Abstract:
A method for control over the level of detail within a rendered object is provided. The method may be a program embodied on a machine readable medium. The method identifies a set of parent vertices defining a polygon within a rendered object. A child vertex of the set of parent vertices is generated and pushed toward a predetermined location within the anticipated contours of the rendered object. One of the parent vertices is then connected to the child vertex to generate an additional polygon. A graphics engine configured to control a level of detail in a rendered object through the generation of additional polygons in the rendered object is also provided.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation and claims the priority benefit of U.S. patent application Ser. No. 10/267,234, entitled “System and Method for Point Pushing to Render Polygons in Environments with Changing Levels of Detail,” filed on Oct. 8, 2002 and now U.S. Pat. No. 7,081,893, which claims the priority benefit of U.S. Provisional Patent Application No. 60/328,453, entitled “Point Pushing Method for Calculating Resolution,” filed on Oct. 10, 2001. The subject matter of the related applications is hereby incorporated by reference. The related applications are commonly assigned. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to computer graphics and more specifically to a system and method for generating additional polygons within the contours of a rendered object to control levels of detail. 
     2. Description of the Background Art 
     The resolution of a rendered object generally relates to the number of polygons used to generate that object. A rendered object that contains a greater number of polygons over a given area typically has a higher resolution than an object that contains fewer polygons over the same area. 
     Graphics engines or graphics software typically implement a technique known as “stripping” when rendering objects. Stripping is a method of generating polygons that enables processors, usually central processing units and graphics processing units, to generate large numbers of polygons while using relatively little processing power. Stripping thereby allows graphics engines or graphics software to render higher resolution objects more quickly and inexpensively. For this reason, producing high resolution graphics for video games and other computer programs and applications that utilize stripping algorithms is simpler and less expensive than producing high resolution graphics for games, programs and applications that do not utilize stripping algorithms. 
     Stripping generally entails linking polygons in a strip such that a graphics engine or graphics software can generate an additional polygon simply by creating new vertices off one end of the strip and connecting those new vertices to the vertices of the last polygon on that end the strip. The additional polygon and the polygon that was last in the strip share the vertices to which the graphics engine or graphics software connected the new vertices. A triangle is the most commonly used polygon in stripping algorithms because a graphics engine or graphics software can render an additional triangle in a strip by creating only one new vertex and connecting that vertex to each of two vertices of the last triangle in the strip. 
     When rendering objects, graphics engines or graphics software also typically divide an image screen into different arrays of polygons, sometimes referred to as “meshes.” At any given time, a particular mesh has one or more levels of resolution or levels of detail (LOD) that correspond to the different levels of resolution of the parts of the rendered object(s) represented in the mesh. A higher LOD area of a mesh contains both smaller polygons and a greater number of polygons than a lower LOD area of the mesh contains. The boundary between a higher LOD area of a mesh and a lower LOD area of a mesh is referred to as an “LOD boundary.” 
     When an LOD boundary intersects one of the polygons in a mesh, the graphics engine or graphics software generates additional polygons on the higher LOD side of the LOD boundary to add detail to that part of the mesh. The area of intersection between the LOD boundary and a side of one of the additional polygons is referred to as a “T-junction.” The result is that only part of the original polygon resides on the lower LOD side of the T-junction (referred to as the “low resolution patch”) and several smaller polygons reside on the higher LOD side of the T-junction (referred to as the “high resolution patch”). Frequently, the low resolution patch and the high resolution patch do not align properly, causing a “crack” in the screen image. A crack is where part of a background image appears in a higher resolution part of a rendered object. This same phenomenon also can occur when a graphics engine or graphics software removes detail from part of a mesh located on a lower LOD side of an LOD boundary. 
     Several schemes exist that address the T-junction problem described above. These prior art solutions, however, tend to compromise the ability of the graphics engine or graphics software to perform stripping. The consequence is that systems designed to address the T-junction problem lose the efficiencies of stripping and therefore produce lower resolution graphics, and systems that preserve stripping frequently produce graphics that show cracks. 
     SUMMARY OF THE INVENTION 
     One embodiment of the present invention provides for controlling a level of detail in a rendered object comprises a graphics engine configured to generate additional polygons in the rendered object. The graphics engine identifies a set of parent vertices defining a polygon within the rendered object. The graphics engine generates a child vertex of the set of the parent vertices. The child vertex is pushed by the graphics engine toward a predetermined location within the anticipated contours of the rendered object. To generate an additional polygon, the graphics engine connects one of the parent vertices to the child vertex. The additional polygon is associated with the level of detail in the rendered object. 
     The graphics engine may connect the child vertex to another child vertex to generate a second additional polygon. The child vertex may be identified as one of the parent vertices of the additional polygon. Additional polygons may be generated if the rendered object moves into an area having a higher level of detail. The graphics engine may use a stripping algorithm to generate the additional polygon. The graphics engine may remove a polygon from the rendered object by pushing one of the parent vertices of the polygon towards another of the parent vertices. 
     A method for controlling a level of detail within the rendered object may be a program embodied on a machine readable medium. The method begins by identifying a set of parent vertices defining a polygon within a rendered object. The next steps comprise generating a child vertex of the set of parent vertices and pushing the child vertex toward a predetermined location within the anticipated contours of the rendered object. Next, the method involves connecting one of the parent vertices to the child vertex to generate an additional polygon. The additional polygon is associated with the level of detail in the rendered object. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of one embodiment of an electronic entertainment system, according to the invention; 
         FIG. 2  is a diagram illustrating the relationship between parent vertices and child vertices of a rendered polygon, according to one embodiment of the invention; 
         FIGS. 3A and 3B  are diagrams illustrating how a graphics engine uses parent vertices and child vertices to add detail to a rendered object as described in conjunction with  FIG. 2 ; 
         FIG. 4  is diagram illustrating a point pushing technique rule, according to one embodiment of the invention; 
         FIG. 5A  is a diagram illustrating one embodiment of a mesh located in a low LOD area of an image screen, according to the invention; 
         FIG. 5B  is a diagram illustrating the mesh of  FIG. 5A  when located in a high LOD area of an image screen as well as the graphics engine&#39;s application of the point pushing technique rule to remove detail from a low LOD area of the mesh, according to one embodiment of the invention; 
         FIG. 6  is a diagram illustrating the migration of the child vertices of  FIG. 5B  to the predetermined parent vertices of  FIG. 5B ; 
         FIG. 7  is a diagram illustrating further migration of the child vertices of  FIG. 5B  to the predetermined parent vertices of  FIG. 5B ; and 
         FIG. 8  is a flowchart of method steps for pushing child vertices to predetermined parent vertices to remove detail from an array of polygons, according to one embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a block diagram of one embodiment of an electronic entertainment system  100 , according to the invention. System  100  includes, but is not limited to, a main memory  110 , a central processing unit (CPU)  112 , vector processing units VU 0   111  and VU 1   113 , a graphics processing unit (GPU)  114 , an input/output processor (IOP)  116 , an IOP memory  118 , a controller interface  120 , a memory card  122 , a Universal Serial Bus (USB) interface  124  and an IEEE 1394 interface  126 . System  100  also includes an operating system read-only memory (OS ROM)  128 , a sound processing unit (SPU)  132 , an optical disc control unit  134  and a hard disc drive (HDD)  136 , which are connected via a bus  146  to IOP  116 . System  100  is preferably an electronic gaming console; however, system  100  may also be implemented as any type of general-purpose computer, set-top box or hand-held gaming device. 
     CPU  112 , VU 0   111 , VU 1   113 , GPU  114  and IOP  116  communicate via a system bus  144 . CPU  112  communicates with main memory  110  via a dedicated bus  142 . VU 1   113  and GPU  114  may also communicate via a dedicated bus  140 . CPU  112  executes programs stored in OS ROM  128  and main memory  110 . Main memory  110  may contain prestored programs and may also contain programs transferred via IOP  116  from a CD-ROM, DVD-ROM or other optical disc (not shown) using optical disc control unit  134 . IOP  116  controls data exchanges between CPU  112 , VU 0   111 , VU 1   113 , GPU  114  and other devices of system  100 , such as controller interface  120 . 
     GPU  114  executes drawing instructions from CPU  112  and VU 0   111  to produce images for display on a display device (not shown). VU 1   113  transforms objects from three-dimensional coordinates to two-dimensional coordinates, and sends the two-dimensional coordinates to GPU  114 . SPU  132  executes instructions to produce sound signals that are output on an audio device (not shown). In one embodiment of the invention, GPU  114 , CPU  112  and certain graphics software in main memory  110  operate in conjunction as a “graphics engine.” 
     A user of system  100  provides instructions via controller interface  120  to CPU  112 . For example, the user may instruct CPU  112  to store certain game information on memory card  122  or may instruct a character in a game to perform some specified action. Other devices may be connected to system  100  via USB interface  124  and IEEE 1394 interface  126 . 
       FIG. 2  is a diagram illustrating the relationship between parent vertices and child vertices of a rendered polygon  210 , according to one embodiment of the invention. As shown, polygon  210  is a triangle, but in other embodiments polygon  210  can be any type of polygon. Polygon  210  has three parent vertices  212 ,  214  and  216 , each of which is a vertex of polygon  210 . In addition, polygon  210  has three child vertices  218 ,  220  and  222 , each of which is a point located on one of the sides of polygon  210  such that each set of two parent vertices has one child vertex. For example, child vertex  218  is the child of parent vertices  212  and  216 , child vertex  220  is the child of parent vertices  212  and  214  and child vertex  222  is the child of parent vertices  214  and  216 . The arrows shown in  FIG. 2  point to the parent vertices of each of child vertices  218 ,  220  and  222 . In one embodiment of the invention, a child vertex is the midpoint between its two parent vertices. 
     Generally speaking, the graphics engine can use parent vertices and child vertices to add detail to or to remove detail from a rendered object (or part of a rendered object). For example, when adding detail, the graphics engine first generates a child vertex for each set of parent vertices of each polygon in the rendered object. The graphics engine then pushes or moves each child vertex to a predetermined location within the anticipated contours of the rendered object (such child vertex movement is referred to as “migration”). The graphics engine also generates additional polygons-within the contours of the rendered object by connecting the child vertices to each other as well as to the parent vertices. The graphics engine can use a stripping algorithm or some other method to generate the additional polygons. Each child vertex becomes a vertex of one or more of the additional polygons and, therefore, a parent vertex of each such additional polygon. The result is that the rendered object is comprised of both smaller polygons and a greater number of polygons than it was comprised of originally, thereby giving the rendered object a higher level of detail than it had originally. 
     When adding yet more detail to the rendered object, the graphics engine repeats the process described above. The only difference is that the rendered object now contains more polygons. The graphics engine first generates a child vertex for each set of parent vertices of each polygon in the rendered object. The graphics engine then causes each child vertex to migrate to a predetermined location within the anticipated contours of the rendered object. The graphics engine again generates additional polygons within the contours of the rendered object by connecting the child vertices to each other as well as to the parent vertices. Again, each child vertex becomes a parent vertex of one or more of the additional polygons. The result is that the rendered object is comprised of both smaller polygons and a greater number of polygons than it was comprised of after adding the first level of detail, thereby giving the rendered object a higher level of detail than it had after adding the first level of detail. 
       FIGS. 3A and 3B  are diagrams illustrating how the graphics engine uses parent vertices and child vertices to add detail to a rendered object  310  as described in conjunction with  FIG. 2 . More specifically,  FIG. 3A  illustrates the graphics engine&#39;s adding detail as rendered object  310  moves from a low LOD area of an image screen to an intermediate LOD area. As shown, rendered object  310  appears as a square in the low LOD area. For simplicity of illustration, assume that one can model rendered object  310  as a single polygon having four parent vertices  312 ,  314 ,  316  and  318 . 
     As rendered object  310  moves in the image screen from the low LOD area to the intermediate LOD area, the graphics engine adds detail to rendered object  310 . As discussed in conjunction with  FIG. 2 , to add the necessary detail, the graphics engine first generates child vertices  320 ,  322 ,  324  and  326  such that each set of parent vertices of rendered object  310  has a child vertex. For example, child vertex  320  is the child of parent vertices  312  and  314 , child vertex  322  is the child of parent vertices  314  and  316 , child vertex  324  is the child of parent vertices  316  and  318  and child vertex  326  is the child of parent vertices  312  and  318 . 
     The graphics engine then moves each child vertex to a predetermined location within the anticipated contours of rendered object  328 . Migration paths  330 ,  332 ,  334  and  336  show the paths over which the graphics engine moves each of child vertices  320 ,  322 ,  324  and  326 , respectively. 
     The graphics engine also generates additional polygons within the contours of rendered object  310  to provide rendered object  310  with the requisite amount of additional detail. For simplicity of illustration,  FIG. 3A  shows only the sides of the additional polygons that constitute connections between child vertices  320 ,  322 ,  324  and  326  and parent vertices  312 ,  314 ,  316  and  318 . The result is a rendered object  328 , an octagon, that has more detail than rendered object  310 , a square. 
       FIG. 3B  illustrates the graphics engine&#39;s adding detail as rendered object  328  moves from the intermediate LOD area of the image screen to a high LOD area. As shown, rendered object  328  appears as an octagon in the intermediate LOD area. Again, for simplicity of illustration, assume that one can model rendered object  328  as a single polygon having eight parent vertices  312 ,  314 ,  316 ,  318 ,  320 ,  322 ,  324  and  326 . 
     As rendered object  328  moves in the image screen from the intermediate LOD area to the high LOD area, the graphics engine adds detail to rendered object  328 . Again, to add the necessary detail, the graphics engine first generates child vertices  338 ,  340 ,  342 ,  344 ,  346 ,  348 ,  350  and  352  such that each set of parent vertices of rendered object  328  has a child vertex. For example, child vertex  338  is the child of parent vertices  312  and  320 , child vertex  340  is the child of parent vertices  314  and  320 , child vertex  342  is the child of parent vertices  314  and  322 , child vertex  344  is the child of parent vertices  316  and  322 , child vertex  346  is the child of parent vertices  316  and  324 , child vertex  348  is the child of parent vertices  318  and  324 , child vertex  350  is the child of parent vertices  318  and  326  and child vertex  352  is the child of parent vertices  312  and  326 . 
     The graphics engine then moves each child vertex to a predetermined location within the anticipated contours of rendered object  354 . Migration paths  356 ,  358 ,  360 ,  362 ,  364 ,  366 ,  368  and  370  show the paths over which the graphics engine moves each of child vertices  338 ,  340 ,  342 ,  344 ,  346 ,  348 ,  350  and  352 , respectively. 
     Again, the graphics engine also generates additional polygons within the contours of rendered object  328  to provide rendered object  328  with the requisite amount of additional detail. For simplicity of illustration,  FIG. 3B  shows only the sides of the additional polygons that constitute connections between child vertices  338 ,  340 ,  342 ,  344 ,  346 ,  348 ,  350  and  352  and parent vertices  312 ,  314 ,  316 ,  318 ,  320 ,  322 ,  324  and  326 . The result is a rendered object  354 , a sixteen-sided polygon, that has more detail than rendered object  328 , an octagon. 
     The graphics engine can remove detail from either rendered object  354  or rendered object  328  by simply reversing the steps described above. For example, if rendered object  354  moves from the high LOD area of the image screen to the intermediate LOD area, the graphics engine can reverse the steps set forth in conjunction with  FIG. 3B  to remove detail from rendered object  354  and transform rendered object  354  into rendered object  328 . Likewise, if rendered object  328  moves from the intermediate LOD area of the image screen to the low LOD area, the graphics engine can reverse the steps set forth in conjunction with  FIG. 3A  to remove detail from rendered object  328  and transform rendered object  328  into rendered object  310 . 
     The examples set forth in conjunction with  FIGS. 3A and 3B  parallel a situation where a circular object, such as a car tire, is a rendered object in an image screen, and the car tire moves among different LOD areas of the image screen. When the car tire is in the background of the overall image, the car tire resides in the low LOD area of the image screen. The image system shows the car tire as a square because the car tire is so small relative to the rest of the image that an image system user is unable to distinguish between a square and a circle. The square car tire therefore appears circular to the user. 
     As the car tire moves more into the foreground of the overall image, the car tire resides in the intermediate LOD area of the image screen. Here, the image system has to present the car tire with more detail because the car tire is larger relative to the rest of the image, enabling the image system user to see the car tire more clearly. For this reason, the image system presents the car tire as an octagon with more detail than the square version of the car tire. 
     As the car tire continues to move farther into the foreground of the overall image, the car tire resides in the high LOD area of the image screen. Here, the image system has to present the car tire with even more detail than the octagon version of the car tire because the car tire is larger and more clearly seen by the image system user than the octagon version. The image system therefore presents the car tire as a sixteen-sided polygon with more detail than the octagon version of the car tire. As the car tire moves closer and closer to the image system user, the graphics engine represents the car tire as a polygon with an increasing number of sides and amount of detail. In the limit, the shape of the car tire approaches that of an actual circle. 
       FIG. 4  is diagram illustrating a point pushing technique rule, according to one embodiment of the invention. As shown, three polygons  410 ,  430  and  450  are displayed in an image screen  400 . Polygon  410  has three parent vertices  418 ,  420  and  422  and three child vertices  412 ,  414  and  416 . Polygon  430  has three parent vertices  438 ,  440  and  442  and three child vertices  432 ,  434  and  436 . Polygon  450  has three parent vertices  458 ,  460  and  462  and three child vertices  452 ,  454  and  456 . An LOD boundary  405  divides-image screen  400  into a low LOD area and a high LOD area. 
     The point pushing technique rule, according to one embodiment of the invention, is as follows. If both parent vertices of a child vertex reside on the low LOD side of the LOD boundary, the graphics engine pushes or moves that child vertex to one of its parent vertices. The system implementing the rule predetermines the parent vertex to which the graphics engine pushes the child vertex (referred to as the “predetermined parent vertex”). If, however, either of the parent vertices of a child vertex resides on the high LOD side of the LOD boundary, the graphics engine does not push or move that child vertex—rather, that child vertex remains in its original position. 
     The point pushing technique rule applies to polygon  410  as follows. The parents of child vertex  412 , parent vertices  418  and  422 , both reside on the low LOD side of LOD boundary  405 . According to the rule, the graphics engine pushes child vertex  412  to predetermined parent vertex  418 , as the arrow in  FIG. 4  depicts. The parents of child vertex  414 , parent vertices  418  and  420 , both reside on the low LOD side of LOD boundary  405 . According to the rule, the graphics engine pushes child vertex  414  to predetermined parent vertex  418 , as the arrow in  FIG. 4  depicts. The parents of child vertex  416 , parent vertices  420  and  422 , both reside on the low LOD side of LOD boundary  405 . Again, according to the rule, the graphics engine pushes child vertex  416  to predetermined parent vertex  420 , as the arrow in  FIG. 4  depicts. 
     The point pushing technique rule applies to polygon  430  as follows. The parents of child vertex  434 , parent vertices  438  and  440 , both reside on the low LOD side of LOD boundary  405 . According to the rule, the graphics engine pushes child vertex  434  to predetermined parent vertex  440 , as the arrow in  FIG. 4  depicts. The parents of child vertex  436 , parent vertices  440  and  442 , reside on opposite sides of LOD boundary  405 . According to the rule, child vertex  436  does not move, remaining in its original position. Similarly, the parents of child vertex  432 , parent vertices  438  and  442 , reside on opposite sides of LOD boundary  405 . According to the rule, child vertex  432  also does not move, remaining in its original position. 
     The point pushing technique rule applies to polygon  450  as follows. The parents of child vertex  452 , parent vertices  458  and  462 , both reside on the high LOD side of LOD boundary  405 . According to the rule, child vertex  452  does not move, remaining in its original position. The parents of child vertex  454 , parent vertices  458  and  460 , both reside on the high LOD side of LOD boundary  405 . According to the rule, child vertex  454  does not move, remaining in its original position. The parent vertices of child vertex  456 , parent vertices  460  and  462 , both reside on the high LOD side of LOD boundary  405 . Again, according to the rule, child vertex  456  also does not move, remaining in its original position. 
     As discussed in conjunction with  FIGS. 3A and 3B , when a rendered object moves from a high LOD to a low LOD area in the image screen, the graphics engine removes detail from the rendered object. The graphics engine accomplishes this objective by removing polygons from the rendered object until the rendered object has an amount of detail commensurate with the low LOD. 
     Related to the foregoing, when a rendered object moves in an image screen, differing types of LOD boundaries intersect the arrays of polygons or meshes into which the graphics engine has divided the image screen. In a situation where a particular mesh initially resides in a high LOD area of the image screen, and then a rendered object moves, causing an LOD boundary to divide the mesh into a low LOD area and a high LOD area, the graphics engine has to remove detail from the low LOD area of the mesh. Similar to removing detail from a rendered object, the graphics engine removes detail from the low LOD area of the mesh by removing polygons in that area until that part of the mesh has an amount of detail commensurate with the low LOD. 
     The discussion set forth below in conjunction with  FIGS. 5A ,  5 B,  6  and  7  discloses how the graphics engine uses the point pushing method of the present invention to remove detail from any area of an array of polygons while (i) avoiding the T-junction problem described above in conjunction with the prior art and (ii) preserving the graphics engine&#39;s ability to generate polygons through stripping. 
       FIG. 5A  is a diagram illustrating one embodiment of a mesh  500  located in a low LOD area of an image screen, according to the invention. Mesh  500  is one embodiment of an array of polygons arranged in horizontal and vertical strips. As shown, mesh  500  contains three horizontal strips of polygons  502 ,  504  and  506  and four vertical strips of polygons  508 ,  510 ,  512  and  514 . Parent vertices of the various polygons also are shown. For example, parent vertices  516 ,  518  and  522  are the vertices of one polygon, parent vertices  518 ,  520  and  522  are the vertices of one polygon, parent vertices  524 ,  526  and  530  are the vertices of one polygon, parent vertices  526 ,  528  and  530  are the vertices of one polygon, parent vertices  532 ,  534  and  538  are the vertices of one polygon and parent vertices  534 ,  536  and  538  are the vertices of yet another polygon. 
       FIG. 5B  is a diagram illustrating mesh  500  of  FIG. 5A  when located in a high LOD area of an image screen as well as the graphics engine&#39;s application of the point pushing technique rule to remove detail from a low LOD area of mesh  500 , according to one embodiment of the invention. As shown, mesh  500  contains six horizontal strips of polygons  539 ,  540 ,  541 ,  542 ,  543  and  544  and eight vertical strips of polygons  545 ,  546 ,  547 ,  548 ,  549 ,  550 ,  551  and  552  when located in the high LOD area of the image screen. As seen by comparing  FIGS. 5A and 5B , mesh  500  contains both smaller polygons and a greater number of polygons when located in the high LOD area of the image screen as compared to when located in the low LOD area. For this reason, mesh  500  shows more detail when located in the high LOD area of the image screen than when located in the low LOD area of the image screen. 
     More specifically,  FIG. 5B  shows that mesh  500  contains four times as many polygons when located in the high LOD area of the image screen than when located in the low LOD area. The graphics engine generates the polygons such that, in the high LOD area, mesh  500  effectively contains four polygons for every one of the polygons depicted in  FIG. 5A  (each referred to as an “original polygon”). For example, the graphics engine effectively has replaced the original polygon defined by vertices  516 ,  518  and  522  (as seen in  FIG. 5A ) with the polygon defined by vertices  516 ,  554  and  562 , the polygon defined by vertices  554 ,  518  and  560 , the polygon defined by vertices  554 ,  560  and  562  and the polygon defined by vertices  562 ,  560  and  522 . Likewise, the graphics engine effectively has replaced the original polygon defined by vertices  526 ,  528  and  530  (as seen in  FIG. 5A ) with the polygon defined by vertices  526 ,  566  and  570 , the polygon defined by vertices  570 ,  566  and  568 , the polygon defined by vertices  570 ,  568  and  530  and the polygon defined by vertices  566 ,  528  and  568 . 
       FIG. 5B  also shows the child vertex of each set of parent vertices of each of the original polygons. For example, child vertex  554  is the child of parent vertices  516  and  518 , child vertex  556  is the child of parent vertices  518  and  520 , child vertex  558  is the child of parent vertices  520  and  522 , child vertex  560  is the child of parent vertices  518  and  522  and child vertex  562  is the child of parent vertices  516  and  522 . Similarly, child vertex  564  is the child of parent vertices  524  and  526 , child vertex  566  is the child of parent vertices  526  and  528 , child vertex  578  is the child of  536  and  538 , child vertex  580  is the child of parent vertices  534  and  538  and child vertex  582  is the child of parent vertices  532  and  538 . 
     Also shown in  FIG. 5B  is an LOD boundary  553  that intersects mesh  500  to create a low LOD area on one side of LOD boundary  553  and a high LOD area on the other side of LOD boundary  553 . As discussed in more detail in conjunction with  FIGS. 6 and 7 , the graphics engine uses the point pushing method of the present invention to remove detail from the low LOD area of mesh  500 . The arrows depicted in  FIG. 5B  indicate the predetermined parent vertex to which the graphics engine pushes each child vertex according to one embodiment of the point pushing technique rule. For example, according to the rule, the graphics engine pushes child vertex  554  to predetermined parent vertex  518  because both parent vertices  516  and  518  reside on the low LOD side of LOD boundary  553 . Similarly, according to the rule, the graphics engine pushes child vertex  574  to predetermined parent vertex  534  because both parent vertices  532  and  534  reside on the low LOD side of LOD boundary  553 . By contrast, according to the rule, child vertex  570  remains in its original position because parent vertex  526  resides on the low LOD side of LOD boundary  553  and parent vertex  530  resides on the high LOD side of LOD boundary  553 . Similarly, according to the rule, child vertex  578  remains in its original position because both parent vertices  536  and  538  reside on the high LOD side of LOD boundary  553 . 
       FIG. 6  is a diagram illustrating the migration of the child vertices of  FIG. 5B  to the predetermined parent vertices of  FIG. 5B . As shown, the graphics engine has pushed certain child vertices located in the low LOD area of mesh  500  partly towards their respective predetermined parent vertices as dictated by the point pushing technique rule applied to mesh  500  as shown in  FIG. 5B . For example, as both indicated in  FIG. 5B  and shown in  FIG. 6 , the graphics engine has pushed child vertex  562  towards predetermined parent vertex  516 , child vertices  554 ,  556  and  560  towards predetermined parent vertex  518 , child vertex  558  towards predetermined parent vertex  520 , child vertex  564  towards predetermined parent vertex  526  and child vertex  574  towards predetermined parent vertex  534 . As also indicated in  FIG. 5B  and shown in  FIG. 6 , child vertices  566 ,  568 ,  570  and  572  as well as child vertices  576 ,  578 ,  580  and  582  remain in their original positions because either one (or both) of the parent vertices of each of these child vertices resides on the high LOD side of LOD boundary  553 . 
     As seen in  FIG. 6 , as certain child vertices in the low LOD area of mesh  500  migrate towards their respective predetermined parent vertices, portions of strips  539 ,  541 ,  546 ,  548 ,  550  and  552  become narrower as many of the polygons in these strips begin to collapse. By contrast, portions of strips  540 ,  542 ,  545 ,  547 ,  549  and  551  simultaneously become wider. The result is that the polygons located at the intersections of strips  540  and  545 , strips  542  and  545 , strips  540  and  547 , strips  542  and  547 , strips  540  and  549 , strips  542  and  549  and strips  540  and  551  increase in size as these polygons fill the space relinquished by the collapsing polygons. The consequence of this phenomenon is that larger and fewer polygons begin to dominate the low LOD area of mesh  500 , which decreases the amount of detail in that area of mesh  500 . 
     Importantly,  FIG. 6  shows that the graphics engine preserves the integrity of each strip in mesh  500  as the various child vertices migrate towards their respective predetermined parent vertices. Although several of the polygons in the strips have not retained their original shapes as right triangles, each strip nonetheless keeps its shape from one end of mesh  500  to the other. 
     Further, the point pushing method of the present invention enables the graphics engine to collapse polygons in the low LOD area of mesh  500  without creating or using T-junctions at the LOD boundary.  FIG. 6  shows that point pushing causes several transition polygons to form along LOD boundary  553 . Polygons  610 ,  612 ,  614 ,  616 ,  618 ,  620 ,  622 ,  624 ,  626 ,  628 ,  630  and  632  are examples of transition polygons. These transition polygons straddle LOD boundary  553  to create a small and effective transition area between the polygons in the low LOD area of mesh  500  and the polygons in the high LOD area. No cracks appear in the image screen because the transition polygons completely fill the transition area, thereby eliminating T-junctions at the boundary between the high resolution patch and the low resolution patch where the patches share vertices. By using the point pushing technique, the graphics engine avoids having to align a high resolution patch and a low resolution patch, the misalignment of which is a frequent source of cracks. 
       FIG. 7  is a diagram illustrating the further migration of the child vertices of  FIG. 5B  to the predetermined parent vertices of  FIG. 5B . As shown, the graphics engine has pushed certain child vertices located in the low LOD area of mesh  500  much closer to their respective predetermined parent vertices as dictated by the point pushing technique rule. For example, as seen in  FIG. 7 , the graphics engine has pushed child vertex  562  closer to predetermined parent vertex  516 , child vertices  554 ,  556  and  560  closer to predetermined parent vertex  518 , child vertex  558  closer to predetermined parent vertex  520 , child vertex  564  closer to predetermined parent vertex  526  and child vertex  574  closer to predetermined parent vertex  534 . Again, as also shown in  FIG. 6 , child vertices  566 ,  568 ,  570  and  572  as well as child vertices  576 ,  578 ,  580  and  582  continue to remain in their original positions because either one (or both) of the parent vertices of each of these child vertices resides on the high LOD side of LOD boundary  553 . 
     As seen in  FIG. 7 , as certain child vertices in the low LOD area of mesh  500  migrate further towards their respective predetermined parent vertices, strips  539 ,  541 ,  546 ,  548 ,  550  and  552  become even narrower as many of the polygons in those strips collapse even further. Again, by contrast, strips  540 ,  542 ,  545 ,  547 ,  549  and  551  simultaneously become even wider. The polygons located at the intersections of strips  540  and  545 , strips  542  and  545 , strips  540  and  547 , strips  542  and  547 , strips  540  and  549 , strips  542  and  549  and strips  540  and  551  continue to increase in size as these polygons continue to fill the space relinquished by the collapsing polygons. The continued consequence of this phenomenon is that a few large polygons dominate the low LOD area of mesh  500 , which decreases even further the amount of detail in that area of mesh  500 . 
     One can see from  FIG. 7  that the graphics engine continues to preserve the integrity of each strip as the migration of the child vertices towards their respective predetermined parent vertices continues. One also can see that when the various child vertices complete their migrations, many of the polygons in strips  539 ,  541 ,  546 ,  548 ,  550  and  552  will collapse fully and disappear. The result is that the low LOD area of mesh  500  will look substantially similar to mesh  500  as depicted in  FIG. 5A  (when all of mesh  500  is located in the low LOD area of the image screen). Further, the high LOD area of mesh  500  will look substantially similar to mesh  500  as depicted in  FIG. 5B  (when all of mesh  500  is located in the high LOD area of the image screen). Lastly, as discussed above in conjunction with  FIG. 6 , once the child vertices complete their migrations, transition polygons will reside between the polygons in the low LOD area of mesh  500  and the polygons in the high LOD area, creating a continuous transition area without cracks. The consequence is that no T-junctions will exist at the boundary between the high resolution patch and the low resolution patch where the patches share vertices. 
       FIG. 8  is a flowchart of method steps for pushing child vertices to predetermined parent vertices to remove detail from a low LOD area of an array of polygons, according to one embodiment of the invention. Although the method steps are described in the context of the graphics engine, which is a subsystem of system  100  illustrated in  FIG. 1 , any type of system, engine, processor, combination of processors or software configured to perform the method steps is within the scope of the invention. 
     As shown in  FIG. 8 , in step  810 , the graphics engine identifies an LOD boundary that divides an array of polygons into a low LOD area and a high LOD area. As discussed above in conjunction with  FIGS. 2 through 5B , these different levels of detail are measured relative to one another. In step  812 , the graphics engine identifies every child vertex in the array of polygons that resides on the low LOD side of the LOD boundary. In step  814 , the graphics engine identifies the parent vertices of each such child vertex. 
     Next, in step  816 , the graphics engine determines which, if any, of the child vertices residing on the low LOD side of the LOD boundary migrates to a parent vertex. The graphics engine uses a point pushing technique rule to make this determination. According to one embodiment of the rule, a child vertex migrates to one of its parent vertices if both parent vertices reside on the low LOD side of the LOD boundary. A child vertex does not migrate, however, if either of its parent vertices resides on the high LOD side of the LOD boundary. 
     In step  818 , for each child vertex that migrates, the graphics engine identifies the parent vertex of the child to which the graphics engine moves that child vertex. As discussed above in conjunction with  FIG. 4 , each of these parent vertices is referred to as a “predetermined parent vertex.” Lastly, in step  820 , the graphics engine pushes or moves each migrating child vertex to its respective predetermined parent vertex. 
     As described above in conjunction with  FIGS. 6 and 7 , when the child vertices complete their migrations to their respective predetermined parent vertices, the low LOD area of the array of polygons has less detail than the high LOD area. Further, the strips of polygons in the array of polygons retain their integrity, and no cracks appear between the low LOD area of the array of polygons and the high LOD area. 
     To add detail to an array of polygons located in a low LOD area of an image screen, according to another embodiment of the invention, the graphics engine essentially reverses the processes described above in conjunction with  FIGS. 5A through 8 . The graphics engine first identifies an LOD boundary that divides the array of polygons into a high LOD area and a low LOD area. The graphics engine then identifies every predetermined parent vertex on the high LOD side of the LOD boundary. The graphics engine also identifies each child vertex having the same position as any of the identified parent vertices and the other parent vertex of each such child vertex (note that the predetermined parent vertex is one of the parents of the child vertex at the same position). 
     Next, the graphics engine determines which, if any, of these child vertices migrates. The graphics engine again uses a point pushing technique rule to make this determination. In one embodiment, the point pushing technique rule dictates that a child vertex migrates if both of its parent vertices reside on the high LOD side of the LOD boundary. A child vertex does not migrate, however, if either of its parent vertices resides on the low LOD side of the LOD boundary. 
     Lastly, the graphics engine pushes each child vertex that migrates to a predetermined location. When these child vertices complete their migrations to their respective predetermined locations, the large polygons that initially resided in the high LOD area of the array of polygons will have decreased in size. Further, the graphics engine will have generated additional polygons in the high LOD area of the array of polygons by connecting the migrating child vertices to each other and to the parent vertices residing in the high LOD area. The result is that the high LOD area of the array of polygons will have both smaller polygons and a greater number of polygons than the low LOD area, which increases the amount of detail in the high LOD area. 
     Similar to when removing detail from an array of polygons, the graphics engine preserves the integrity of the strips of polygons in the array of polygons when adding detail to the high LOD area of the array. Further, the graphics engine generates transition polygons on either side of the LOD boundary, which prevents cracks from appearing between the low LOD area of the array of polygons and the high LOD area. 
     The invention has been described above with reference to specific embodiments. Persons skilled in the art, however, will understand that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention as set forth in the appended claims. For example, for simplicity of illustration, the embodiments of the invention referenced in the discussion and examples set forth above include arrays of polygons containing small numbers of polygons with simple geometries (i.e., triangles). Other embodiments of the invention, though, can include arrays of polygons containing any number of polygons with any type of shape, whether simple or complex. The foregoing description and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.