Patent Application: US-66242696-A

Abstract:
in computer graphics systems , a view of scene of primitives is represented by pixel data associated with a set s of pixels . the present invention identifies whether a given primitive is visible at the set s of pixels by storing in a buffer , for each pixel p belonging to set s , a depth value z old associated with the pixel p . the depth value z old is partitioned into a plurality of portions including a most significant portion and at least one less significant portion . the buffer comprises a plurality of contiguous blocks each storing corresponding portions of the depth value z old for a given set sp of consecutive pixels belonging to set s . a set sq of consecutive pixels belonging to set s that cover the given primitive is determined . the most significant portion of the depth value z old of the set sq of consecutive pixels are fetched from the buffer . for each pixel q belonging to set sq , the most significant portion of the depth value z old of the particular pixel is compared to the most significant portion of the computed depth value z new of the particular pixel to determine if one of three conditions is satisfied : a ) the given primitive is visible at the particular pixel , b ) the given primitive is hidden at the particular pixel , or c ) it is undetermined whether the given primitive is either visible or hidden at the particular pixel . if condition a ) is satisfied , the blocks of the buffer associated with the particular pixel is updated to store the computed depth value z new of the particular pixel . if condition b ) is satisfied , the processing ends with respect to the particular pixel . if condition c ) is satisfied , the fetching step and comparing step above is repeated for the next less significant portion of the depth values z old and z new associated with the particular pixel until the least significant portion of the depth values z old and z new has been processed .

Description:
as shown in fig2 a conventional graphics system 100 includes a host processor 102 which is coupled to a system memory 104 via a system bus 106 . the system memory 104 consists of random access memory ( ram ) that stores graphics data defining the objects contained in one or more three dimensional models . the graphics data that defines each object consists of coordinates and attributes ( e . g . color , reflectance , texture ) of primitives . the primitives are geometric entities such as a polygon , line or surface . typically , the primitives are triangles defined by the coordinates of three vertices . in this case , the system memory 104 includes an ordered list of vertices of the triangles that define the surfaces of objects that make up a three dimensional scene . in addition , the system memory 104 may store a list of triangle identifiers that correspond to each of the triangles and transformation matrices that specify how the triangles are situated and oriented in the scene . input / output ( i / o ) devices 108 interface to the host processor 102 via the system bus 106 . the i / o devices may include a keyboard , template or touch pad for text entry , a pointing device such as a mouse , trackball , spaceball or light pen for user input , and non - volatile storage such as a hard disk or cd - rom for storing the graphics data and any application software . as is conventional , the graphics data and application software is loaded from the non - volatile storage to the system memory 104 for access by the host processor 102 . the graphics system 100 also includes a graphics subsystem 110 that interfaces to the system memory 104 via the system bus 106 . generally , the graphics subsystem 110 operates to render the graphics data stored in the system memory 104 for display on a display area of a display device 112 according to graphics orders transferred from the host processor 102 to the graphics subsystem 110 . the display device 112 may utilize raster scan techniques or liquid crystal display techniques to display the pixels . the pixel data generated by the graphics subsystem 110 is in digital form . typically , the display device 112 requires the pixel data in analog form . in this case , as shown in fig3 a digital - to - analog converter 114 may be placed between the graphics subsystem 110 and the display device 112 to convert the pixel data from a digital to an analog form . the graphics orders typically are generated by application software that are stored in the system memory 104 and executed by the system processor 102 . the graphics orders typically consist of a sequence of data blocks that include , or point to , the graphics data ( e . g . coordinates and attributes of one or more objects ) that defines the objects of the scene , associated transformation matrices , and any other necessary information required by the graphics subsystem 110 . the primitives associated with the graphics orders are typically defined by the value of the geometric coordinates or homogeneous coordinates for each vertex of the primitive . in addition , graphics orders typically include , or point to , data defining the reflectance normal vectors for the vertices of each primitive . the values of these coordinates and normal vectors are assumed to be specified in a coordinate system designated as the model coordinate system . although the graphics subsystem 110 is illustrated as part of a graphics work station , the scope of the present invention is not limited thereto . moreover , the graphics subsystem 110 of the present invention as described below may be implemented in hardware such as a gate array or a chip set that includes at least one programmable sequencer , memory , at least one integer processing unit and at least one floating point processing unit , if needed . in addition , the graphics subsystem 110 may include a parallel and / or pipelined architecture as shown in u . s . pat . no . 4 , 876 , 644 , commonly assigned to the assignee of the present invention and incorporated by reference herein in its entirety . in the alternative , the graphics subsystem 110 ( or portions thereof ) as described below may be implemented in software together with a processor . the processor may be a conventional general purpose processor , a part of the host processor 102 , or part of a co - processor integrated with the host processor 102 . more specifically , as shown in fig3 the graphics subsystem 110 includes a control unit 200 that supervises the operation of the graphics subsystem 110 . upon receiving a graphics order to render a scene , the control unit 200 passes the graphics data associated with the graphics order on to a geometry engine 202 . the geometry engine 202 transforms the graphics data associated with the graphics order from the model coordinate system to a normalized device coordinate system ( sometimes referred to as the view coordinate system ) and clips the graphics data against a predetermined view volume . typically , this transformation involves a series of transformations including a modeling transformation from the model coordinate system to a world coordinate system , a view orientation transformation from the world coordinate system to a view reference coordinate system and a view mapping transformation from the view reference coordinate system to the normalized device coordinate system . in addition , the transformation from the model coordinate system to the normalized device may involve a perspective projection or a parallel projection . for example , consider a system wherein the coordinates of the view reference coordinate system are represented as ( x eye , y eye , z eye ). in this case , the perspective projection for the z coordinate z eye may be computed as follows : where z far and z near are the far and near clipping planes . similarly , the parallel projection for the z coordinate z eye may be computed as follows : where z far and z near are the far and near clipping planes . a more detailed description of the geometric transformations performed by the geometry engine 202 may be found in foley et . al ., &# 34 ; computer graphics : principles and practice &# 34 ;, pp . 201 - 281 ( 2nd ed . 1990 ), and in u . s . patent application ser . no . 08 , 586 , 266 , entitled computer graphics system having efficient texture mapping with perspective correction , filed jan . 16 , 1996 , herein incorporated by reference in their entirety . in addition , depending upon the shading algorithm to be applied , an illumination model is evaluated at various locations ( i . e ., the vertices of the primitives and / or the pixels covered by a given primitive ). the graphics data generated by the geometry engine , which represents the transformed primitives in the normalized device coordinate system , is then passed on to a rasterization stage 212 that converts the transformed primitives into pixels , and generally stores each primitive &# 39 ; s contribution at each pixel in at least one frame buffer 216 and a z buffer 214 . the operation of the rasterization stage 212 may be divided into three tasks as described above : scan conversion , shading , and visibility determination . the pixel data is periodically output from the frame buffer 216 for display on the display device 112 . the functionality of the geometry engine 202 and rasterization stage 212 may be organized in a variety of architectures . a more detailed discussion of such architectures may be found in foley et . al ., &# 34 ; computer graphics : principles and practice &# 34 ;, pp . 855 - 920 ( 2nd ed . 1990 ), herein incorporated by reference in its entirety . the frame buffer 216 typically stores pixel data that represents the color of each pixel of the display area of the display device 112 . in the alternative , the pixel data stored in the frame buffer 216 may be scaled up or down to satisfy the resolution of the display area of the display device . the description below assumes that the frame buffer 216 stores pixel data that represents the color of each pixel of the display area of the display device 112 . the pixel data is periodically output from the frame buffer 216 for display in the display area of the display device 112 . in addition , the graphics subsystem 110 may include more than one frame buffer . as is conventional , one of the frame buffers serves as the active display portion , while another one of the frame buffers may be updated for subsequent display . any one of the frame buffers may change from being active to inactive in accordance with the needs of the system ; the particular manner in which the changeover is accomplished is not relevant to the present invention . according to the present invention , as shown in fig6 the rasterization stage 212 includes comparison logic 303 , a write sorter 305 ( that interfaces to the frame buffer 216 and the z buffer 214 ), and a fetch sorter 307 ( that interfaces to the z buffer 214 ) that operate cooperatively to perform the visibility determination task of the rasterization stage 212 . more specifically , the rasterization stage 212 of the present invention preferably includes transformation logic 301 that maps the normalized device coordinates ( x ndc , y ndc , z ndc ), which are typically floating point numbers , of the vertices of each primitive output from the geometry engine 202 to an integer based window coordinate system ( x w , y w , z b ). the mapping typically includes a scaling and translate operation which are described in more detail in foley et . al ., &# 34 ; computer graphics : principles and practice &# 34 ;, pg . 278 ( 2nd ed . 1990 ), herein incorporated by reference in its entirety . preferably , the transformation logic 301 generates the transformed depth value z b as follows : where zbits represents the width of the z buffer entry corresponding to a given pixel . for example , zbits may be 24 ( or 3 bytes ). in this case , an example of the mapping of z eye to z ndc to z b is illustrated in the following table . in the table , z eye is bounded by two planes , z near = 10 . 0 and z far = 1000000 . 0 , which are reasonable approximations to zero and infinity . for example , the units could be centimeters indicating that the closest object is at least 10 cm away and the farthest object to be viewed is 10 km away in a real world situation . ______________________________________z . sub . b z . sub . eye z . sub . b z . sub . eye______________________________________0 - 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14 . 065877 ca0000 - 47 . 4056434b0000 - 14 . 143588 cb0000 - 48 . 3000494c0000 - 14 . 222162 cc0000 - 49 . 2288514d0000 - 14 . 301615 cd0000 - 50 . 1940734e0000 - 14 . 381960 ce0000 - 51 . 1979034f0000 - 14 . 463213 cf0000 - 52 . 242702500000 - 14 . 545388 d00000 - 53 . 331036510000 - 14 . 628504 d10000 - 54 . 465679520000 - 14 . 712575 d20000 - 55 . 649647530000 - 14 . 797617 d30000 - 56 . 886238540000 - 14 . 883649 d40000 - 58 . 179031550000 - 14 . 970686 d50000 - 59 . 531952560000 - 15 . 058747 d60000 - 60 . 949295570000 - 15 . 147851 d70000 - 62 . 435768580000 - 15 . 238016 d80000 - 63 . 996563590000 - 15 . 329260 d90000 - 65 . 6373985a0000 - 15 . 421603 da0000 - 67 . 3645785b0000 - 15 . 515066 db0000 - 69 . 1851205c0000 - 15 . 609669 dc0000 - 71 . 1067895d0000 - 15 . 705432 dd0000 - 73 . 1382685e0000 - 15 . 802378 de0000 - 75 . 2892305f0000 - 15 . 900528 df0000 - 77 . 570541600000 - 15 . 999905 e00000 - 79 . 994431610000 - 16 . 100531 e10000 - 82 . 574684620000 - 16 . 202431 e20000 - 85 . 326942630000 - 16 . 305630 e30000 - 88 . 268990640000 - 16 . 410152 e40000 - 91 . 421165650000 - 16 . 516022 e50000 - 94 . 806816660000 - 16 . 623266 e60000 - 98 . 452873670000 - 16 . 731915 e70000 - 102 . 390587680000 - 16 . 841991 e80000 - 106 . 656410690000 - 16 . 953526 e90000 - 111 . 2931296a0000 - 17 . 066547 ea0000 - 116 . 3513266b0000 - 17 . 181086 eb0000 - 121 . 8911906c0000 - 17 . 297171 ec0000 - 127 . 9849786d0000 - 17 . 414837 ed0000 - 134 . 7201236e0000 - 17 . 534115 ec0000 - 142 . 2035226f0000 - 17 . 655037 ef0000 - 150 . 567169700000 - 17 . 777639 f00000 - 159 . 976120710000 - 17 . 901957 f10000 - 170 . 639389720000 - 18 . 028025 f20000 - 182 . 825699730000 - 18 . 155882 f30000 - 196 . 886459740000 - 18 . 285563 f40000 - 213 . 290176750000 - 18 . 417112 f50000 - 232 . 675705760000 - 18 . 550568 f60000 - 255 . 937347770000 - 18 . 685970 f70000 - 284 . 366791780000 - 18 . 823364 f80000 - 319 . 901306790000 - 18 . 962793 f90000 - 365 . 5848697a0000 - 19 . 104305 fa0000 - 426 . 4898077b0000 - 19 . 247944 fb0000 - 511 . 7443247c0000 - 19 . 393759 fc0000 - 639 . 5989387d0000 - 19 . 541800 fd0000 - 852 . 6176767c0000 - 19 . 692118 fe0000 - 1278 . 3840337f0000 - 19 . 844767 ff0000 - 2553 . 518799______________________________________ in addition , the rasterization stage 212 includes scan conversion and shading logic 302 that determines the set of pixels which cover a given primitive , and computes rgb color data , alpha blending data a ( if need be ), and the depth value z b of the given primitive at the pixels within the set . as is conventional , the rgba data and depth value z b of the given primitive at the pixels within the set is preferably determined by interpolating the corresponding data values at the vertices of the given primitive . a more detailed description of the scan conversion operation performed by the scan conversion and shading logic 302 may be found in foley et . al ., &# 34 ; computer graphics : principles and practice &# 34 ;, pp . 945 - 965 ( 2d edition 1990 ), herein incorporated by reference in its entirety . in addition , a more detailed description of the shading operation performed by the scan conversion and shading logic may be found in foley et . al ., &# 34 ; computer graphics : principles and practice &# 34 ;, pp . 734 - 741 ( 2d edition 1990 ), herein incorporated by reference in its entirety . the scan conversion and shading logic 302 supplies to comparison logic 303 a pixel address which identifies one or more pixels within the set of pixels that cover the given primitive , in addition to the rgba data and z b data of the given primitive at the one or more pixels identified by the accompanying pixel address . the comparison logic 303 , together with the write sorter 305 and fetch sorter 307 , perform the visibility determination task of the rasterization stage 212 for the given primitive for the one or more pixels identified by the accompanying pixel address . a more detailed description of the operation of the comparison logic 303 , write sorter 305 , and fetch sorter 307 is set forth below . the frame buffer 216 preferably stores rgb color data and alpha blending data a , if need be , for each pixel in the display area of the display device 112 . preferably , the color data and alpha blending data of a given pixel is stored in contiguous blocks r | g | b | a of the frame buffer 216 as shown in fig4 . for example , the color and alpha blending data of a pixel a may be stored in four contiguous bytes ra | ba | ga | aa in the frame buffer 216 . in addition , the rgb color data and alpha blending data a of consecutive pixels in the display area of the display device 112 are preferably stored in contiguous blocks of the frame buffer 216 as shown in fig4 . for the sake of this description , consecutive pixels are adjacent to one another in the order of the rasterization scheme . for example , consecutive pixels may represent a horizontal line , a vertical line , or a square block . because a horizontal order is assumed by many rasterization schemes , a horizontal order will be assumed in the description below . to further illustrate the organization of the frame buffer 216 , consider four consecutive pixels a , b , c , and d each represented by four contiguous bytes of data r | g | b | a . in this scenario , the color data rgb and alpha blending data a of the four consecutive pixels a , b , c , d would be represented by sixteen contiguous bytes ( or four words ) ra | ba | ga | aa | rb | bb | gb | ab | rc | bc | gc | ac | rd . vertline . bd | gd | ad in the frame buffer 216 . the z buffer 214 stores the depth value z b of the visible primitive for each pixel of the display area of the display device 112 . the depth value z b of the visible primitive at each pixel is segmented into portions z n , z n - 1 , . . . z 1 , z 0 . for example , the depth value z b of the visible primitive at each pixel may be segmented into byte portions . in this example , if the width of the z buffer entry corresponding to a given pixel is three bytes ( i . e ., zbits = 24 ), the depth value z b of the visible primitive for each pixel may be segmented into three portions each one byte long . in this example , the depth value z b of the visible primitive at a pixel a may be segmented into three byte portions za2 , za1 , za0 where za2 is the most significant byte , za1 is the next significant byte , and za0 is the least significant byte . the comparison logic 303 , together with the write sorter 305 and fetch sorter 307 , perform the visibility determination task of the rasterization stage 212 for a primitive p for one or more pixels that cover the primitive p . more specifically , the comparison logic 303 receives from the scan conversion and shading logic 302 a pixel address which identifies one or more pixels that cover the primitive p in addition to the rgba data and z b data corresponding to the color and depth of the primitive p at the one or more pixels . for each of the one or more pixels that cover the primitive p , the comparison logic 303 requests that the fetch sorter 307 fetch from the z buffer 214 the most significant portion of the depth value z b that is associated with the given pixel , denoted zold n . the comparison logic 303 then compares zold n to the most significant portion of the depth value z b of the primitive p at the given pixel , denoted znew n , which was supplied by the scan conversion and shading logic 302 , to determine if the most significant portions zold n and znew n indicate that the primitive p is visible at the given pixel . if the most significant portions zold n and znew n indicate that the primitive p is visible ( for example , when znew n & lt ; zold n ), then comparison logic 303 sends the pixel address along with the rgba color data and depth value z b of the primitive p at the given pixel to the write sorter 305 . the write sorter 305 writes the rgba color data to the entry of the frame buffer 216 that corresponds to the supplied pixel address , and writes the depth value z b to the entry of the z buffer 214 that corresponds to the supplied pixel address . if the most significant portions zold n and znew n indicate that the primitive p is hidden ( for example , when znew n & gt ; zold n ), then the operation of the comparison logic 303 ends with respect to the given pixel . however , if the most significant portions zold n and znew n fail to indicate that the primitive p is either visible or hidden ( for example , when znew n = zold n ), then the comparison logic 303 requests that the fetch sorter 307 fetch from the z buffer 214 the next significant portion of the depth value z b that is associated with the given pixel , denoted zold n - 1 . the comparison logic 303 then compares zold n - 1 to the next significant portion of the depth value z b of the primitive p at the given pixel , denoted znew n - 1 , which was supplied by the scan conversion and shading logic 302 to determine if the next significant portions zold n - 1 and znew n - 1 indicate that the primitive p is visible at the given pixel . if the next significant portions zold n - 1 and znew n - 1 indicate that the primitive p is visible ( for example , when znew n - 1 & lt ; zold n - 1 ), then comparison logic 303 sends the pixel address along with the rgba color data and depth value z b of the primitive p at the given pixel to the write sorter 305 . the write sorter 305 writes the rgba color data to the entry of the frame buffer 216 that corresponds to the supplied pixel address , and writes the depth value z b to the entry of the z buffer 214 that corresponds to the supplied pixel address . if the next significant portions zold n - 1 and znew n - 1 indicate that the primitive p is hidden ( for example , when znew n - 1 & gt ; zold n - 1 ), then the operation of the comparison logic 303 ends with respect to the given pixel . however , if the next significant portions zold n - 1 and znew n - 1 fail to indicate that the primitive p is either visible or hidden ( for example , when znew n - 1 = zold n - 1 ), then the comparison logic 303 performs the same operations for the next significant portion of the depth value z b that is associated with the given pixel until all portions of the depth value z b that is associated with the given pixel have been processed as described above . after all portions have been processed , the operation of the comparison logic ends with respect to the given pixel . by performing the above operations , in most instances the comparison logic 303 resolves the z compare operation by analyzing only the most significant portions zold n and znew n . in few instances , the less significant portions zold n - 1 and znew n - 1 , . . . may be required to be analyzed to resolve the compare operation . advantageously , this results in an overall reduction of the z buffer bandwidth requirement for the system . in an alternative embodiment , the comparison logic 303 may integrate the comparison operations described above for a predetermined number of consecutive pixels . in this embodiment , the z buffer 214 is preferably organized such that the corresponding portions of the depth value z b of the visible primitive at the predetermined number of consecutive pixels are stored in contiguous blocks of the z buffer 214 . for example , consider the scenario presented above wherein pixels a , b , c , d are consecutive pixels each having a depth value z b of the visible primitive at that pixel that is 24 bits wide and segmented into three byte portions . thus , the depth value z b of the visible primitive at pixel a is segmented into three byte portions za2 , za1 , za0 , the depth value z b of the visible primitive at pixel b is segmented into three byte portions zb2 , zb1 , zb0 , the depth value z b of the visible primitive at pixel c is segmented into three byte portions zc2 , zc1 , zc0 , and the depth value z b of the visible primitive at pixel d is segmented into three byte portions zd2 , zd1 , zd0 . in this case , the z buffer 214 may be organized such that the corresponding portions ( za2 , zb2 , zc2 , zd2 and za1 , zb1 , zc1 , zd1 and za0 , zb0 , zc0 , zd0 ) of the depth value z b for the visible primitive at the four consecutive pixels are stored in contiguous blocks of the z buffer 214 as shown in fig5 . in this example , a word in the z buffer 214 contains za2 | zb2 | zc2 | zd2 , the next contiguous word contains za1 | zb1 | zc1 | zd1 , and the following contiguous word contains za0 | zb0 | zc0 | zd0 . in this alternate embodiment , the comparison logic 303 preferably operates as illustrated in the following pseudo - code : __________________________________________________________________________q0 : wait for pixel address , rgba data and associated incoming zb data forpixels a , b , c , dpixel address a , pixel address b , pixel address c , pixel address dra | ba | ga | aa | rb | bb | gb | ab | rc | bc | gc | ac | rd . vertline . bd | gd | ad andiza2 | iza1 | iza0 , izb2 | izb1 | izb0 , izc2 | izc1 | izc0 , izd2 | izd1 | izd0j = 2 ; l0 : request zaj | zbj | zcj | zdj from fetch sorterwait for zaj | zbj | zcj | zdj from fetch sorter /* pixel a */ if ( izaj & lt ; zaj ) { send pixel address a , ra | ga | ba | aa and iza2 | iza1 | iza0 to write sorter ; } else if ( izaj & gt ; zaj ) { do nothing ; /* go to pixel b */ } l1 : else { if ( j & gt ; 0 ) { request zaj - 1 from fetch sorter } /* later pixel with equal z wins */ else { send pixel address a , ra | ga | ba | aa . to write sorter ; } }/* pixel b */ if ( izbj & lt ; zbj ) { send pixel address b , rb | gb | bb | ab and izb2 | izb1 | izb0 to write sorter ; } else if ( izbj & gt ; zbj ) { do nothing ; /* go to pixel c */ } else { if ( j & gt ; 0 ) { request zbj - 1 from fetch sorter } /* later pixel with equal z wins */ else { send pixel address b and rb | gb | bb | ab to write sorter ; } }/* pixel c */ if ( izcj & lt ; zcj ) { send pixel address c , rc | gc | bc | ac and izc2 | izc1 | izc0 to write sorter ; } else if ( izcj & gt ; zcj ) { do nothing ; /* goto pixel d */ } else { if ( j & gt ; 0 ) { request zcj - 1 from fetch sorter } /* later pixel with equal z wins */ else { send pixel address c and rc | gc | bc . vertline . ac to write sorter ; } }/* pixel d */ if ( izdj & lt ; zdj ) { send pixel address d , rd | gd | bd | ad and izd2 | izd1 | izd0 to write sorter ; } else if ( izdj & gt ; zdj ) { do nothing ; /* goto l2 */ } else { if ( j & gt ; 0 ) { request zdj - 1 from fetch sorter } /* later pixel with equal z wins */ else { send pixel address d and rd | gd | bd . vertline . ad to write sorter ; } } l2 : j = j - 1 ; if ( j = 0 ) { go to q0 ; } else { go to l0 ; } __________________________________________________________________________ by performing the above operations , in many instances the comparison logic 303 is performs the z compare operation for the predetermined number of consecutive pixels by analyzing only the most significant portions zold n and znew n corresponding to each of the predetermined number of consecutive pixels . in this case , only a single z buffer read operation is required . advantageously , this results in an overall reduction of the z buffer bandwidth requirement for the system . in the alternate embodiment of the present invention as described above , the z buffer 214 is preferably organized such that the corresponding portions of the depth value z b of the visible primitive at the predetermined number of consecutive pixels are stored in contiguous blocks of the z buffer 214 as shown in fig5 . in this scenario , the write sorter 305 preferably stores , for each pixel in a set of pixels , pixel address data , rgba color data and z b data associated with the given pixel . the write sorter 305 generates a z buffer write signal that represents , for those portions of the depth value z b at the predetermined number of consecutive pixels that are to be updated , the updated portion of the depth value z b at the given pixel , and forwards the z buffer write signal to the z buffer 214 via data path 311 . preferably , the z buffer write signal is sectioned into segments each corresponding to a portion of the depth value z b at the predetermined number of consecutive pixels . as shown in fig8 ( a ), each segment preferably includes an address field 801 , a data field 803 , and a mask 805 . the address field 801 identifies , for the given segment , the z buffer entry that holds the portion of the of the depth value z b at the predetermined number of consecutive pixels that corresponds to the given segment . the data field 803 includes a plurality of sub - fields each corresponding to one of the predetermined number of consecutive pixels . each sub - field stores , if need be , the portion of the depth value z b that is to be updated at the given pixel . the mask 805 identifies which sub - fields of the data field 803 store updated depth value portion for the predetermined number of consecutive pixels . for example , consider the consider the scenario presented above wherein pixels a , b , c , d are consecutive pixels and the z buffer 214 contains contiguous entries za2 | zb2 | zc2 | zd2 , za1 | zb1 | zc1 | zd1 , and za0 | zb0 | zc0 | zd0 . in this case , as shown in fig8 ( b ), the segment of the z buffer write signal corresponding to the most significant portion of the consecutive pixels a , b , c , d would include : 1 ) an address field 801 that identifies the address of the z buffer entry holding za2 | zb2 | zc2 | zd2 ; 2 ) a data field 803 that includes sub - fields holding the updated most significant portions za2 , zb2 , zc2 , zd2 of the depth value z b for the consecutive pixels a , b , c , d ; and 3 ) a mask 805 that identifies which sub - fields of the data field 803 store an updated depth value portions for the predetermined number of consecutive pixels . the mask 805 may include a bits corresponding to each of the sub - fields of the data field 803 , wherein the bit being set (` 1 `) indicates that the corresponding sub - field stores an updated depth value portion and the bit being cleared (` 0 `) indicates that the corresponding sub - field does not store an updated depth value portion . for example , the mask may be is set is set to ` 1111 ` as shown indicating that all four sub - fields of the data field 803 store an updated depth value portion . the segments of the z buffer write signal that correspond to the less significant portions of the depth value z b at the predetermined number of consecutive pixels share this same format . upon receiving the z buffer write signal , the z buffer 214 updates the block ( s ) of data identified by the pixel address encoded in the write signal . the z buffer 214 preferably updates such block ( s ) by overwriting only those portion ( s ) of the block ( s ) identified by the mask encoded in the signal with the updated portion ( s ) of such block ( s ) encoded in the signal . the write sorter 305 in this alternate embodiment preferably operates as illustrated in the following pseudo - code : __________________________________________________________________________writer sorter -------------------------------------------------- w0 : while ( requests exist in sorter ) { send address and rgba data to frame buffer ; sort z write requests by pixel address ; for set of consecutive pixels { build z buffer write signal ; send z buffer write signal to z buffer } } go to w0 ; __________________________________________________________________________ as described above , the fetch sorter 307 fetches from the z buffer 214 the portions of the depth value z b that are associated with one or more pixels according to a request supplied by the comparison logic 303 . preferably , the fetch sorter 307 generates a z buffer read signal that identifies one or more pixels and the portion of the depth value z b at the one or more pixels that is to be retrieved . the fetch sorter 307 then forwards the z buffer read signal to the z buffer 214 via data path 311 . preferably , the z buffer read signal includes an address field that identifies the z buffer entry that holds the portion of the of the depth value z b at the one or more pixels that is to be retrieved . upon receiving the z buffer read signal , the z buffer 214 preferably retrieves the z buffer entry identified by the address field of the z buffer read signal , and forwards the entry to the fetch sorter 307 via data path 309 . in some instances , the portions of the most recent z b value of a pixel may not be stored in the z buffer 214 , but may be stored in write sorter 305 . thus , it is necessary that the fetch sorter 307 check whether the correct portion of the z b data corresponding to a given pixel is stored in the write sorter 305 , and if so grab that portion from the write sorter 305 . in this case , the fetch sorter 307 preferably operates as illustrated in the following pseudo - code : __________________________________________________________________________fetch sorter -------------------------------------------------- f0 : while ( requests exist in sorter ) { sort z fetch requests by pixel address ; form mask identifying fetched portions to update ; if portion to be updated present in write sorter { grab it from write sorter ; } send z buffer read signal to z buffer ; substitute portions grabbed from write sorter for the fetched portions ; send updated portions identified by mask to comparison logic ; } go to f0 ; __________________________________________________________________________ the comparison logic 303 of the present invention as described may have a pipelined architecture to reduce the processing time associated with the compare operations for the corresponding z value portions . in this case , a first stage processes the most significant portions znew n , zold n , and a second stage processes the next significant portions znew n - 1 , zold n - 1 , . . . . moreover , the comparison logic 303 of the present invention as described may include prediction logic that predicts the outcome of such compare operations , and controls the fetch sorter 307 to fetch the appropriate data based upon such predictions . in this case , the fetched data may or may not be used depending upon the actual resolution of such compare operations . in addition , the present invention as described above may be adapted to perform alpha blending operations . in this case , the frame buffer write operation performed by the write sorter 305 may require a frame buffer read operation that reads the rgba data of the given pixel stored in the frame buffer and a blending operation that blends the rgb data read from the frame buffer according to the alpha blending data a read from the frame buffer . alternatively , the frame buffer may perform the such operations internally . the advantages of the present invention is evident from the following example . consider the situation presented above where z eye is bounded by two planes z near = 10 . 0 and z far = 1000000 . 0 and wherein z eye is mapped to z b as set forth in the table above . consider two objects which have z eye of - 500 and - 525 . the upper byte of the respective z b values is 0 × fa and 0 × fb respectively . in this case , the visibility determination operation can be done by comparing the upper byte and ignoring the two lower bytes . consider another two objects which have z eye of - 10 . 85 and - 10 . 90 . the upper byte of the respective z b values is 0 × 14 and 0 × 15 respectively . again , in this case , the visibility determination operation can be done by comparing the upper byte and ignoring the two lower bytes . thus , for objects closer to the eye , even small differences can be disambiguated by comparing only the upper byte , and avoiding a compare operation of all three bytes of z b . if the upper bytes of the two depths match , then the next byte has to be looked at and so on till the least significant byte is reached . in addition , z near and z far may be varied from those values discussed above . fig7 ( a ) and ( b ) illustrate the effect of varying z near and keeping z far fixed at 10000 . 0 . in fig7 ( a ) and 7 ( b ), the z near value is varied from 100 . 0 to 200 . in fig7 ( a ) and ( b ), the x axis shows the upper byte portion of z b , the y axis shows z near , and the z axis shows the corresponding z eye value . in fig7 ( a ), the upper byte varies from 0 × 00 to 0 × 80 . in fig7 ( b ), the upper byte varies from 0 × 00 to 0 × ff . thus , as the value for z near is increased , more and more of the range of z eye is covered by checking the upper byte portion of z b . below is a table of z near , z far and z eye for two particular values of z b ( 0 × 0f0000 and 0 × ff0000 ). ______________________________________ z . sub . eye for z . sub . eye forz . sub . near z . sub . far z . sub . b = 0x0f0000 z . sub . b = 0xff0000______________________________________1 . 0 1000000 . 0 - 1 . 06 - 255 . 9410 . 0 1000000 . 0 - 10 . 62 - 2553 . 52100 . 0 1000000 . 0 - 1006 . 22 - 24963 . 761000 . 0 1000000 . 0 - 10062 . 17 - 203986 . 56______________________________________ clearly , the analysis present above can be extended to view situation where the visibility determination may be performed utilized the upper two bytes of the z b values . the present invention is also applicable to systems that perform parallel projections . in these systems , in these systems , z eye and z b are linearly related . thus , in order to perform visibility determination based solely on the upper byte values , the separation in z eye should be ( z far - z near )/( 2 ** 16 ). the nature of gains for a parallel projection are therefore different from those for a perspective projection . there is no extra benefit for objects close to the z near plane . however , parallel projections , which are used for architectural drawings of buildings and parts are utilized less often than perspective projections . in such cases , the z far value need not be at infinity , and bounds for z far and z near can be tightened such that ( z far - z near )/( 2 ** 16 ) is small . moreover , in these cases the depth complexity can be expected to be much higher than 2 , which results in significant performance gains when utilizing the visibility determination scheme of the present invention . other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein . it is intended that the specification and examples be considered as examples only , with the true scope of the invention being indicated by the claims .