit square 20 into two equal rectangular subdivision 22 and 24 wherein division line segment 26 is parallel to the y-axis. Rectangular subdivision 22 is closer to the coordinate origin than rectangular subdivision 24. Hence, in accordance with the above naming convention, a zero (0) is added to the right hand side of the name of rectangular subdivision 22 and a one (1) is added to the right hand side of the name of rectangular subdivision 24. Thus, rectangular subdivision 22 is named or coded 0 and rectangular subdivision 24 is named or coded 1. Figure 4C illustrates the results of further subdividing rectangular region 24 into two equal rectangular subdivisions 32 and 34 wherein division line segment 28 is parallel to the x-axis. Rectangular subdivision 32 is closer to the x-axis than rectangular subdivision 34. Hence, in accordance with the above naming convention, a zero (0) is added to the right hand side of rectangular subdivision 32 and a one (1) is added to the right hand side of rectangular subdivision 34. Thus, rectangular subdivision 32 is named 11 and rectangular subdivision 34 is named 10. Figure 4D illustrates the results of still further subdividing rectangular region 34 into two equal rectangular subdivisions 38 and 39 wherein division line segment 36 is parallel to the y-axis. Rectangular subdivision 38 is closer to the coordinate origin than rectangular subdivision 39. Hence, in accordance with the above naming convention, a zero (0) is added to the right hand side of the name of rectangular subdivision 38 and a one (1) is added to the right hand side of the name of rectangular subdivision 39. Thus, rectangular subdivision 38 is named 110 and rectangular subdivision 39 is named 111. The forgoing process is repeated until a predefined maximum number of subdivisions is reached. The number of symbols in the name defines the number of divisions. The names of all subdivision are stored in memory. FIGURE 5 - MINIMAL SUBDIVISION FOR A BOUNDING RECTANGLE Figures 5 A and 5B each illustrate a conventional bounding volume, namely a bounding rectangle, in accordance with the teachings herein. As is well known in the art, a bounding rectangle for an object is a rectangule in two-dimensional space, with sides parallel to the coordinate planes, that contains (or surrounds) the object. Other types of bounding volumes, e.g., bounding sphere, may also be used. Figure 5A illustrates a two-dimensional bounding rectangle 40 in unit square 20 surrounding an object 42. In Figure 5B there is shown two bounding rectangles abhe and abed contain part of the object 42. The boundary edges of bounding rectangles 40 (sides of rectangle 40 in Figure 5A), abhe and abed, are parallel to the coordinate axes. A minimal subdivision for a bounding rectangle is defined as a subdivision containing a diagonal segment of the bounding box, which cannot be further divided in accordance with the mode of subdivision described herein without intersecting the bounding box. That is, minimal subdivisions for a bounding box are defined as subdivisions, which contain the entire bounding box. In order to determine, whether subdivision contains bounding box it is enough to determine if subdivision contains diagonal segment of the bounding box. The minimal subdivision for bounding box is defined as the minimal among subdivisions, which contains the entire bounding box. Minimal subdivision is determined for diagonal segment of bounding box. Figures 5 A and 5B illustrate this point. In Figure 5 A bounding rectangle 40 encloses object 42. In Figure 5B bounding rectangles abed and abhe encloses certain parts of object 42. As shown in Figure 5A, left subdivision 44 of unit cube 20 contains object with bounding rectangle 40. Subdivision 44 contains diagonal segment 46 of bounding rectangle 40. Accordingly, in Figure 5A and 5B subdivision 44 contains entire bounding rectangle 40 of object 42. Subdivision 44 is minimal subdivision for bounding rectangle 40. The next division line 48 (Figure 5B) of subdivision 44 intersects with bounding rectangle 40. In Figure 5B side ae of the bounding rectangle abhe and side ad of the bounding rectangle abed coincide with division line 48 of the bounding rectangle 44. Both bounding rectangles abhe and abed are contained inside subdivision 52, which resulted from division of subdivision 44 by division line 48. Subdivision 52 is a minimal subdivision for bounding rectangle abed since the division line 50 of subdivision 52 intersects with bounding rectangle abed and its diagonal segment bd. Subdivision 52 is not minimal for bounding rectangle abhe since the division line 50 of subdivision 52 does not intersect with bounding rectangle abhe. FIGURE 6 - DETERMINING A MINIMAL SUBDIVISION USING DIAGONAL SEGMENT A minimal/smallest subdivision containing a bounding rectangle of an object is determined by processing the diagonal segment of the bounding rectangle in accordance with the teachings herein. Thus, the endpoints of the diagonal segment will be used to determine the name of the minimal subdivision containing the bounding box. Figure 6A and 6B illustrate a technique for determining a minimal subdivision for a line segment L (that is, a diagonal segment from an arbitrary bounding box) in normalized decimal two-dimensional space having as endpoints, endpoint 1 (xl, yl) and endpoint 2 (x2, y2) whose corresponding decimal values are endpoint 1 (0.55, 0.57) and endpoint 2 (0.69, 0.81) respectively. First, the coordinates of endpoint 1 (0.55, 0.57) and endpoint 2 (0.69, 0.81) are converted into binary strings or forms omitting the "decimal" point. (The term "decimal" point as used herein means the "." before the fractional part of the number). Thus, in this example, the coordinates of endpoint 1 (0.55, 0.57) are converted into endpoint 1 (100011000000, 100100010000) and the coordinates of endpoint 2 (0.69, 0.81) are converted into endpoint 2 (101100000000, 110011110000). Recall that the longest possible length of the name of a subdivision is determined by the size of the smallest subdivision, which in turn, is predefined according to the particular task. Next, an x-coordinate prefix and a y-coordinate prefix are determined. The vertical doted line in Figure 6 denotes this part. As shown, the equivalent initial part of the two binary strings for the two x-coordinates of the two endpoints is further defined as the x-coordinate prefix. The equivalent initial part of the two binary strings for the two y-coordinates of the two endpoints is further defined as the y-coordinate prefix. A name of a minimal subdivision is determined by combining the x- coordinate prefix and the y-coordinate prefix according to the following procedure. Specifically, if the x-coordinate prefix is empty then the name of minimal subdivision coincides with the name of initial subdivision, that is, EMPTY. Otherwise, the name of the minimal subdivision is constructed by copying in turn one symbol from the x-coordinate prefix and then one symbol from the y-coordinate prefix, repeating this process until there are no more binary symbols to copy in either of one of the x- or y-coordinate prefix. In this example, the binary name that is constracted is 110. The subdivision with name 110 is a minimal subdivision for the bounding rectangle having diagonal line segment L. In short, a subdivision is associated with one or more objects (and vice versa) by simply processing the diagonal segment of an object's bounding rectangle to determine the name of the minimal/smallest subdivision at least partially containing the bounding rectangle and storing this information in one or more data structures for subsequent processing. FIGURE 7 - CONSTRUCTING ARRAY 60 and 64 Figure 7 is an example of one or more practical data structures, which may be used in the present instance to store a minimum subdivision data and bounding rectangle data. ARRAY 60 After subdividing a region into a plurality of subdivisions, all subdivisions are stored in an array data structure, namely, an array of all subdivisions 60 ("array 60"). It is appreciated by those skilled in the art, however, that other types of data structures may also be used. The length of array 60, that is, the total number of elements in array 60, is based on a predefined size of the smallest subdivision. Generally, the smallest size of a subdivision is determined in accordance with the desired image quality or resolution. Typically, this occurs when the smallest size of a subdivision is an order of pixel size. However, the smallest subdivision may be defined according to the natural limitations of the task. For example, in certain instances the smallest predefined subdivision may be greater or less than a single pixel size. Accordingly, the length of the array(s) is equal to 2 * N - 1 , where N is maximum number of subdivisions of the smallest predefined size. ARRAY 64 Each element of array 60 references an array of bounding rectangles 64 (array 64). Each element 62 of array 64 references a bounding box, which is entirely contained in the subdivision. Array 60 is constructed in accordance with the following procedure. Each subdivision's array index is derived from its name. One technique for determining a given subdivision's array index follows, bearing in mind that what follows is merely exemplary as other techniques may also be used. First, the initial undivided area corresponding to the dimensions of a unit cube or square named/coded EMPTY is stored at index zero (0). For the two child subdivisions, which are created when a parent subdivision or the initial area is divided, the indices of these child subdivisions are determined as follows: For the child subdivision, which is nearest to the coordinate origin, its index is determined as follows: an offset equal to 1 is added to the index of the parent subdivision. For the remaining child subdivision, its index is determined as follows: an offset equal to the total number of possible subdivisions of the parent subdivision is added to the index of the parent subdivision. A second exemplary technique for determining a given subdivision's aπay index follows: First, the initial undivided area coπesponding to the dimensions of a unit cube or square named/coded EMPTY is stored at index zero (0). For the two child subdivisions, which are created when a parent subdivision or the initial area is divided, the indices of these child subdivisions are determined as follows: For the nearest to the coordinate origin subdivision resulted from division, offset 1 is added to the index of subdivision, which was divided. For the farthest subdivision resulted from division, offset, which is equal to the number of possible subdivisions in the nearest subdivision, is added to the index of subdivision, which was divided. FIGURE 8 - ARRAY 60 INDICES Figures 8A and 8B graphically illustrate the above two techniques. Figure 8A depicts the first technique. Figure 8B depicts the second technique. In both, aπay indices are derived from the names of the subdivisions shown in Figures 4A, 4B, 4C and 4D. In this example, the total number of possible subdivisions is set to eight. FIGURE 9 - PHYSICAL CONFIGURATION OF GRAPHICS PROCESSING SYSTEM 1 Several functional elements are included in an exemplary graphics processing system of the present solution. These functional elements could be implemented by suitably programming a conventional programmable graphics processing system. Alternatively, the functional elements could be provided as separate hardwired circuits. In any event and referring more specifically to Figure 9, there is shown an exemplary graphics processing system 1 constructed in accordance with the teachings of the present invention. In a basic embodiment, the system 1 comprises a plurality of interconnecting components, namely, a pre-processing unit 72, a processing unit 76, a memory unit 78, and an index-memory unit 76. Processing unit 76 further comprises a plurality of interconnecting subcomponents, namely, a determining bounding rectangle component 80, a minimal subdivision unit 82, and an associating objects with subdivisions unit 84, and a index-memory unit 86. Furthermore, there is included in system 1 an input bus 70 and an output bus 79. Pre-processing unit 72 receives object data comprising surfaces and performs certain preprocessing activities on the object data, such as transformations, culling, etc. Thereafter, pre-processed surface data is transmitted to processing unit 74 for further processing. Processing unit 74 receives the pre-processed data from pre-processing unit 72 and, together with memory unit 78 and index-memory unit 76, associates surfaces with subdivisions in accordance with the present solution. The specifics of each of the forgoing functional elements will become better understood with regard to the following description and accompanying drawings. INPUT BUS 70 Object data including associated surface data describing a scene in coordinate space is transfeπed via input bus 70 to preprocessing unit 72. PRE-PROCESSING UNIT 72 Pre-processing unit 72 defines a unit volume, (for example, square/cube in two/three-dimensional space, respectively) and transforms object data into normalized-coordinate data, and determines bounding volumes (in the present instance a bounding rectangles) for objects/surfaces/polygons or parts of these objects/surfaces/polygons comprising the scene according to conventional techniques. Next, preprocessing unit 72 transmits transformed object data and associated bounding rectangle data to processing unit 74 for subsequent processing. PROCESSING UNIT 74 Processing unit 74 associates objects with subdivisions by directly manipulating the bounding rectangles of the objects instead of the objects themselves. To perform these functions, processing unit 74 includes several interconnecting components, namely, processing bounding box unit 80, a minimal subdivision unit 82 ("Component 82"), an associating objects with subdivisions unit 84 ("Component 84"), and a stack-memory unit 86 ("Component 86"). 1. Component 80 Component 80 receives each bounding rectangle from unit 72 and determines which minimal subdivision to which it belongs. 2. Component 82 Next, Component 82 receives each bounding rectangle from unit 72 and determines which minimal subdivision to which it belongs. Specifically, Component 82 determines a minimal subdivision for each bounding box, that is, the smallest subdivision containing the bounding rectangle in accordance with the teachings herein. Recall that a minimal subdivision for a bounding rectangle is defined as a subdivision containing a diagonal segment of the bounding box, which cannot be further divided in accordance with the mode of subdivision described herein without intersecting the bounding box. In doing so, a diagonal of the cuπent bounding rectangle is calculated and the endpoints of bounding rectangle is used to determine the name of subdivision containing segment. After a minimal subdivision to which a bounding rectangle belongs is determined, the minimal subdivision for the cuπent bounding box, the bounding rectangle and the object itself are transfeπed to Component 84 for subsequent processing. 3. Component 84 Component 84 associates objects with subdivisions using bounding rectangle information. That is, for each subdivision, Component 84 determines all bounding boxes, which are contained entirely inside the instant subdivision. In performing this function, Component 84 constructs and stores object, subdivision and bounding rectangle information in one or more data structures for subsequent processing. Specifically, Component 84 constructs and stores . aπay 60 in index-memory unit 76 and constructs and stores the plurality of aπays 64 in memory unit 78. In a prefeπed embodiment of the present solution, processing unit 74 is capable of executing in parallel read/write operations from to memory unit 78 and index-memory unit 76. 4. Component 86 Component 86 receives from and transmits to Component 80 of unit 74 cuπent bounding box, object data and associated subdivision information for storage thereto during the operation of graphics processing system 1. INDEX-MEMORY UNIT 76 AND MEMORY UNIT 78 As was previously mentioned aπay 60 is stored in index-memory unit 76 and the plurality of aπays 64 are stored in memory unit 78. Processing unit 74 reads/writes from/to memory unit 78 and index-memory unit 76 in parallel. OUTPUT BUS 79 Finally, associated surface/subdivision information is transmitted via output bus 79 for further processing within the graphics pipeline. FIGURE 10 - PROCESSING ELEMENT 80 Because of the important role Component 80 plays herein, it is now desirable at this juncture to provide a detailed description of the same to facilitate the reader's overall comprehension of certain aspects of the present solution. Hence, Figure 10 illustrates an exemplary process flow diagram of Component 80 in accordance with the teachings herein. As is shown in Figure 10, a cuπent bounding rectangle together with its object data is fed to block 90. Block 90 activates component 82 for determining a minimal subdivision for the cuπent bounding rectangle. Next, execution passes to control block 92. At control block 92, depending on a particular defined task, one of two distinct paths process flow/execution is performed. Namely, execution either passes to block 94 or to block 96. Block 94 activates Component 84 for associating objects with subdivisions in accordance with the teachings herein. At block 96 the cuπent object is broken up into parts and bounding rectangles for these parts are determined. These parts are considered as new objects and pushed to stack-memory (i.e., Component 86) together with their bounding rectangles. The first object in the stack-memory and its bounding rectangle data is set as the cuπent object, popped from stack and transmitted for subsequent processmg to block 90. The remaining objects and their bounding rectangles are stored in stack-memory. Finally, after all objects/object parts have been processed (that is, associated with subdivisions), execution passes to terminating block 98. At block 98, if the stack-memory is empty, then processing unit 74 finishes processing the cuπent object and its bounding rectangle data. Otherwise, block 98 pops, one by one, all object and bounding rectangle data that was previously pushed to (stored in) stack memory, from stack-memory and transmits each in turn to the block 90 for further processing. Reference will now return to the exemplary graphics processing system utilizing a ray-tracing-like method. MEMORY UNIT 6 - 3D DATABASE Memory unit 6 includes a database for storing three-dimensional image data including object/surface/polygon and other related geometric information comprising a three-dimensional image to be projected onto a display medium. Stored object information can include location, attributes (such as radius for spheres), color, and optional texture map of each object. Other stored surface/polygon information include the following: RAY TRACING UNIT 7 In accordance with the teachings herein, ray-tracing unit 7 traces the path of light/projection rays from each pixel position in a given tile to integrate the tasks of shading, shadow generation, hidden surface removal, projection and scan conversion into a single computational process. SOLVE FOR D Ray tracing unit 7 determines ray/surface intersections for each pixel. If an object/surface is represented by a set of convex polygons one approach for testing a ray individually against each polygon follows: Obtain an equation for the plane containing the polygon; Check for an intersection between this plane and the ray; Check that this intersection is contained by the polygon. For example, if the equation describing a plane containing a surface/polygon is: Ax + By + Cz + D = 0; for a pixel (x,y) on an image plane/screen the distance/depth from a ray/surface/polygon intersection point to the image plane can be determined by solving the following equation for D D = A* x + B* y + C (1) where A, B and C are constant coefficients of the plane equation; and x and y are the coordinates of pixel(x, y) on the image plane. Figures 3 A and 3B illustrates this point further. Figure 3 A and 3 B show different views of a screen/image plane 12 including a triangle projection 10 thereon. Lines 14, 16 and 18 make up the sides/edges/boundaries of triangle projection 10. SOLVE FOR XI , X2 and X3 Mathematically, the x coordinate of the points of intersection of lines 14, 16 and 18 may be described according to the following equations: XI = al* y + bl (2) X2 = a2* y + b2 (3) X3 = a3* y + b3 (4) where al, bl, a2, b2, a3, b3 are constant coefficients of lines 14, 15 and 16 respectively; and y is the y coordinate of the point of intersection of lines 14, 16 and 18 respectively. Together the above equations (2), (3) and (4) for a surface/polygon projection on an image plane, here a triangle, determine, whether the projection ray passing through the point (x, y) intersects with this projection. Depth value D for the point of intersection (x, y) is calculated from equation (1). SOLVE FOR S 1 , S2 AND S3 Three boolean values si, s2 and s3 determine, on which side of the lines 14, 16 and 18 in the direction of x-axis projection 10 of triangle is located. In Figure 3B triangle 10 is located on the right hand side of the line 18 and on the left hand side of the lines 14 and 16 in the direction of x-axis. The same structure is associated with shadow and light open surfaces. Points xl , . . . , xi, xi+1 , ... , xm along a y-scan line on the screen have the same y coordinate and are positioned equidistant r from each other. Thus, the depth value Di+1 for the triangle/surface plane in an arbitrary point (xi+1 , y) can be determined using the depth value Di for the triangle/surface plane in point (xi, y) using the following recursive expression: Di+1 = A*(xi+l) + B* y + C (replaced (xi+1) with (xi) + r) = A * ((xi) + r) + B* y + C = A* xi + B* y + C + A* r = Di + A* r (5) (replaced A*xi + B* Y + C with Di) where r is some power of 2 herein. FIGURE 3C - OPAQUE/TRANSPARENT SURFACES Lines 14, 16 and 18 determine the boundaries/edges of the polygon/triangle/object. Thus, only need process the set of x coordinates lying within the boundaries of the polygon/surface/triangle. For each horizontal scan line y = yl all points of this line belonging to the projection of triangle are located inside the boundaries of segment - interval. Figure 3C/D, illustrates an Interval {xb, xe} 20 along a given horizontal scan line y. Specifically, Interval {xb, xe} 20 conesponds to the interior pixels along a horizontal scan line y passing through a polygon area in which xb and xe are the rightmost and leftmost x-coordinate pixel intersection positions with the polygon's boundaries. That is, xb and xe are the two beginning and ending pixel intersection positions with the polygon' s boundaries which define the stretch of interior pixels from xb to xe. For each horizontal scan line y of interest, the values for xb and xe (and thus, Interval {xb, xe}) are determined as follows: 1) Determine the x coordinates of points of intersections of lines 14, 16, 18 with scan line yl using the following equations and store the results in variables XI , X2 and X3 : XI : = al* yl + bl; (2) X2 : = a2* yl + b2; (3) X3 : = a3* yl + b3; (4) 2) Choose the lines (16 and 18), for which projection of triangle is located on the left hand side. 3) Choose their x coordinates of intersection with the line y = y 1 (X2 and X3). 4) Determine the minimal of these coordinates Xmin (Xmin : = X2). 5) Choose the line (14), for which projection of triangle is located on the right hand side. 6) Choose their x coordinates of intersection with the line y = yl (XI). 7) Determine maximal of these coordinates Xmax (Xmax : = XI). 8) If Xmax is less than Xmin then xb : = Xmax; xe : = Xmin; else Interval is empty. FIGURE 3D - SHADOW/LIGHT SURFACES The aforementioned procedure is also used for determining the intervals for shadow and light open side surfaces. Reference is now made to Figure 3D, which illustrates a projection QUVW of a shadow or light surface on a screen 12. Segment UV and rays UQ and VW limit projection of shadow or light open surface in Figure 3D. Generally, an image on a view plane is constructed by scanning the image plane in a raster type fashion. Thus for any particular surface, after the starting depth has been calculated using Equation 1 above, the depth at each pixel can be calculated by incrementing by A as we traverse in a horizontal direction in the image plane, and by B as we traverse in the vertical direction. Several possible architectures of the overall ray tracing unit 7, which can process opaque, transparent, shadow and light objects is described below with reference to Figures 8, 11, 13 and 18. Specifically, Figures 8, 11, 13 and 18 each illustrate an alternative embodiment of an exemplary system in accordance with the present solution. Before describing the overall system, what follows are descriptions of certain processing elements, which form part of the embodiments illustrated in the various Figures. FIGURE 4A: PROCESSING ELEMENT 30: D = A* x+ B * y + C. Figures 4A and 4B illustrate schematic diagrams of exemplary processing element 30 for evaluating the expression D = A* x+ B* y + C. As shown in Figure 4A, processing element 30 further comprises processing elements 32 and 34. Each of elements 32 and 34 includes an adder + and a multiplier *. Element 32 receives as input x, A, C, processes the input and outputs the value for the expression A*x+C to Element 34. Element 34, in turn, receives as input y, B and the output of element 32, that is, A*x+C, processes its inputs and outputs D. FIGURE 4B: PROCESSING ELEMENT 34: Di+1 = Di + A* r Figure 4B illustrates a schematic diagram of an exemplary processing element 36 for evaluating the expression Di+1 = Di + A* r wherein r is a predefined constant value equal to some power of 2. As shown, element 36 comprises a shift register 38 SH (for evaluating the expression A*r) and an Adder +. Element 36 takes as input A and Di, processes the input, and thereafter outputs the value for Di+ 1. FIGURE 5: Processing Element 40: Interval {x b eginnin . Xend} Figure 5 illustrates a schematic diagram of several exemplary processing elements, that is, processing elements 32 and 40, which can be used for evaluating Interval {xb, xe} according to the teachings herein. As shown, three processing elements 32 are used to process Equations (2), (3) and (4) for XI , X2 and X3. Recall that XI : = al* yl + bl; (2) X2 : = a2* yl + b2; (3) X3 : = a3* yl + b3; (4) The values of XI, X2 and X3 are fed to processing element 40, which in turn, determines the Interval {xb, xe} . Processing element 40 includes processing elements 42, 44, 48 and 46. Processing element 42 selects the x-coordinates of points of intersection with lines, which are located on the left hand side of projection of triangle. In this example, element 42 has only two outputs because an arbitrary straight line can only intersect a triangle's boundaries/edge in two positions. This output is then fed to processing element 46, which determines the largest of the two output values. This value is set as the boundary point xe of the Interval {xb, xe}. Processing element 44 selects the x-coordinates of the points of intersection with lines, which are located on the right hand side of projection of triangle. Like element 46, element 44 has only two outputs because an arbitrary straight line can only intersect a triangle's boundaries/edge in two positions. This output is then fed to processing sub-element 48, which determines the smallest of the two output values. This value is set as the boundary point xb of the Interval {xb, xe}. Both elements 42 and 44 process the values of si, s2 and s3 to determine the position of a triangle's projection relative to the boundary lines 14, 16, and 18. MODIFICATION OF PROCESSING ELEMENT 40 TO ACCOUNT FOR POLYGONS OF VARIOUS SHAPES To process surfaces which are represented as arbitrary flat convex polygons certain modifications to processing element 40 must be made. A modified processing element 40 calculates the interval by utilizing the number of points of intersection equal to the number of edges in the polygon. Additional information about edges of polygon will also appear in structures coπesponding to surfaces of objects of scene. The surface structure for triangle must be expanded by adding pairs of coefficients for equations of straight lines coπesponding to the additional edges of polygon and boolean values s4, ... , sn defining relative position of projection. Finally, screen coordinates of interval {xb, xe} are transformed to tile coordinates {Xb, Xe} in order to reduce the number of bits in coordinate representation. FIGURE 6 - PROCESSING ELEMENT 50 - SORT SURFACE INTERSECTIONS POINTS USING D Figure 6 illustrates a schematic diagram of an exemplary processing element, that is, processing element 50, which can be used for depth value storage and comparisons according to the teachings herein. Processing element 50 includes several processing elements, namely COMP 54, AND 56 and CONTROL 58 and several registers, that is, register REGl and register REG2. Processing element 50 take as input certain surface/polygon/triangle information/data, that is, I, D and N, processes the inputs in accordance with the teachings herein. Input data includes, I, D and N. I is TRUE when the cuπent elementary area (pixel) is inside the cuπent processed surface's projection and FALSE otherwise. D is the depth value of the cuπent processed surface's in the cuπent pixel or elementary area and N contains certain information about the cuπent processed surface. N is a data structure/record comprising two fields. The first field stores information about a particular surface, for example, certain surface attributes. The second field stores an operation code, which is used by the processing element to process a surface. For example, different types of surfaces may require different procedures to generate the final pixel image on the screen. Moreover, depth values of opaque, transparent, shadow and light surfaces are not processed in the same way when generating pixel color. In short, the operation code controls the proper use of the depth value D. The COMP element compares depth values of a first surface and a second surface and in dependence on the comparisons with the cuπent value stored in REGl and whether the new surface and the stored surface are forward or reverse, may update the value stored in REGl and REGl . If REGl is updated then REG2 which stores surface attributes will also be updated. Registers REGl and REG2 can be enabled or disabled for write access. REGl and REG2 store the values of D and N. For opaque triangles/polygons, register REGl stores the depth value D of the triangle/polygon nearest to the screen and register REG2 stores the identifying information N coπesponding to this triangle/polygon. For example, a new depth value D is compared in comparator 54 with the depth value D already stored in register REGl . If the new depth value is less than the depth value stored in register REGl and I is TRUE, then the output value of sub-element 56 is TRUE. This value is then fed to sub-element CONTROL 58, which in turn, enables data to be written into registers REGl and REG2. The new depth value D is stored in REGl and is associated identifying surface information N is stored in REG2. For other types of surfaces processing element stores identifying and intermediate data about surface in REG2 This data depends on the depth value of surface. Final pixel information is sent via output bus OUT to texture shading unit 8 for further processing. FIGURE 7 - PIXEL PROCESSING ELEMENT/CELL 60 Figure 7 illustrates a schematic diagram of an exemplary processing element, that is, processing element/cell 60, which can be used for processing depth value for each pixel (x, y) of an image plane. Processing element 60 includes aforementioned processing elements 36, 50, several new processing elements 62 and 64, and several registers, that is, registers 66, which store the cuπent values of A, D, N, Xb, I and Xe. Each pixel of a tile would have a associated therewith a processing element 60. Each processor 60 has a number NUM associated therewith coπesponding to its position along a scan line. Thus, the processor 60 associated with pixel 1 would be assigned NUM=1, processor 5 associated with pixel 5 would be assigned NUM=5, etc. Data representing A, D, N, Xb, I, Xe are fed to their coπesponding registers 66 (A, D, N, Xb, I, Xe) for subsequent processing. As previously mentioned, input values A and D are fed to sub-element 36 where the expression Di + A* r is evaluated. Input values Xb and Xe are fed to sub-elements 62, 64, where together with the AND gate the boolean value of I is determined. As mentioned before, processing element 50 takes as input D, N and I for depth value storage and comparisons according to the teachings herein. Elements 62 and 64 compare the input values Xb and Xe with NUM. If NUM belongs to the Interval {Xb, Xe} then I is TRUE otherwise I is FALSE. I is equal to TRUE when the cuπent elementary area (pixel) is inside the surface projection otherwise it is FALSE. The values for Xb and Xe are the same (constant, not changing) for the same scan-line. Given a pixel processing element 60 designated as NUM, input signal I, which is passed to processing element 50, is determined by pixel processing element 60 designated as NUM-1. Output signal I, is passed to the next pixel processing element 60 in sequence, that is, the pixel processing element 60 designated as NUM +1. FIGURE 8 - SINGLE SCAN LINE PROCESSING Figure 8 illustrates a schematic diagram of an exemplary processing element 85 which can be used for parallel processing of pixels along a scan line. Processing element 85 includes a processing element 70 and a processing element 80. Processing element 70 includes a plurality of processing elements LI, L2, ... , Lm, designated individually as numeral 60, aπanged in pipeline fashion. Processing element 80 includes several aforementioned processing elements, namely processing elements 30, 32 and 36 and new processing elements 40 and 82. Processing element 80 acquires as an input information about the cuπent processed surface/triangle/polygon and the coordinates (xl,yl) of the initial pixel of the scan-line yl (that is, xl, yl, A, C, B, N, al, bl, si, a2, b2, s2, a3, b3, s3). Certain information is fed to processing element 30, namely xl , yl , A, C, yl and B for determining a depth value D for the plane of surface in the initial point. Specifically, processing elements 32 and 34 together calculate D as was mentioned above. That is, element 32 1 calculates all points of intersection, if any, of horizontal scan-line y = yl with all straight lines forming projection of surface. Element 34 has been previously described with reference to Figure 4A. Certain of the remaining input data, that is, al, bl, yl, a2, b2, yl and a3, b3, yl, is fed to elements 32 2 , 32 3 and 32 4 for calculating all points of intersection, if any, with horizontal scan-line y = yl with all straight lines forming projection of surface as was mentioned above. The out of elements XI, X2 and X3 is fed, together with si, s2 and s3, to element 84 for subsequent processing. Element 84 includes elements 40 and 82. Element 84 determines the coordinates of interval and boolean value I determining if initial point belongs to this interval. Element 40 receives as input XI, X2, X3, si, s2 and s3 and determines the values for xb and xe. These values are then fed to Element 82 where they are transformed into tile coordinates Xb and Xe. In addition, element 82 also determines if the initial point (xl,yl) belongs to the Interval {xe, xb} and sets the appropriate boolean value for I. Element 80 then feeds its output, that is A, D, N, Xb, Xe and I, to Element 70 for further processing. Element 70 determines depth values D for each pixel along a scan line, here scan line yl . As mentioned above, element 70 comprises several cascading processing elements 60, that is, LI, L2, ... , Lm. The total number of processing elements 60 will equal the number of pixels along one row of a tile. Thus, for example, if a tile is 32 pixel wide there will be 32 processing elements 60, that is LI ...L32, cascaded together. Each processing element 60 calculates and stores the depth value D of the nearest triangle/surface/polygon and stores the surface identifying information N for its associated pixel. Thus processing element LI calculates pixel information for pixel xl,yl . Processing element Li, will calculate pixel information for pixel xi, yl and so on. Thus, referring to Figure 3B, depth values in points xl, . . . , xi, xi+1, ... , xm are simultaneously calculated in elements LI, ... ,Li, Li+1, ... ,Lm. Final pixel information is sent via output bus OUT to texture shading unit 8 for further processing. FIGURE 9 What now follows is a description of one exemplary technique of simultaneously processing a plurality of horizontal scan lines of a tile - that is scan line by scan line in the y direction. A plurality of processing elements 85 of Figure 8 can simultaneously process a plurality of scan lines. Certain initializing operations are common for all sequences and can be executed only once for all sequences. All initial values ofx in Equation (1), that is, D = A* x + B* y + C, which is calculated, are equal/the same for all processed scan-lines. Therefore, the reduced expression of Equation (5), that is, A* x + C, which is calculated in element 32, is also common for all sequences. As shown in Figure 9, for each consecutive scan-line j of a tile, its coπesponding y value may be determined as follows: y = yl + 0 * - l)* r where r = 1. FIGURE 10 Figure 10 illustrates a schematic diagram of an exemplary processing element 87, which modifies the embodiment of Figure 8 to further provide for parallel processing of scan lines. As shown, element 87 includes a modified processing element 30 1 . Processing element 30 1 also includes processing elements 36, 34 and register J-l. Register j-l stores the number of the cuπent scan-line minus 1. Inputs, A, the expression A*x+C , yl and B are fed to processing element 30 i where yl is received by processing element 36 and the remaining data received by processing element 34. Element 36 reads the value stored in register j-l, evaluates the expression y = yl + (j - 1)* r and sends the result, that is, the value of y, to elements 34, 32 2 , 33 3 , 33 4 for further processing as previously mentioned The present solution takes advantage of various coherence properties of a scene that is to be displayed. Coherence means that the properties of one part of a scene are related in some way to other parts of the scene so that the relationship can be used to reduce processing. Coherence methods often involve incremental calculations applied along a single scan line or between successive scan lines. An obvious parallel implementation of this algorithm is to assign each scan line crossing the polygon area to a separate pixel processing unit. What now follows is a description of how a tile is processed in accordance with the present solution. FIGURE 11 Figure 11 illustrates a schematic block diagram of an exemplary processor 1 for processing a kXm tile in accordance with the teachings herein. As shown, there are k sequences 100 of m + 1 processing elements. Figure 7 illustrates in more detail the plurality of processing elements 60 designated with ILL.kLl to ILm to kLm. Figure 10 illustrates in more detail the plurality of processing elements 90 designated lL0..kL0. Figure 11 illustrates in more detail initializing processing element 32. Thus, for each pixel of a tile having k*m pixels, matrix 101 simultaneously determines the depth value of the nearest triangle/surface/polygon. Upon conclusion of the forgoing process, final pixel information is sent via output bus OUT to texture shading unit 8 for further processing. Figure 1 IB is an exemplary timing sequence, which illustrates how the processor 1 of Figure 11 processes a tile, clock cycle by clock cycle, in accordance with the teachings herein. Here, there is demonstrated how planes coπesponding to surfaces/triangles are processed during four successive clock cycles of processor 1 of Figure 11. The numbers in the rectangles coπespond to the number of the plane, which is cuπently processed by processor 1. The pixels on the screen/view plane, the coordinate points on the planes and the pixel processing elements/cells 60 in processor 1 are in a one-to-one relationship with each other. During the first cycle, processor 1 processes fours pixel of the first plane. During the second cycle, processor 1 processes fours pixel of second plane and four pixels of the first plane. During the third cycle, processor 1 processes four pixels of the third plane, four pixels of the second plane and four pixels of the first plane. During the fourth cycle, processor 1 l processes s four pixels of the fourth plane, four pixels of the third plane, four pixels of the second plane and four pixels of the first plane. What now follows is an alternative embodiment of the present invention/solution, which seeks to further improve the performance of processing element 90 illustrated in Figures 10 and 11. FIGURE 12 Figure 12 illustrates a schematic block diagram of such an improved processing element 90, designated as numeral 110. As shown, processing element 110 replaces the four multipliers of processing element 90 with four adders in order to reduce processing time - multipliers use more processor time than adders. FIGURE 13 Figure 13 illustrates a schematic block diagram of an alternative embodiment of a processor 1 including a plurality of aforementioned processing elements 110 for processing a kXm tile in accordance with the teachings herein. As shown, k processing elements 110 (one for each scan line) are coupled together to form an initializing sequence 114, which receives data for a processing element 112. Element 112 performs certain pre-processing functions using processing elements 30, 32 l9 32 2 , and 33 3 and sends the results to sequence 114 for subsequent processing. Specifically, element 30 evaluates the expression (1), that is, D = A* x + B* y + C, for point (xl,yl) to determine the depth value of the nearest surface/triangle/polygon in point (xl, yl). Elements 30, 32 1} 32 2 , and 33 3 evaluate the various expressions (2),(3) and (4) (that is, x = al * yl + bl ; x = a2* yl + b2; and x = a3* yl + b3, respectively) to determine the x- coordinates of the points of intersection of scan-line y = yl with the cuπent/nearest surface/triangle/polygon's boundary lines/edges (e.g., Lines 14, 16, 18 of Figures 3 A and 3B). Finally, N comprises identifying information about the nearest surface/polygon/triangle. The results, initial data D, N, XI, X2, X3, si, s2 and s3 is fed to initializing sequence 114. Sequence 114 processes this initial data/information and thereafter, unlike the parallel configuration illustrated in Figure 11, serially loads the processed initial data into each l..k sequence 70 of processing elements 60. Finally, final pixel information is sent via output bus OUT to the next component, e.g. texture shading unit 8, for further processing. What now follows is a description of alternative embodiments of the present invention for processing tiles of both fixed and variable size. FIGURE 16: Modification of Element 50 of Figure 6 - Depth Sorting and Storage Figure 16 illustrates an alternative embodiment of the processing element 50 of Figure 6, designated as processing element 50 , for depth sorting and storage. As shown, processing element 50 1 further includes three multiplexors, Mi, M 2 and M 3 , and an input bus IN. Multiplexor M directs intermediate depth values either to registers REGl for the first NUM -1 polygons, or to in internal memory for polygon number NUM. Multiplexor M 2 and Multiplexor M 3 are used for data transfer, via input bus IN, from the internal memory into registers REGl and REG2. Input bus IN and output bus OUT saves and restores registers REGl and REG2 in an internal memory unit 3 (not shown). In one embodiment of the present invention, the internal memory unit 3 includes two ports, one for read access and the other for write access. The ports may be accessed simultaneously. In an alternative embodiment of the present invention, the internal memory unit 3 has only one port for access via one bus. Unlike processing element 50 of Figure 6, data, which was previously stored in registers REGl and REG2 during a CPU cycle, is now stored/saved in the internal memory unit 3. The data from the internal memory unit is restored in registers REGl and REG2. Control element 122 performs additional functions, such as controlling read and write operations to external memory units. In the description provided herein above the size of FIFO buffer depends on the number of surfaces processed in cuπent tile. In order to avoid this disadvantage the following improvement to the system is introduced. Intermediate data in registers REGl and REG2 is stored in internal memory. FIGURE 17 - Modification of Element 60 of Figure 7 Figure 17 illustrates an alternative embodiment of the processing element 60 of Figure 7, designated as processing element 60 1 . As shown, processing element 60 ' includes element 50 ' . FIGURE 15 - Modification of Element 110 of Figure 12 Figure 15 illustrates an alternative embodiment of the processing element 110 of Figure 12, designated as processing element 110 1 . As shown, element 110 1 includes a plurality of multiplexers, Mi, Ml ...M13, a plurality of FIFO buffers, FI ...FI 3, a plurality of shift registers, SHI ...SH5, a control element 121, and three additional adders, ADD 1... ADD3. As shown, each of A, B, D, N, al, XI, a2, X2, a3, X3, si, s2, and s3 input values have associated therewith a FIFO buffer F and a multiplexer M. Control element 121 controls the operation of the FIFO buffers and multiplexors. Control element 121 initializes the various multiplexors Ml...M13 in accordance with the type of operation that is stored in the operation code field of N. The number of words in each FIFO buffer of element 110 1 is equal to the length of a sequence 70 1 of matrix processor 126 1 . The shift registers SHI ... SH5 sets an input value/variable to 0, multiplies an input value/variable by a power of #, (here # equals two) or sets the sign (+ or -) of an output variable/value. Together, the shift registers SHI ...SH5, the adders Al ... A4, and/or the multiplexors are used in processing the data in accordance with the teachings herein. For example, two Sh elements/registers and one adder "+" are used for determining each of XI , X2 and X3 and two Sh elements/registers, one adder "+", and multiplexor Mi are used for determining D. FIGURE 18 - Modification of System of Figure 13 Figure 18 illustrates an alternative embodiment of the processor 1 of Figure 13, designated generally as numeral 1 ', for processing a tile of both fixed and arbitrary size in accordance with the teachings herein. As shown, processor 1 l includes processing elements 50 1 , 60 1 , and 110 1 of Figures 15, 16 and 17, respectively. Moreover, processor 1 ' further includes a plurality of interconnected processing elements, namely, memory controller 130, processing element 112, initializing sequence 114 1 having a plurality of processing elements 110 1 , a matrix 126 1 of kxm processing elements 60 aπanged in m processing sequences 70 1 , and 1..m MEMORY units. Memory controller 130 receives initial scene data from memory unit 6 and sends this initial data to initializing sequence 114 ' via processing element 112. Processing element 112 performs certain pre-processing functions using processing elements 30, 32ι, 32 2 , and 33 3 and sends the results to initializing sequence 114 1 for subsequent processing. Initializing sequence 114 1 receives the initial data, processes the initial data and transmits the processed data to matrix 126 1 , wherein each column 1..m of processing elements is connected via one or more internal input and output buses to an internal memory unit MEMORY. The maximum memory size of all internal memory units MEMORY 1..m equals the maximum tile size, that is, it is equal in bytes to the size of the two internal registers REGl and REG2 multiplied by two. Each row sequence 70 1 of matrix 126 1 processes surface data along a scan/tile line in successive cycles. Specifically, save and restore operations to and from an internal memory unit MEMORY i are executed in one processing element jLi in a column i during one cycle. Each internal memory unit MEMORY1...m includes two equal switching banks (not shown), which connect in turn to either an internal input bus (not shown), an internal output bus (not shown) or to an external output bus OUT. For each pixel of a tile, visible surfaces attributes including their associated parameters of shading are transmitted via the output bus OUT to an texture shading unit 8 for subsequent processing. Figure 18B is an exemplary timing sequence, which illustrates how the processor 1 ' of Figure 11 processes a tile, clock cycle by clock cycle, in accordance with the teachings herein. Here, there is demonstrated how planes coπesponding to surfaces/triangles are processed during four successive clock cycles of processor l 1 of Figure 18. The numbers in the rectangles coπespond to the number of the plane, which is cuπently processed by processor 1 l . The pixels on the screen/view plane, the coordinate points on the planes and the pixel processing elements/cells 60 in processor 1 ! are in a one-to-one relationship with each other. During the first cycle, processor 1 ' processes one pixel of the first plane. During the second cycle, processor 1 ' processes one pixel of second plane and two pixels of the first plane. During the third cycle, processor 1 ' processes one pixel of third plane and two pixels of the second plane and three pixels of first plane. During the fourth cycle, processor 1 ' processes one pixel of fourth plane and two pixels of the third plane three pixels of the second plane and four pixels of the first plane, and continuing on in an reiterative process. FIGURE 14A - APPLICATION Figure 14A is a conceptual depiction of how an exemplary embodiment of the tile processor 1 ! of Figure 18 having a fixed size (here, 4x4) processes a tile 116 having the same fixed size as the tile 116 in accordance with the teachings herein. As shown, each processor element 60 of processor 1 ! is associated with a pixel in the 4x4 tile 116. Sequences tl , t2, t3 and t4, coπesponding to the sequences 70 1 of processor l 1 , processes scan lines 1, 2, 3 and 4, respectively, of tile 116. Pixels (1,1), (1,2), (1,3), (1,4) of tile 116 supply initial surface/polygon/triangle data to initializing elements 110 1 of initializing sequence 114 1 , i.e., II, 12, 13 and 14 (not shown). Each of II, 12, 13 and 14 further transfers processed initial data to a coπesponding sequence 70 1 , i.e., tl, t2, t3 and t4, for subsequent processing. FIGURE 14B - APPLICATION Figure 14B is a conceptual depiction of how an exemplary embodiment of the tile processor 1 l of Figure 18 having a fixed size processes a tile 119 having variable size in accordance with the teachings herein. In this example, the size of the tile to be processed is larger than the tile processor 1 '. That is, here the dimensions of the tile processor 1 ' are 4x4 while the dimensions of the tile 119 to be processed is 16x16. It is appreciated that tile sizes smaller than the tile processor are contemplated as falling within the scope of the present solution. In the section that follows is a brief overview of an exemplary way processor 1 l processes the scan-lines of tile 119 in accordance with the present teachings. In a following section is a more detailed description. The entire plurality of polygons/triangles associated with cuπent tile is subdivided into sets each one containing NUM polygons. It is clear that the last set may contain lesser than NUM polygons/triangles. This fact will be ignored in the following description as soon as it is unimportant. The maximal value of NUM is determined by the size of F FIFO buffer in processing element 120 (Figure 15). Functioning of element 120 will be described later. 1) Tile processor 116 processes the first NUM polygons/triangles for scan-lines 1 and 5. Pixels in scan-lines are processed with sequences tl,t4 and t2,t3 as is demonstrated in Fig 14B. 2) scan-lines 2 and 6 are processed with sequences tl,t4 and t2,t3, 3) scan-lines 3 and 7 are processed with sequences tl,t4 and t2,t3, 4) scan-lines 4 and 8 are processed with sequences tl ,t4 and t2,t3; 5) The tile processor finishes to determine depth values for the set of NUM polygons/triangles. These depth values are determined for all pixels of tile 119. Thereafter, another set of NUM polygons is supplied to tile processor and scan-lines are the entire process is repeated. What now follows is a more detailed description of the forgoing order of execution. Processing of Scan Line 1 and 5 Pixels (1,1), (1,5), (5,5), (5,1) of tile 119 supply initial surface/polygon/triangle data to initializing elements 110 1 of initializing sequence 114 1 , i.e., II, 12, 13 and 14 (not shown in figure 14B). Each of II, 12, 13 and 14 further transfers processed initial data to an associated sequence 70 1 , i.e., tl, t2, t3 and t4, for subsequent processing. During the processing of scan lines 1 and 5 of tile 119, all multiplexors Ml ...m of each initializer II , 12, 13 and 14, receive input data directly from the register to which its coupled to. For example, as illustrated in Figure 15, element 121 would instruct/signal multiplexor Ml to receive input data representing the constant value A. Multiplexor Ml would then select/open/switch to the appropriate input port for receipt of A. Here register A is coupled to multiplexor Ml via its right input port. Accordingly, multiplexor Ml selects/opens its right input port. Processing of tl - Scan line 1 Initializer II receives input data from the input registers coupled to it, processes and transfers initial pixel (1,1) data in accordance with the teachings herein. That is, initializer II simultaneously performs the following functions: 1) it transfers the initial data it receives to initializer 12; 2) it stores the initial data it receives in its FIFO buffers; and 3) it transfers processed initial data to the first element of sequence tl for subsequent ray/intersection/depth determination. In processing initial data for pixel (1,1), each shift register SH of II assigns a 0 to its output. Accordingly, the determined/calculated values of XI, X2, X3 and D are transfeπed unchanged to the first element of the sequence tl for further processing thereby in accordance with the above teachings. Processing of t2 - Scan line 5 Initializer 12 receives initial pixel data from II . Thereafter, initializer 12 processes and transfers initial pixel (5,1) data in accordance with the teachings herein. That is, initializer 12 simultaneously performs the following functions: 1) transfers the initial data it receives to initializer 13; 2) stores the initial data it receives in its FIFO buffers; and 3) transfers processed initial data to the first element of sequence t2 for subsequent ray/intersection/depth determination. In processing initial data for pixel (5,1), each shift register SH associated with B, al, a2, and a3 shifts the digital representation of its respective coefficient by two digits to the right thereby multiplying each of the coefficients B, al, a2 and a3 by a factor of +4. Next, multiplexor Ml selects B. The newly determined values for B, al, a2 and a3 are transfeπed to the first element of sequence t2 for further processing thereby in accordance with the above teachings. Processing of t3 - Scan line 5 Initializer 13 receives initial pixel data from 12. Thereafter, initializer 13 processes and transfers initial pixel (5,5) data in accordance with the teachings herein. That is, initializer 13 simultaneously performs the following functions: 1) transfers the initial data it receives to initializer 14; 2) stores the initial data it receives in its FIFO buffers; and 3) transfers processed initial data to the first element of sequence t2 for subsequent ray/intersection/depth determination for further processing thereby. In processing initial data for pixel (5,5), the shift register SH coupled to the register which stores the coefficient A shifts the digital representation of A by two digits to the right thereby multiplying A by a factor of -4. The shift registers SH coupled to the registers, which stores the coefficients al, a2, and a3 sets its associated coefficient/variable to 0. Next, multiplexor Ml selects A. The newly determined values for A, al, a2 and a3 are transfeπed to the first element of sequence t3 for further processing thereby. Processing of t4 - Scan Line 1 Initializer 14, the last initializer in the sequence of initializers, receives initial pixel data from initializer 13. Thereafter, initializer 14 processes and transfers initial data for pixel (1,5) in accordance with the teachings herein. Specifically, initializer 14 simultaneously performs the following: 1) stores the initial data it receives fro initializer 13 in its FIFO buffers; and 2) transfers processed initial data to the first element of sequence t4 for subsequent ray/intersection/depth determination for further processing thereby. In processing initial data for pixel (1 ,5), the shift register SH coupled to the register which stores the coefficient A shifts the digital representation of A by two digits to the left and changes the sign of the value thereby multiplying A by a factor of -4. The shift registers SH coupled to the registers, which stores the coefficients al, a2, and a3 sets its associated coefficient/variable to 0. Next, multiplexor Ml selects B. The newly determined values for A, and al , a2 and a3 are transfeπed to the first element of sequence t4 for further processing thereby. For the remaining scan line pairs of tile 119, the multiplexors Ml ...Mm of each initializer II , 12, 13 and 14, receive input data directly from FIFO buffers instead of the input registers. For example, as illustrated in Figure 15, control element 121 of II would instruct/signal multiplexor Ml to receive input data representing the constant value A from FIFO buffer F 1. Multiplexor Ml would then select/open/switch to the appropriate input port for receipt of A. Processing of Scan lines 2 and 6 Processing of tl — Scan Line 2 Initializer II receives input data from its FIFO buffers FI ...F , processes and transfers initial pixel (2,1) data in accordance with the teachings herein. That is, initializer II simultaneously performs the following functions: 1) it transfers the initial data it receives to initializer 12; 2) it stores the initial data it receives in its FIFO buffers; and 3) it transfers processed initial data to the first element of sequence tl for subsequent ray/intersection/depth determination. In processing initial data for pixel (2,1), each of the shift registers SH associated with B, al , a2, and a3 of II shifts its respective value by a factor of +1. Finally, multiplexor Ml of II selects B. Processing of t2 - Scan Line 6 Initializer 12 receives input data, processes and transfers initial data of pixel (6,1) data in accordance with the teachings herein. That is, initializer II simultaneously performs the following functions: 1) it transfers the initial data it receives to initializer 13; 2) it stores the initial data it receives in its FIFO buffers; and 3) it transfers processed initial data to the first element of sequence t2 for subsequent ray/intersection/depth determination. In processing initial data for pixel (6,1), each of the shift registers SH associated with B, al, a2, and a3 of 12 shifts its respective value by a factor of +1. Finally, multiplexor Ml of 12 selects B. Processing oft3 - Scan line 2 Initializer 13 receives input data, processes and transfers initial data of pixel (6,5) data in accordance with the teachings herein. That is, initializer II simultaneously performs the following functions: 1) it transfers the initial data it receives to initializer 14; 2) it stores the initial data it receives in its FIFO buffers; and 3) it transfers processed initial data to the first element of sequence t3 for subsequent ray/intersection/depth determination. In processing initial data for pixel (6,5), each of the shift registers SH associated with B, al, a2, and a3 of 13 shifts its respective value by a factor of +1. Finally, multiplexor Ml of 13 selects B. Processing oft4 - Scan Line 6 Initializer 14, the last initializer in the sequence of initializers, receives initial pixel data from initializer 13. Thereafter, initializer 14 processes and transfers initial data for pixel (2,5) in accordance with the teachings herein. Specifically, initializer 14 simultaneously performs the following: 1) stores the initial data it receives from initializer 13 in its FIFO buffers; and 2) transfers processed initial data to the first element of sequence t4 for subsequent ray/intersection/depth determination. In processing initial data for pixel (2,5), each of the shift registers SH associated with B, al, a2, and a3 of 14 shifts its respective value by a factor of +1. Finally, multiplexor Ml of 14 selects B. Processing of Subsequent Scan Lines The above steps with respect scan line pairs 2 and 6 are done for scan line pairs 3 and 7 and thereafter scan line pairs 4 and 8. Control element 121 operates the FIFO buffers and multiplexors so that the buffers and multiplexors can process the remaining scan-lines of tile 119 for the set of surfaces associated with tile 119. RAY TRACING METHOD What now follows is a description of how ray-tracing unit 7 renders a simple three-dimensional scene in accordance with the teachings herein. In the following description, certain pre-conditions are set before processing occurs. Namely, no more than eight sources of light are in the scene. Moreover, for each pixel of the screen, no more than eight transparent surfaces are located in front of a visible opaque surface. N is a 32 bit value in which the first 24 bits stores an index in the aπay of surfaces in scene database in memory unit 6. The remaining 8 bits stores an operation code. An operation code controls the element 58 (Figure 6). The type of surface - opaque, transparent, light and shadow - is defined by the last two bits of operation code. The actual forms of operation codes for each type of surface are described herein below. Register REGl of element 50 is a 32 bit register intended for storing depth value. Register REG2 of element 50 is a 96 bit register intended for storing: 1. index in the aπay of surfaces in scene database in memory unit. (24 bits), 2. field of lighting flags for 8 possible light sources (8 bits), 3. data about 8 transparent surfaces - 8 bit field for each surface (64 bit). Element 58 contains a counter, which can increment and decrement it's value on 1. The size and functional features of these means may differ. Ray-tracing unit 7 processes the various surfaces comprising a scene as follows: For each pixel in the x,y location on the screen, a ray is cast Opaque Surfaces 1. Ray-tracing unit consequently reads from memory unit structures of opaque surfaces from aπay of surfaces. The order of reading of opaque surfaces is arbitrary. The operation code for opaque surfaces contains START_OPAQUE tag for the first opaque surface, OPAQUE tag for the next surfaces and END_OPAQUE tag for the last surface. After passing of the last opaque surface through element 60 register REG2 of element 50 contains in the first 24 bits index of surface visible in this pixel and register REGl contains depth value of this surface. Light Surfaces 2. On the next step ray-tracing unit consequently reads structures of light surfaces coπesponding to light volumes. The surfaces coπesponding to the same light volume are grouped together. Order of reading of back and front-faced surfaces is arbitrary. The operation code contains tag STARTJLIGHT for the first light surface and tag ENDJLIGHT for the last light surface. The first surface data structure coπesponding to certain light volume has operation code with tag START_LIGHT_VOLUME, the last surface structure has operation code with tag END_LIGHT VOLUME. The third tag for light surfaces with two possible values FRONT or BACK conesponds to front or back faced surfaces. The number of source of light is stored in the first 3 bits of N, coπesponding to this surface. For the first light surface of the first light volume with tags START_LIGHT and START_LIGHT_VOLUME N in its first 11 bits contains the number of source of light coπesponding to this surface and also the 8 bit set defining all light sources of the scene. The coπesponding bit is equal to 1 if light source has light volume and 0 otherwise. These bits are reinterpreted for visible opaque surface in pixel as bits of lighting 0 or shadowing 1. Therefore it is set at the beginning of processing of light surfaces that the visible opaque surfaces in pixel are considered shadowed for light sources with light volumes and vice versa. Control element 58 copies these 8 bits into field of lighting flags of REG2 when it receives operation codes with tags STARTJLIGHT and START_LIGHT_VOLUME. Element 58 in Figure 6 is working in the following way: • The counter in element 58 is set to 0 for surface with tag START_LIGHT_VOLUME in operation code. • If incoming surface has FRONT tag in operation code and it is located in front of visible opaque surface then counter is incremented on 1. • If incoming surface has BACK tag in operation code and it is located in front of visible opaque surface then counter is decremented on 1. • When surface with tag END_LIGHT_VOLUME in operation code is encountered then if counter in element 58 is greater than 0 then 0 is stored in bit coπesponding to number of light source in field of lighting flags. It means that visible opaque surface in pixel is located inside processed light volume. Shadows 3. The processing of shadow volumes is executed after the processing of light volumes and just in the same manner. Ray-tracing unit consequently reads stractures of shadow surfaces coπesponding to shadow volumes. The surfaces coπesponding to the same shadow volume are grouped together. Order of reading of back and front-faced surfaces is arbitrary. The operation code contains tag START_SHADOW for the first shadow surface and tag END_SHADOW for the last shadow surface. The first surface data structure coπesponding to certain shadow volume has operation code with tag START_SHADOW_VOLUME, the last surface structure has operation code with tag END_SHADOW_VOLUME. The third tag for shadow surfaces with two possible values FRONT or BACK conesponds to front or back faced surfaces. The number of source of light is stored in the first 3 bits of N, coπesponding to this surface. Control element 58 sets the field of lighting flags of REG2 to 0 for the first shadow surface of the first shadow volume with tags START_SHADOW and START_SHADOW_VOLUME if there was no surface with tag STARTJLIGHT in operation code. Element 58 in Figure 6 is working in the following way: • The counter in element 58 is set to 0 for surface with tag START_SHADOW_VOLUME in operation code. • If incoming surface has FRONT tag in operation code and it is located in front of visible opaque surface then counter is incremented on 1. • If incoming surface has BACK tag in operation code and it is located in front of visible opaque surface then counter is decremented on 1. • When surface with tag END_SHADOW_VOLUME in operation code is encountered then if counter in element 58 is greater than 0 then 1 is stored in bit coπesponding to number of light source in field of lighting flags. It means that visible opaque surface in pixel is located inside processed shadow volume. Transparent Surfaces 4. Transparent surfaces are processed on the last step. Ray-tracing unit consequently reads structures of transparent surfaces from aπay of surfaces in memory unit. Order of reading of these surfaces is arbitrary. The operation code contains tag STARTJTRANSPARENT for the first transparent surface and tag END TRANSPARENT for the last surface. For the surfaces located in front of the visible opaque surface in the pixel 8 bits of identifying information about this transparent surface are stored in the first empty field of REG2 for storing fransparent surfaces. The final information about pixel (x, y) is transmitted via output bus OUT to the texture shading unit for subsequent processing. The forgoing process is done for each pixel in the tile. CONCLUSION Having now described a several embodiments of the present invention, it should be apparent to those skilled in the art that the foregoing is illustrative only and not limiting, having been presented by way of example only. All the features disclosed in this specification (including any accompanying claims, abstract, and drawings) may be replaced by alternative features serving the same purpose, and equivalents or similar purpose, unless expressly stated otherwise. Therefore, numerous other embodiments of the modifications thereof are contemplated as falling within the scope of the present invention as defined by the appended claims and equivalents thereto. For example, object data may be represented not only by polygons but by other well-known forms. For example, if curved surfaces are to be projected, object data may be defined by a set of parametric equations with bounding polygonal volume. Moreover, the techniques described herein may be implemented in hardware or software, or a combination of the two. The techniques may be implemented in control programs executing on programmable devices that each include at least a processor and a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements). Each program is may be implemented in a high level procedural or obj ect oriented programming language to communicate with a computer system, however, the programs can be implemented in assembly or machine language, if desired. Each such computer program is may be stored on a storage medium or device (e.g., CD-ROM, hard disk or magnetic diskette) that is readable by a general or special purpose programmable computer for configuring and 80

Claims: operating the computer when the storage medium or device is read by the computer to perform the procedures described in this document. The system may also be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner. CLAIMS What is claimed is: 1. An apparatus for facilitating rendering of a three dimensional image from a list of surfaces defining said image; said rendering to occur on an image plane for display on a display medium; said image plane having a plurality of elementary areas; said apparatus comprising; (a) a plurality of processing elements for determining depth values for ones of said surfaces in said image for each elementary area of said image plane in dependence on the distance of said one of said surfaces from said image plane; said plurality of processing elements arranged in columns and rows; said plurality of processing elements coupled together wherein data is transferred from some of said processing elements in a first of said columns to both adjacent processing elements in its column and its row and the data from the some of said remaining of said processing elements is transferred to the next adjacent processing element in its row. 2. An apparatus according to claim 1 wherein said apparatus is provided on a single integrated circuit. 3. In an apparatus having a plurality of processing elements in communication with each other; a method for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of elementary areas based on a pre-determined image resolution; said method comprising the steps of: (b) providing a list of surfaces defining said image; (c) subdividing said image plane into a plurality of tiles in accordance with a predetermined mode of subdivision; (d) associating with a tile one or more surface(s) contained at least partially within said tile; and (e) for each tile in said image plane determining depth values for ones of said surfaces in said image for each elementary area of said image plane in dependence on the distance of said one of said surfaces from said image plane; said plurality of processing elements arranged in columns and rows; said plurality of processing elements coupled together wherein data is transferred from some of said processing elements in a first of said columns to both adjacent processing elements in its column and its row and the data from the some of said remaining of said processing elements is transferred to the next adjacent processing element in its row. 4. A method for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of elementary areas in accordance with a pre-defined image resolution; said method comprising the steps of: (a) generating a list of surfaces defining said image; (b) subdividing said image plane into a plurality of tiles; (c) associating with a tile one or more surface(s) contained at least partially within that tile; (d) for each pixel on a tile (i). projecting a light ray into said image; (ii). determining any ray/surface intersections with said one or more surfaces associated with said tile; and (iii). determining a color of said pixel based on the results of the preceding step further accounting for light and shadow. 5. A method for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of elementary areas; said method comprising the steps of: (a) providing a list/group of surfaces defining said image; (b) subdividing said image plane into a plurality of tiles; each of said tiles having rows and columns of elementary areas; (c) associating with a tile one or more surface(s) contained at least partially within said tile; (d) for each elementary area of said tile: (i) generating a depth value for each surface in dependence on the distance of that surface from said image plane; (i). determining whether any surface is visible at that elementary area; and (ii). determining the appropriate color of said elementary area accounting for shadows and light based on said results of said determination in the preceding step. 6. A method for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of pixels; said method comprising the steps of: (a) providing a list of surfaces defining said image; (b) subdividing said image plane into a plurality of tiles; (c) associating with a tile one or more surface(s) contained at least partially within said tile; and (d) for each pixel of a tile; (i). projecting a ray into said image; (ϋ). determining a ray/surface intersection with said one or more surfaces; (iii). generating a surface depth value for each of said one or more surfaces in dependence on the distance of that surface from said image plane; (iv). determining whether any surface is visible at that pixel; and (v). determining color attributes of that pixel accounting for shadows and light based on said results of said determination in the preceding step. 7. A method as in claim 6 further comprising the step of using said surface depth value of one pixel of said tile for determining said surface depth value of another pixel of said tile. 8. A method as in claim 6 wherein step (d) is done simultaneously in parallel for all pixels of said tile. 9. A method as in claim 6 wherein each of said surfaces include surface boundaries. 10. A method as in claim 6 wherein each of said surfaces are open surfaces having parts of infinite planes limited by mutually intersecting straight lines which define surface boundaries. 11. A method according to claims 9, wherein said ray/surface intersection points for adjacent pixels within surface boundaries are determined by generating and using an interval being part of a scan line whose extent begins and ends with points of intersection of said scan line with said surface boundaries. 12. A method according to claim 11, wherein said scan line is a horizontal straight line passing through a pixel. 13. A method according to claim 11, wherein said interval is generated only once for all pixels belonging to said scan line. 14. An apparatus having a plurality of components in communication with each other; said apparatus for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of pixels; said apparatus comprising: (a) a first component for providing a list of surfaces defining said image; (b) a second component for subdividing said image plane into a plurality of tiles; (c) a third component for associating with a tile one or more surface(s) contained at least partially within said tile; and (d) a fourth component for performing the following: 1 for each pixel of a tile; 2 (i). projecting a ray into said image; 3 (ii). determining a ray/surface intersection with said one or 4 more surfaces; 5 (iii). generating a surface depth value for each of said one or 6 more surfaces in dependence on the distance of that surface 7 from said image plane; 8 (iv). determining whether any surface is visible at that pixel; 9 and 10 (v). determining color attributes of that pixel accounting for 11 shadows and light based on said results of said determination in 12 the preceding step. ι3 14 15. An apparatus according to claim 14 wherein said fourth component uses 15 said surface depth value of one pixel of said tile for determining said surface 16 depth value of another pixel of said tile. 17 18 16. An apparatus according to claim 14 wherein said fourth component 19 performs its functions simultaneously in parallel for all pixels of said tile. 0 1 17. An apparatus according to claim 14 wherein each of said surfaces include 2 surface boundaries. 3 18. An apparatus according claim 14 wherein each of said surfaces are open surfaces having parts of infinite planes limited by mutually intersecting straight lines which define surface boundaries. 19. An apparatus according to claims 17, wherein said ray/surface intersection points for adjacent pixels within surface boundaries are determined by generating and using an interval being part of a scan line whose extent begins and ends with points of intersection of said scan line with said surface boundaries. 20. An apparatus according to claim 19 wherein said scan line is a horizontal straight line passing through a pixel. 21. An apparatus according to claim 19 wherein said interval is generated only once for all pixels belonging to said scan line. 22. An apparatus according to claim 14 wherein said apparatus is provided on a single integrated circuit. 23. An apparatus having a plurality of interconnected components; said apparatus for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of pixels; said apparatus comprising: (a) an input component for providing input data representing surfaces defining said image; (b) a geometry processing component in communication with said input component for receiving said input data and performing certain pre- processing activities on said input data including determining parameters of light and shadow; clipping, culling, and geometric transformations; (c) an image plane component in communication with said geometry component for subdividing said image plane into a plurality of tiles and associating with a tile one or more surface(s) contained at least partially within said tile; (d) a ray-tracing component in communication with said image plane component for performing the following: for each pixel of a tile; (i). projecting a ray into said image; (ii). determining a ray/surface intersection with said one or more surfaces; (iii). generating a surface depth value for each of said one or more surfaces in dependence on the distance of that surface from said image plane; (iv). determining whether any surface is visible at that pixel; and (v). determining color attributes of that pixel accounting for shadows and light based on said results of said determination in the preceding step. and; (e) memory in which said geometry processing component writes to and said ray-tracing component reads from. 24. An apparatus according to claim 23 wherein certain functions of said ray tracing component is carried out at least in part by a plurality of pixel processing elements; each of said pixel processing elements associated with a pixel of a tile; said plurality of pixel processing elements arranged in one or more sequences such that said output of a first pixel processing element of a sequence is transferred to an adjacent second pixel processing element in the same sequence. 25. An apparatus according to claim 24, wherein said ray tracing component further comprises a plurality of initializing processing elements, each of which is associated with a sequence of pixel processing elements; said initializing processing element for providing initial data for said associated sequence of pixel processing elements. 26. An apparatus according to claim 26, wherein each of said initializing processing elements comprise one or more FIFO memory buffers and wherein each initializing processing element provide initial data for said associated sequence of pixel processing elements using said FIFO memory buffers. 27. An apparatus according to claim 26, wherein each of said initializing processing elements read/write from/to said FIFO memory buffers simultaneously in parallel. 28. An apparatus according to claim 23 wherein said apparatus is provided on a single integrated circuit. 29. An apparatus for determining visible parts of surfaces of three-dimensional objects for display on a display device, said apparatus comprising: a. a first component for providing input data defining surfaces of three-dimensional objects, b. a second component in communication with said first component determining for each elementary area of each subdivision among the surfaces left after culling only those surfaces, which are projected on this elementary area by means of determining points of intersection of scan line, which belongs to this elementary area, with lines forming projections of the surfaces left after culling, c. a third component for utilizing of said points of intersection of one scan line with the lines forming projection of surface for determining points of intersection of another scan line with the same lines, d. a fourth component for each elementary area of each subdivision for surfaces left after culling calculating of depth values, wherein said depth value depends on the distance from the center of projection to point of intersection of surface with projection ray passing through the elementary area, e. a fifth component for utilizing of said calculated depth value for one elementary area for calculating of depth value for another elementary area, (f) a sixth component for determining for each elementary area of each subdivision visible surface and parameters of shading of this surface, wherein said determining is executed by comparing calculated depth values simultaneously in parallel for plurality of elementary areas. 30. The method according to claim 29, wherein said surfaces are flat convex polygons or open surfaces i.e. parts of infinite planes limited by two or three mutually intersecting straight lines. 31. The method according to claim 30, wherein said determining whether the surface is projected on the elementary area is executed by means of determining interval, said interval is a part of scan line, which entirely belongs to proj ection of the surface and is calculated from points of intersection of said scan line with all straight lines forming the projection. 32. The method according to claim 31 , wherein a horizontal straight line passing through the elementary area is chosen as the scan line. 33. The method according to claim 32, wherein said points of intersection of said scan line with all straight lines forming projection of surface are defined only by their horizontal coordinate. 34. The method according to claim 33, wherein said interval is calculated only once for all elementary areas belonging to said scan line. 35. The method according to claim 33, wherein with each said subdivision the plurality of projections of surfaces is associated and depth values for elementary areas of the subdivision are determined for this surfaces. 36. The method according to claim 35, wherein said associated with each subdivision plurality projections of surfaces includes surfaces, which are projected at least partially inside said subdivision. 37. An apparatus for determining visible parts of surfaces of three-dimensional objects on a screen and parameters of shading of said parts accounting for light and shadow volumes, the system including the following units: geometry processor unit comprising: means for input of data defining the surfaces of three-dimensional objects and light sources, means for processing input data in order to obtain surfaces of light and shadow volumes, means for processing of back-faced surfaces and means for culling of back-faced surfaces of three-dimensional objects, which are represented only by opaque surfaces, ray-tracing unit comprising: means for said determining for each elementary area among the surfaces left after culling only those surfaces, which are projected on this elementary area, means for utilizing of points of intersection of one scan line with the lines forming projection of surface for determining points of intersection of another scan line with the same lines, means for calculating of said depth values, means for utilizing of said calculated depth value for one elementary area for calculating of depth value for another elementary area and means for determining visible surface and parameters of shading of this surface, ray-tracing unit implementing said means with the help of plurality of processing elements, which work simultaneously in parallel, transfer results of their work to other processing elements of the same plurality and read/write said results from/to internal registers, memory unit providing intermediate data buffer means, in which data is written by geometry processor and, from which data is read by ray-tracing unit. 38. An apparatus according to claim 37, wherein said plurality of processing elements is aπanged into sequences of processing elements, and the result of work of each processing element can be transferred to another element in the sequence. 39. An apparatus according to claim 38, wherein sequence of initializing processing elements is utilized to provide initial data for said sequences of processing elements, said initializing processing elements also can transfer the results of their work to processing elements of other sequences. 40. An apparatus according to claim 39, wherein said transfer of results of work of initializing processing elements to processing elements of other sequences is executed via a FIFO memory buffers. 41. An apparatus according to claim 40, wherein readwrite from/to FIFO memory buffers is executed simultaneously in parallel. 42. An apparatus according to claim 37, wherein all said sequences of processing elements have equal number of enumerated processing elements, and there is the same number of enumerated internal memory units, only processing elements with equal numbers can read/write data from/to internal memory unit with the same number. 43. An apparatus according to claim 42, wherein read operations are executed for processing elements with different numbers from the same addresses in internal memory units simultaneously in parallel, write operations are executed for processing elements with different numbers to the same addresses in internal memory units simultaneously in parallel. 44. An apparatus according to claim 43, wherein only processing elements of the same sequence are executing read/write operations from/to the same addresses in internal memory units simultaneously in parallel. 45. An apparatus according to claim 37, wherein geometry processor comprises means for associating with each said subdivision the plurality of projections of surfaces, which are projected at least partially inside said subdivision. 46. A method for associating surface projections on an initial area in coordinate space with regions of said initial area; said coordinate space being defined by one or more coordinate axes and method for facilitating rendering of a three dimensional image on an image plane for display on a display medium; said image plane having a plurality of elementary areas in accordance with a pre-defined image resolution; said combined method comprising the steps of: (a) generating a list of surfaces defining said image; (b) subdividing said image plane into a plurality of tiles; (c) associating with a tile one or more surface(s) contained at least partially within that tile; (d) for each pixel on a tile (i). projecting a light ray into said image; (ii). determining any ray/surface intersections with said one or more surfaces associated with said tile; and (iii). determining a color of said pixel based on the results of the preceding step further accounting for light and shadow, (a) generating a list of said surface proj ections; (e) determining a bounding volume for at least some of said surface projections in said list; (f) subdividing said initial area into a plurality of minimal subdivisions in accordance with a predefined mode of subdivision having associated therewith a predefined naming convention; and (g) for a minimal subdivision: (i) determining whether one or more of said bounding volumes are at least partially contained within that minimal subdivision based upon said predefined naming convention associated with said mode of subdivision; and (ii) based on the results of said determination in said preceding step, associating said one or more bounding volumes with that minimal subdivision thereby associating with that minimal subdivision said surface projections contained within said associated one or more bounding volumes.

Inventors: MAKAROV IGOR, ZVIAGUINA NATALIA, MAKAROV, IGOR, ZVIAGUINA, NATALIA
Applicants: MAKAROV IGOR, ZVIAGUINA NATALIA, MAKAROV, IGOR, ZVIAGUINA, NATALIA
Application year: 2001
Main classification: G06T
IPC codes: G06T15