Patent Publication Number: US-6700586-B1

Title: Low cost graphics with stitching processing hardware support for skeletal animation

Description:
This application claims the benefit of U.S. Provisional Application No. 60/226,914, filed Aug. 23, 2000, the entire content of which is hereby incorporated by reference in this application. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to computer graphics, and more particularly to interactive graphics systems such as home video game platforms. Still more particularly, to systems and methods for providing skinning or stitching (e.g., to support skeletal animation/inverse kinematic techniques) in a low cost graphics system. 
     BACKGROUND AND SUMMARY OF THE INVENTION 
     Many of us have seen films containing remarkably realistic dinosaurs, aliens, animated toys and other fanciful creatures. Such animations are made possible by computer graphics. Using such techniques, a computer graphics artist can specify how each object should look and how it should change in appearance over time, and a computer then models the objects and displays them on a display such as your television or a computer screen. The computer takes care of performing the many tasks required to make sure that each part of the displayed image is colored and shaped just right based on the position and orientation of each object in a scene, the direction in which light seems to strike each object, the surface texture of each object, and other factors. 
     Because computer graphics generation is complex, computer-generated three-dimensional graphics just a few years ago were mostly limited to expensive specialized flight simulators, high-end graphics workstations and supercomputers. The public saw some of the images generated by these computer systems in movies and expensive television advertisements, but most of us couldn&#39;t actually interact with the computers doing the graphics generation. All this has changed with the availability of relatively inexpensive 3D graphics platforms such as. for example, the Nintendo 64® and various 3D graphics cards now available for personal computers. It is now possible to interact with exciting 3D animations and simulations on relatively inexpensive computer graphics systems in your home or office. 
     A problem graphics system designers have confronted is how to efficiently model and render realistic looking animations in real time or close to real time. To achieve more interesting dynamic animation, a number of video and computer games have used a technique called inverse kinematics to model animated people and animals. Inverse kinematics allows a graphics artist to model animated objects in a hierarchical way so that movement of one part of the object causes another, connected part of the object to move. 
     For example if you raise your arm, you know your hand will move with your arm, and that your fingers will move with your hand. For example, inverse kinematics allows the animator to connect the torso, upper arm, lower arm, hand and fingers of a computer model so that moving the hand will cause the lower arm to move, moving the lower arm will cause the upper arm to move, etc. This is intuitive in the real world, but not all models behave this way in the world of animation. 
     The hierarchical model of an inverse kinematics model is sometimes called a skeleton, with each part of the skeleton being called a bone. The bones don&#39;t need to accurately model real bones in terms of their shape—they can be rigid line segments. To create images using such a kinematic skeletal model, one usually attaches “skin” surfaces to each of the bones. Once the “skin” surfaces are attached, they can automatically follow the movement of the bones when the bones are moved. By modeling a human or animal as a skeleton of interconnected bones (i.e., the same way that real human beings and animals are constructed), it is possible to achieve realistic, natural-looking motion. Game animators have been able to achieve remarkably realistic animated motion using such techniques. 
     One weakness of skeletal animation is the way it handles joints between bones. Generally each bone is rigid, and its movement is defined by a transform. If the transforms cause the joint to bend, an unsightly gap can be created. For example, the elbow where the upper and lower arms of an animated character meet, or the shoulder where the character&#39;s upper arm meets its torso ought to appear as natural as possible across a wide range of motion. Unnatural gaps at these points of connection mav destroy the illusion of realism. 
     The skin and flesh of real humans and animals at the intersection (joints) between bones is actually attached to and influenced by each of the various intersecting bones. For example if you “make a muscle” by closing your elbow, you will notice that the skin and flesh of your upper arm is influenced not only by your lower arm position/movement but also by your upper arm position/movement. If surfaces in joint regions of animated models are influenced by only a single bone, then some unsightly deformations may result—degrading the realism and impact of the animation. People are relatively unforgiving when it comes to evaluating the realism of animated human models. The more realistic the animated model, the more you will notice (and perhaps be dissatisfied with) unnatural or unrealistic characteristics of the model&#39;s appearance. 
     This weakness can be overcome using a technique called skinning, which adjusts and blends the positions of the vertices around the joint to create a continuous, flexible skin covering surface that provides a smooth transition between “bones” where the bones meet one another. This transitional “skin” surface can adapt to the different relative positions of two or more intersecting “bones” across a range of positions and relative motions. The resulting effect can significantly add to the illusion of realism. 
     On a more detailed level, the skin is typically defined by a mesh of vertices. Skinning is generally accomplished by allowing the position of each vertex in the mesh to be influenced by the movement of more than one bone in the skeletal animation model. The influence of different bones can be determined by assigning them different weights in computing the skin vertex position. A model can be animated by defining the movement of its skeleton, and the movements of the vertices that define the skin can be generated automatically (e.g., mathematically) by the graphics system. 
     Mathematical functions called matrix transformations are usually used to compute the location of each vertex in each frame of a skeletal animation. A separate transformation matrix is typically used for each bone that influences a given vertex. For example, if a skin vertex is located near the intersection of two bones, two transformation matrices are usually required—one for each of the two bones that influence that vertex. In order to make joints that flex naturally, it is desirable to allow the weightings of each matrix to vary for each vertex. Different vertex weightings for each vertex around a joint allow the vertex skin mesh to blend gradually from one bone to another (“vertex skinning”). 
     Such vertex skinning techniques for modeling animated objects have been quite successful in providing a high degree of realism. Many high end animation rendering engines and modeling tools support such techniques. However, one problem with skinning is that the matrix transformations required for vertex skinning are very computationally intensive. To provide surface information for skinning/stitching, you normally need multiple interpolation points between two vertex locations. This implies the need for additional unique transformations per texture coordinate based off a single vertex specification—and unique texture transformations applied to the geometry or normal per texture. Thus, a plurality of matrix multiplications are required to accurately transform the skinning surface. The complexity increases with each additional matrix used. 
     Matrix multiplications are of course commonplace in graphics rendering systems. For example, it is common to provide matrix multiplication to transform model parameters from one space to another (e.g from modeling space to eye space) in order to project a 3D object representation onto a 2D viewing plane. However, real time systems typically minimize the number of matrix multiplications they perform. This is because each matrix multiplication can take many processor cycles if computed in software, and matrix multiplication hardware can require large amounts of “real estate” on a graphics chip. For this reason, there has not be much skinning support available in low cost real time rendering systems such as home video game platforms and inexpensive personal computer graphics accelerator cards. While the general purpose processor of such systems can be used to perform the skinning matrix multiplication calculations, such calculations are usually so time-consuming that the animator must sacrifice image complexity or speed performance if he or she wants skinning effects. 
     The present invention provides a solution to this problem In accordance with one aspect of this invention, a low cost computer graphics system includes hardware support for a more limited version of skinning called “stitching.” Stitching allows a surface to be transformed based on two per-vertex values corresponding to different vertices. An additional interpolation/matrix multiplication provides a limited (piecewise linear) version of skinning (“stitching”) that does not slow down the rendering pipeline. 
     In accordance with an aspect of this invention, a real time graphics rendering system includes a pair of matrix multiplication dot product computational elements. The first dot product computational element in the cascade can be used in a conventional manner to perform a modelview (or other) transformation. The second dot product computation element can be used to perform an additional interpolation to provide stitching. The two dot product computation elements can operate successively on the same texture coordinate values to provide transformed “stitched” texture coordinates for use in texture mapping a skin surface onto a vertex mesh. 
     In accordance with another aspect provided by this invention, a normalization block is provided between the two dot product computation units. The normalization function helps to avoid distortions that could otherwise occur under certain circumstances, e.g., when surfaces are deformed. 
     The additional dot product computation unit and associated matrix memory and the normalization block are relatively compact and do not occupy much chip real estate. They are not capable of full skinning, but a piecewise linear approximation of skinning can nevertheless be used to provide realistic interconnections between “bones” of the skeletal animation model while relieving the game animation processor from performing skinning computations. The additional matrix multiplication computation unit does not adversely impact on rendering pipeline speed performance. Pipeline latency increases can be absorbed through buffering. The system allows per-vertex specification of transform matrix indices to permit selection of different transformation matrices on a vertex-by-vertex basis. 
     The second matrix multiplication computation unit provided in the example implementation can be used for applications other than stitching. For example, various types of environment and/or reflection mapping can be performed using this additional texture coordinate matrix transformation. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features and advantages provided by the invention will be better and more completely understood by referring to the following detailed description of presently preferred embodiments in conjunction with the drawings. The file of this patent contains at least one drawing executed in color. Copies of this patent with color drawing(s) will be provided by the Patent and Trademark Office upon request and payment of the necessary fee. The drawings are briefly described as follows: 
     FIG. 1 is an overall view of an example interactive computer graphics system; 
     FIG. 2 is a block diagram of the FIG. 1 example computer graphics system; 
     FIG. 3 is a block diagram of the example graphics and audio processor shown in FIG. 2; 
     FIG. 4 is a block diagram of the example 3D graphics processor shown in FIG. 3; 
     FIG. 5 is an example logical flow diagram of the FIG. 4 graphics and audio processor; 
     FIG. 6 shows an example stitched texture coordinate generation and texturing pipeline; 
     FIG. 7 shows a more detailed example stitched texture coordinate generator; 
     FIG. 8 shows an example block diagram of transform unit  300 : 
     FIG. 9 shows example stitched imaging results provided by an example implementation; and 
     FIGS. 10A and 10B show example alternative compatible implementations. 
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION 
     FIG. 1 shows an example interactive 3D computer graphics system  50 . System  50  can be used to play interactive 3D video games with interesting stereo sound. It can also be used for a variety of other applications. time, In this example, system  50  is capable of processing interactively in real time, a digital representation or model of a three-dimensional world. System  50  can display some or all of the world from any arbitrary viewpoint. For example, system  50  can interactively change the viewpoint in response to real time inputs from handheld controllers  52   a ,  52   b  or other input devices. This allows the game player to see the world through the eyes of someone within or outside of the world. System  50  can be used for applications that do not require real time 3D interactive display (e.g., 2D display generation and/or non-interactive display), but the capability of displaying quality 3D images very quickly can be used to create very realistic and exciting game play or other graphical interactions. 
     To play a video game or other application using system  50 , the user first connects a main unit  54  to his or her color television set  56  or other display device by connecting a cable  58  between the two. Main unit  54  produces both video signals and audio signals for controlling color television set  56 . The video signals are what controls the images displayed on the television screen  59 , and the audio signals are played back as sound through television stereo loudspeakers  61 L.  61 R. 
     The user also needs to connect main unit  54  to a power source. This power source may be a conventional AC adapter (not shown) that plugs into a standard home electrical wall socket and converts the house current into a lower DC voltage signal suitable for powering the main unit  54 . Batteries could be used in other implementations. 
     The user may use hand controllers  52   a ,  52   b  to control main unit  54 . Controls  60  can be used, for example, to specify the direction (up or down, left or right, closer or further away) that a character displayed on television  56  should move within a 3D world. Controls  60  also provide input for other applications (e.g., menu selection, pointer/cursor control, etc.). Controllers  52  can take a variety of forms. In this example, controllers  52  shown each include controls  60  such as joysticks, push buttons and/or directional switches. Controllers  52  may be connected to main unit  54  by cables or wirelessly via electromagnetic (e.g., radio or infrared) waves. 
     To play an application such as a game, the user selects an appropriate storage medium  62  storing the video game or other application he or she wants to play, and inserts that storage medium into a slot  64  in main unit  54 . Storage medium  62  may, for example, be a specially encoded and/or encrypted optical and/or magnetic disk. The user may operate a power switch  66  to turn on main unit  54  and cause the main unit to begin running the video game or other application based on the software stored in the storage medium  62 . The user may operate controllers  52  to provide inputs to main unit  54 . For example, operating a control  60  may cause the game or other application to start. Moving other controls  60  can cause animated characters to move in different directions or change the user&#39;s point of view in a 3D world. Depending upon the particular software stored within the storage medium  62 , the various controls  60  on the controller  52  can perform different functions at different times. 
     Example Electronics of Overall System 
     FIG. 2 shows a block diagram of example components of system  50 . The primary components include: 
     a main processor (CPU)  110 , 
     a main memory  112 , and 
     a graphics and audio processor  114 . 
     In this example, main processor  110  (e.g., an enhanced IBM Power PC 750) receives inputs from handheld controllers  108  (and/or other input devices) via graphics and audio processor  114 . Main processor  110  interactively responds to user inputs, and executes a video game or other program supplied, for example, by external storage media  62  via a mass storage access device  106  such as an optical disk drive. As one example, in the context of video game play, main processor  110  can perform collision detection and animation processing in addition to a variety of interactive and control functions. 
     In this example, main processor  110  generates 3D graphics and audio commands and sends them to graphics and audio processor  114 . The graphics and audio processor  114  processes these commands to generate interesting visual images on display  59  and interesting stereo sound on stereo loudspeakers  61 R,  61 L or other suitable sound-generating devices. 
     Example system  50  includes avideo encoder  120  that receives image signals from graphics and audio processor  114  and converts the image signals into analog and/or digital video signals suitable for display on a standard display device such as a computer monitor or home color television set  56 . System  50  also includes an audio codec (compressor/decompressor)  122  that compresses and decompresses digitized audio signals and may also convert between digital and analog audio signaling formats as needed. Audio codec  122  can receive audio inputs via a buffer  124  and provide them to graphics and audio processor  114  for processing (e.g., mixing with other audio signals the processor generates and/or receives via a streaming audio output of mass storage access device  106 ). Graphics and audio processor  114  in this example can store audio related information in an audio memory  126  that is available for audio tasks. Graphics and audio processor  114  provides the resulting audio output signals to audio codec  122  for decompression and conversion to analog signals (e.g., via buffer amplifiers  128 L,  128 R) so they can be reproduced by loudspeakers  61 L.  61 R. 
     Graphics and audio processor  114  has the ability to communicate with various additional devices that may be present within system  50 . For example, a parallel digital bus  130  may be used to communicate with mass storage access device  106  and/or other components. A serial peripheral bus  132  may communicate with a variety of peripheral or other devices including, for example: 
     a programmable read-only memory and/or real time clock  134 , 
     a modem  136  or other networking interface (which may in turn connect system  50  to a telecommunications network  138  such as the Internet or other digital network from/to which program instructions and/or data can be downloaded or uploaded), and 
     flash memory  140 . 
     A further external serial bus  142  may be used to communicate with additional expansion memory  144  (e.g., a memory card) or other devices. Connectors may be used to connect various devices to busses  130 ,  132 ,  142 . 
     Example Graphics and Audio Processor 
     FIG. 3 is a block diagram of an example graphics and audio processor  114 . Graphics and audio processor  114  in one example may be a single-chip ASIC (application specific integrated circuit). In this example, graphics and audio processor  114  includes: 
     a processor interface  150 , 
     a memory interface/controller  152 , 
     a 3D graphics processor  154 . 
     an audio digital signal processor (DSP)  156 , 
     an audio memory interface  158 , 
     an audio interface and mixer  160 , 
     a peripheral controller  162 , and 
     a display controller  164 . 
     3D graphics processor  154  performs graphics processing tasks. Audio digital signal processor  156  performs audio processing tasks. Display controller  164  accesses image information from main memory  112  and provides it to video encoder  120  for display on display device  56 . Audio interface and mixer  160  interfaces with audio codec  122 , and can also mix audio from different sources (e.g., streaming audio from mass storage access device  106 , the output of audio DSP  156 , and external audio input received via audio codec  122 ). Processor interface  150  provides a data and control interface between main processor  110  and graphics and audio processor  114 . 
     Memory interface  152  provides a data and control interface between graphics and audio processor  114  and memory  112 . In this example, main processor  110  accesses main memory  112  via processor interface  150  and memory interface  152  that are part of graphics and audio processor  114 . Peripheral controller  162  provides a data and control interface between graphics and audio processor  114  and the various peripherals mentioned above. Audio memory interface  158  provides an interface with audio memory  126 . 
     Example Graphics Pipeline 
     FIG. 4 shows a more detailed view of an example 3D graphics processor  154 . 3D graphics processor  154  includes, among other things, a command processor  200  and a 3D graphics pipeline  180 . Main processor  110  communicates streams of data (e.g., graphics command streams and display lists) to command processor  200 . Main processor  110  has a two-level cache  115  to minimize memory latency, and also has a write-gathering buffer  111  for uncached data streams targeted for the graphics and audio processor  114 . The write-gathering buffer  111  collects partial cache lines into full cache lines and sends the data out to the graphics and audio processor  114  one cache line at a time for maximum bus usage. 
     Command processor  200  receives display commands from main processor  110  and parses them—obtaining any additional data necessary to process them from shared memory  112 . The command processor  200  provides a stream of vertex commands to graphics pipeline  180  for 2D and/or 3D processing and rendering. Graphics pipeline  180  generates images based on these commands. The resulting image information may be transferred to main memory  112  for access by display controller/video interface unit  164 —which displays the frame buffer output of pipeline  180  on display  56 . 
     FIG. 5 is a logical flow diagram of graphics processor  154 . Main processor  110  may store graphics command streams  210 , display lists  212  and vertex arrays  214  in main memory  112 , and pass pointers to command processor  200  via bus interface  150 . The main processor  110  stores graphics commands in one or more graphics first-in-first-out (FIFO) buffers  210  it allocates in main memory  110 . The command processor  200  fetches: 
     command streams from main memory  112  via an on-chip FIFO memory buffer  216  that receives and buffers the graphics commands for synchronization/flow control and load balancing, 
     display lists  212  from main memory  112  via an on-chip call FIFO memory buffer  218 , and 
     vertex attributes from the command stream and/or from vertex arrays  214  in main memory  112  via a vertex cache  220 . 
     Command processor  200  performs command processing operations  200   a  that convert attribute types to floating point format, and pass the resulting complete vertex polygon data to graphics pipeline  180  for rendering/rasterization. A programmable memory arbitration circuitry  130  (see FIG. 4) arbitrates access to shared main memory  112  between graphics pipeline  180 , command processor  200  and display controller/video interface unit  164 . 
     FIG. 4 shows that graphics pipeline  180  may include: 
     a transform unit  300 , 
     a setup/rasterizer  400 . 
     a texture unit  500 , 
     a texture environment unit  600 , and 
     a pixel engine  700 . 
     Transform unit  300  performs a variety of 2D and 3D transform and other operations  300   a  (see FIG.  5 ). Transform unit  300  may include one or more matrix memories  300   b  for storing matrices used in transformation processing  300   a . Transform unit  300  transforms incoming geometry per vertex from object space to screen space; and transforms incoming texture coordinates and computes projective texture coordinates ( 300   c ). Transform unit  300  may also perform polygon clipping/culling  300   d . Lighting processing  300   e  also performed by transform unit  300   b  provides per vertex lighting computations for up to eight independent lights in one example embodiment. Transform unit  300  can also perform texture coordinate generation ( 300   c ) for embossed type bump mapping effects, as well as polygon clipping/culling operations ( 300   d ). 
     Setup/rasterizer  400  includes a setup unit which receives vertex data from transform unit  300  and sends triangle setup information to one or more rasterizer units ( 400   b ) performing edge rasterization, texture coordinate rasterization and color rasterization. 
     Texture unit  500  (which may include an on-chip texture memory (TMEM)  502 ) performs various tasks related to texturing including for example: 
     retrieving textures  504  from main memory  112 . 
     texture processing ( 500   a ) including, for example, multi-texture handling, post-cache texture decompression, texture filtering, embossing, shadows and lighting through the use of projective textures, and BLIT with alpha transparency and depth, 
     bump map processing for computing texture- coordinate displacements for bump mapping, pseudo texture and texture tiling effects ( 500   b ), and 
     indirect texture processing ( 500   c ). 
     Texture unit  500  outputs filtered texture values to the texture environment unit  600  for texture environment processing ( 600   a ). Texture environment unit  600  blends polygon and texture color/alpha/depth, and can also perform texture fog processing ( 600   b ) to achieve inverse range based fog effects. Texture environment unit  600  can provide multiple stages to perform a variety of other interesting environment-related functions based for example on color/alpha modulation, embossing, detail texturing, texture swapping, clamping, and depth blending,. 
     Pixel engine  700  performs depth (z) compare ( 700   a ) and pixel blending ( 700   b ). In this example, pixel engine  700  stores data into an embedded (on-chip) frame buffer memory  702 . Graphics pipeline  180  may include one or more embedded DRAM memories  702  to store frame buffer and/or texture information ran locally. Z compares  700   a ′ can also be performed at an earlier stage in the graphics pipeline  180  depending on the rendering mode currently in effect (e.g., z compares can be performed earlier if alpha blending is not required). The pixel engine  700  includes a copy operation  700   c  that periodically writes on-chip frame buffer  702  to main memory  112  for access by display/video interface unit  164 . This copy operation  700   c  can also be used to copy embedded frame buffer  702  contents to textures in the main memory  112  for dynamic texture synthesis effects. Anti-aliasing and other filtering can be performed during the copy-out operation. The frame buffer output of graphics pipeline  180  (which is ultimately stored in main memory  112 ) is read each frame by display/video interface unit  164 . Display controller/video interface  164  provides digital RGB pixel values for display on display  102 . 
     Example Dual Texture Coordinate Transform for Stitching and Other Applications 
     FIG. 6 shows an example stitched texture coordinate generation and texturing pipeline that can be implemented by system  50 . In this example, transform unit  300  includes, among other things, a dot product calculator (matrix transform)  302 , a normalizer  304 , and a second dot product calculator (matrix transform)  306 . 
     Dot product calculator  302  receives texture generation source data defining texture coordinates, geometry or normals pertaining to a surface in object space, and applies a matrix transformation based on a first vertex to produce (projected) texture coordinates s′, t′ (and optionally, q′) in homogeneous eye space. The resulting texture coordinates so generated are optionally normalized by normalizer block  304 , and applied to a second dot product calculator  306  that performs an additional matrix transformation on the texture coordinates. This additional matrix transformation interpolates the texture coordinate with respect to a second vertex to provide stitched texture coordinates s″, t″. These stitched texture coordinates may be applied to a texture mapper  500 . Texture mapper  500  stores a stitching/skinning texture tx within texture memory  502 . Texture mapper  500  maps texture tx onto a skinning surface defined by the vertices to provide texels for blending with rasterized pixels representing the transform rasterized surface. Blending is performed by texture environment block  600   a  in the example embodiment. The blended output is stored in embedded frame buffer  702  for display. 
     In more detail, transform unit  300  receives, from main processor  110 , per-vertex data specifying a stitching surface to be imaged. The example embodiment transform unit  300  can accept such data in the form of geometry (x, y, z) specification of a vertex in object space, or it mav be the specification of the normals (i.e., Normal, Binormal, and Tangent) corresponding to the surface. Transform unit  300  performs a conventional modelview (or other) transformation to generate new geometry and/or new normals in homogeneous (e.g., eye) space. 
     Transform unit  300  provides a parallel operation to transform model space per-vertex source values (e.g., vertex geometry [x, y, z] or normals [N x , N y , N z ], or texture coordinates [s, t]) into corresponding texture coordinates. This texture coordinate generation dot product calculation (FIG. 6, block  302 ) generates texture coordinates in homogeneous (e.g., eye) space. The matrix used for the transformation could be the modelview matrix, or it could be some different texture transformation matrix. The matrix transformation performed by block  302  is on a per-vertex basis, and provides an appropriate set of texture coordinates s′, t′ [2′] for the particular vertex. Different transformation matrices may be selected through matrix indices specified with other vertex information. 
     Using one matrix per vertex allows boundary polygons to stretch to cover joints between “bones.” However, the stretching is not necessarily smooth. Stitching usually requires more matrix transformations to achieve a smooth joint by interpolating between additional vertices. The preferred example implementation economizes by performing a single matrix multiply (block  306 ) in addition to the one (block  302 ) used for transforming the texture coordinates to homogeneous space. The second, cascaded matrix transformation performed by dot product calculator  306  performs a different texture transformation on the same texture coordinates—but this time for a second vertex. This provides an interpolation between the first vertex and the second vertex. For example, the second vertex may be a vertex on another “bone” of a skeletal animation model. The method of interpolation is not required to be linear (unlike typical skinning, applications). The second texture transformation  306  provides an ability to interpolate between these two vertices to provide texture coordinates specifying appropriate points between them. This provides a stitching interpolation of two vertices. Only one matrix is used to transform a given vertex, but different matrices can be used for different vertices. 
     While it is possible to recirculate dot product calculator  302  to apply a unique transformation for each output texture that is desired, the resulting decrease in speed performance resulting from an additional per-vertex delay for every vertex involving in stitching, is undesirable. To maximize performance, the preferred embodiment transform unit  300  provides a second hardwaire-based dot product calculator  306  cascaded with the first dot product calculator  302  which can take the first pass texture coordinates from dot product calculator  302  and generate a new set of transformed texture coordinates that can be used as stitched texture coordinates because they provide a future transformation to a second vertex. 
     We also provide a normalizer  304  between the first dot product calculator  302  and the second dot product calculator  306 . Normalizer  304  can be used to eliminate distortions as the surface becomes deformed and the normals get stretched out. The texture coordinates generated by a model view transformation performed by block  302  may not be normalized—but the texture transform performed by block  306  may assume normalized inputs. It may therefore be desirable to apply an inverse normalization to get valid data for the second transform. The inverse normalization changes on a per-vertex basis, making it difficult for main processor  110  to provide appropriate texture transformation matrices that account for this effect. Normalizer  304  takes care of this by taking the texture coordinates s′, t′ (and the implied q′ coordinate) generated by dot product calculator  302 , and renormalizing these texture coordinates before applying them to the second dot product calculator  306 . 
     Normalizer  304  guarantees that the computed vertex data is renormalized before it is applied to the normalized transformation performed by block  306  which does the interpolation to generate stitching coordinates of the texture. Normalizer  304  avoids surface warpage due to distortion of the normals. Without normalizer  304 , stretching of the texture coordinates under certain circumstances would provide unattractive visual effects. However, in the example embodiment, normalizer  304  can be selectively enabled and disabled, and the normalizer may not be needed or used under all circumstances. 
     While the FIG. 6 pipeline is especially useful for stitching, it could be used for other applications such as environment maps and reflection maps. A first dot product calculator  302  can operate on any parameter the main processor  110  provides on a per-vertex basis (e.g., the normals, color, another set of texture coordinates, binormals, etc.). The transformation provided by dot product calculator  302  transforms the source to any desired position, while the second dot product calculator  306  applies a remapping from homogeneous space to texture coordinate space for texture generation. These techniques are general purpose and could be used for any type of texturing dependent on the geometry of the object (e.g., environment mapping, reflection mapping, and other applications). 
     More Detailed Example Embodiment 
     FIG. 7 shows a more detailed example stitching texture coordinate generation pipeline provided by transform unit  300 . In this example, transform unit  300  can deal with a plurality of pairs of texture coordinates per vertex. First dot product calculator  302  transforms, using a corresponding plurality of texture matrices, each set of texture pairs/triplets or pairs of texture coordinates. The input coordinates can be any of the following quartets in the example embodiment: 
     S n , t n  1.0, 1.0 texture coordinates from main processor  110 , 
     x, y, z, 1.0 vertex geometry in model space from main processor  110 , 
     n x , n y , n z , 1.0 normals in model space. 
     The input coordinates in this example are in object coordinates (i.e., before any transformation). The (n) index is a texture based address for the texture matrix. A unique index n is used for each possible texture coordinate. 
     A matrix memory  308  is provided for storing the various texture transform matrices for use by block  302 . Matrix selection is performed automatically by the hardware based on texture number. 
     Second dot product calculator  306  performs a “second pass” transformation to the texture coordinates. This additional transformation can be optionally applied to all texture coordinates. When enabled, this additional transformation is applied to all active regular texture coordinates in the example implementation. 
     The FIG. 7 pipeline can be operated with or without calculation of a third texture coordinate q. Calculation of q may be suppressed in order to achieve higher speed performance. When in its performance case (one regular texture with only two texture coordinates s, t), an implied q t  equal 1.0 is used to compute St′ n  and Tt′ n , but no Qt′ n  is computed. In other cases, all three (St′ n , Tt′ n , Qt′ n ) dual pass texture coordinates are computed—even if ST generation (implied Q) is specified for the first pass. 
     In the example embodiment, the second dot product calculator uses a separate set of texture transform matrices stored in a “dual texture” matrix memory  310  which is a separate memory area from matrix memory  308 . The format of the matrices stored in memory  310  may be the same as the format of the matrices stored in memory  308  except that in the example embodiment, all of the “dual texture” transform matrices in matrix memory  310  have three rows (i.e., they are all 3×4 matrices). The per-vertex information provided by main processor  110  includes a matrix index per vertex—which allows selection of a different matrix and associated transformation on a per-vertex basis. 
     As mentioned above, an optional normalization of texture coordinates can be performed by block  304 . Basically, each incoming texture triplet is scaled by the inverse of its norm. The selection between (St n , Tt n , Qt n , 1.0) or (Sn n , Tn n , Qn n , 1.0) can be done in a per texture coordinate basis. When a performance case (no Q coordinate) is used with normalization (which is not generally useful), no normalization occurs. 
     Normalizer  304  can, for example, be implemented using a 24-bit floating point calculator to do the squaring, and a limited precision 12-bit lookup to do the square root calculation and generate the normalization. This provides approximately 12 to 14 bits of precision, which is acceptable for 10 bits of texture coordinate precision and 8 bits of sub-pixel accuracy. Errors due to round off could be compensated for by using a smaller texture (e.g., 512×512 as opposed to 1024×1024). Of course, different implementations could use different precisions altogether. 
     In the example implementation, when the “dual pass” transform is not active (i.e., the second dot product calculator  306  is not enabled), this feature is completely disabled and does not affect any texture coordinates. This is illustrated in FIG. 7 by a multiplexer  314  that can select either the output of second dot product calculator  306  (when it is enabled) or the output of the first dot product calculator  302  (when the second dot product calculator is not enabled) for application as texture coordinates to texture unit  500 . 
     In the particular example implementation, normalizer  304  and the second dot product calculator  306  are not available for geometry computation, nor can they be used for normal/geometry calculations for lighting. In addition, the regular texture coordinates generated by the second dot product calculator  306  should, in general, be used for embossing. Accordingly, if embossing is enabled, multiplexer  314  in the example implementation always selects the output of the first dot product calculator  302 . In addition, in the example implementation, the normalizer  304  and the second dot product calculator  306  are sourced from the output of the first dot product calculator  302 . Of course, other implementations could provide different arrangements and additional flexibility. 
     FIG. 8 shows an example overall high level block diagram of transform unit  300 . For further details, see commonly assigned U.S. patent application Ser. No. 09/726,216 entitled “Achromatic Lighting Unit With Low Cost Improvements” and its corresponding provisional application, Ser. No. 60/227,007, filed Aug. 23, 2000, both of which are incorporated herein by this reference. The following are some example register definitions for various registers that main processor  110  may use to control transform unit  300  to perform stitching (among other things): 
     
       
         
           
               
               
               
             
               
                   
               
               
                 Register 
                   
                   
               
               
                 Address 
                 Definition 
                 Configuration 
               
               
                   
               
             
            
               
                 0x1000 
                 Error 
                   
               
               
                 0x1001 
                 Diagnostics 
               
               
                 0x1002 
                 State0 
                 Internal state register0 
               
               
                 0x1003 
                 State1 
                 Internal state register1 
               
               
                 0x1004 
                 Xf_clock 
                 Enables power saving mode 
               
               
                   
                   
                 0: No power saving when idle 
               
               
                   
                   
                 1: Enable power saving when idle 
               
               
                 0x1005 
                 ClipDisable 
                 Disables some or all of clipping 
               
               
                   
                   
                 B[0]: When set, disables clipping detection 
               
               
                   
                   
                    (0 default) 
               
               
                   
                   
                 B[1]: When set, disables trivial rejection 
               
               
                   
                   
                    (0 default) 
               
               
                   
                   
                 B[2]: When set, disables cpoly clipping 
               
               
                   
                   
                    acceleration (0 default) 
               
               
                 0x1006 
                 Perf0 
                 Performance monitor selects 
               
               
                 0x1007 
                 Perf1 
                 Xform target performance register: 
               
               
                   
                   
                 [6:0]: Xform internal target performance 
               
               
                   
                   
                    (Cycles/vertex) 
               
               
                 0x1008 
                 In VertexSpec 
                 B[1:0]: Specifies host supplied color0 usage: 
               
               
                   
                   
                 0: No host supplied color information 
               
               
                   
                   
                 1: Host supplied color0 
               
               
                   
                   
                 2: Host supplied color0 and color1 
               
               
                   
                   
                 B[3:2]: Specifies host supplied normal: 
               
               
                   
                   
                 0: No host supplied normal 
               
               
                   
                   
                 1: Host supplied normal 
               
               
                   
                   
                 2: Host supplied normal and binormals 
               
               
                   
                   
                 B[7:4]: Specifies # of host supplied texture 
               
               
                   
                   
                    coordinates 
               
               
                   
                   
                 0: No host supplied textures 
               
               
                   
                   
                 1: 1 host supplied texture pair (SO, TO) 
               
               
                   
                   
                 2-8: 2-8 host supplied texturepairs 
               
               
                   
                   
                 9-15: Reserved 
               
               
                 0x1009 
                 NumColors 
                 Specifies the number of colors to output: 
               
               
                   
                   
                 0: No xform colors active 
               
               
                   
                   
                 1: Xform supplies 1 color (host supplied or 
               
               
                   
                   
                   computed) 
               
               
                   
                   
                 2: Xform supplies 2 colors (host supplied or 
               
               
                   
                   
                   computed) 
               
               
                 0x100a 
                 Ambient0 
                 32b: RGBA (8b/comp) Ambient color0 
               
               
                   
                   
                   specifications 
               
               
                 0x100b 
                 Ambient1 
                 32b: RGBA (8b/comp) Ambient color1 
               
               
                   
                   
                   specifications 
               
               
                 0x100c 
                 Material 0 
                 32b: RGBA (8b/comp) global color0 material 
               
               
                   
                   
                   specifications 
               
               
                 0x100d 
                 Material 1 
                 32b: RGBF (8b/comp) global color1 material 
               
               
                   
                   
                   specification 
               
               
                 0x100e 
                 Color0Cntrl 
                 B[0]: Color0 Material source 
               
               
                   
                   
                 0: Use register (Material 0) 
               
               
                   
                   
                 1: Use CP supplied Vertex color 0 
               
               
                   
                   
                 B[1]: Color0 LightFunc 
               
               
                   
                   
                 0: Use 1.0 
               
               
                   
                   
                 1: Use Illum0 
               
               
                   
                   
                 B[2]: Light0 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[3]: Light1 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[4]: Light2 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[5]: Light3 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[6]: Ambient source 
               
               
                   
                   
                 0: Use register Ambient0 register 
               
               
                   
                   
                 1: Use CP supplied vertex color 0 
               
               
                   
                   
                 B[8:7]: DiffuseAtten function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select N.L, signed 
               
               
                   
                   
                 2: Select N.L clamped to [0,1.0] 
               
               
                   
                   
                 B[9]: AttenEnable function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select Attenuation fraction 
               
               
                   
                   
                 B[10]: AttenSelect function 
               
               
                   
                   
                 0: Select specular (N.H) attenuation 
               
               
                   
                   
                 1: Select diffuse spotlight (L.Ldir) attenuation 
               
               
                   
                   
                 B[11]: Light 4 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[12]: Light 5 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[13]: Light 6 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[14]: Light 7 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                 0x100f 
                 Color1Cntrl 
                 B[0]: Color Material source 
               
               
                   
                   
                 0: Use register (Material 1) 
               
               
                   
                   
                 1: Use CP supplied Vertex color 1 
               
               
                   
                   
                 B[1]: Color1 LightFunc 
               
               
                   
                   
                 0: Use 1.0 
               
               
                   
                   
                 1: Use Illum1 
               
               
                   
                   
                 B[2]: Light0 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[3]: Light1 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[4]: Light2 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[5]: Light3 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[6]: Ambient source 
               
               
                   
                   
                 0: Use register Ambient1 register 
               
               
                   
                   
                 1: Use CP supplied vertex color 1 
               
               
                   
                   
                 B[8,7]: DiffuseAtten function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select N.L, signed 
               
               
                   
                   
                 2: Select N.L clamped to [0,1.0] 
               
               
                   
                   
                 B[9]: AttenEnable function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select Attenuation fraction 
               
               
                   
                   
                 B[10]: AttenSelect function 
               
               
                   
                   
                 0: Select specular (N.H) attenuation 
               
               
                   
                   
                 1: Select difftise spotlight (L.Ldir) attenuation 
               
               
                   
                   
                 B[11]: Light 4 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[12]: Light 5 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[13]: Light 6 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[14]: Light 7 is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                 0x1010 
                 Alpha0Cntrl 
                 B[0]: Color0 alpha Material source 
               
               
                   
                   
                 0: Use register (Material 0 alpha) 
               
               
                   
                   
                 1: Use CP supplied Vertex color 0 alpha 
               
               
                   
                   
                 B[1]: Color0 alpha LightFunc 
               
               
                   
                   
                 0: Use 1.0 
               
               
                   
                   
                 1: Use Illum0 
               
               
                   
                   
                 B[2]: Light0 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[3]: Light1 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[4]: Light2 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[5]: Light 3 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[6]: Ambient source 
               
               
                   
                   
                 0: Use register Ambient0 alpha register 
               
               
                   
                   
                 1: Use CP supplied vertex color 0 alpha 
               
               
                   
                   
                 B[8:7]: DiffuseAtten function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select N.L, signed 
               
               
                   
                   
                 2: Select N.L clamped to [0,1.0] 
               
               
                   
                   
                 B[9]: AttenEnable function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select Attenuation fraction 
               
               
                   
                   
                 B[1-]: AttenSelect function 
               
               
                   
                   
                 0: Select specular (N.H) attenuation 
               
               
                   
                   
                 1: Select diffuse spotlight (L.Ldir) attenuation 
               
               
                   
                   
                 B[11]: Light 4 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[12]: Light 5 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[13]: Light 6 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[14]: Light 7 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                 0x1011 
                 Alpha1Cntrl 
                 B[0]: Color1 alpha Material source 
               
               
                   
                   
                 0: Use CP supplied Vertex color 1 alpha 
               
               
                   
                   
                 B[1]: Color1 alpha LightFunc 
               
               
                   
                   
                 0: Use 1.0 
               
               
                   
                   
                 1: Use Illum0 
               
               
                   
                   
                 B[2]: Light0 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[3]: Light1 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[4]: Light2 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[5]: Light3 alpha is source 
               
               
                   
                   
                 0: Do not use light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[6]: Ambient source 
               
               
                   
                   
                 0: Use register Ambient1 alpha register 
               
               
                   
                   
                 1: Use CP supplied vertex color 1 alpha 
               
               
                   
                   
                 B[8:7]: DiffuseAtten function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select N.L, signed 
               
               
                   
                   
                 2: Select N.L clamped to [0,2.0] 
               
               
                   
                   
                 B[9]: AttenEnable function 
               
               
                   
                   
                 0: Select 1.0 
               
               
                   
                   
                 1: Select Attenuation fraction 
               
               
                   
                   
                 B[10]: AttenSelect function 
               
               
                   
                   
                 0: Select specular (N.H) attenuation 
               
               
                   
                   
                 1: Select diffuse spotlight (L.Ldir) attenuation 
               
               
                   
                   
                 B[11]: Light 4 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[12]: Light 5 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[13]: Light 6 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                   
                   
                 B[14]: Light 7 is source 
               
               
                   
                   
                 0: Do not use Light 
               
               
                   
                   
                 1: Use light 
               
               
                 0x1012 
                 DualTexTran 
                 B[0]: When set(1), enables dual transform for 
               
               
                   
                   
                    all texture coordinates. When reset (0), 
               
               
                   
                   
                    disables dual texture transform feature 
               
               
                 0x1018 
                 MatrixIndex0 
                 B[5:0]: Geometry matrix index 
               
               
                   
                   
                 B[11:6]: Tex0 matrix index 
               
               
                   
                   
                 B[17:12]: Tex1 matrix index 
               
               
                   
                   
                 B[23:18]: Tex2 matrix index 
               
               
                   
                   
                 B[29:24]: Tex3 matrix index 
               
               
                 0x1019 
                 MatrixIndex1 
                 B[5:0]: Tex4 matrix index 
               
               
                   
                   
                 B[11:6]: Tex5 matrix index 
               
               
                   
                   
                 B[17:12]: Tex6 matrix index 
               
               
                   
                   
                 B[23:18]: Tex7 matrix index 
               
               
                 0x101a 
                 ScaleX 
                 Viewport scale X 
               
               
                 0x101b 
                 ScaleY 
                 Viewport scale Y 
               
               
                 0x101c 
                 ScaleZ 
                 Viewport scale Z 
               
               
                 0x101d 
                 OffsetX 
                 Viewport offset X 
               
               
                 0x101e 
                 OffsetY 
                 Viewport offset Y 
               
               
                 0x101f 
                 OffsetZ 
                 Viewport offset Z 
               
               
                 0x1020 
                 ProjectionA 
                 A parameter in projection equations 
               
               
                 0x1021 
                 ProjectionB 
                 B parameter in projection equations 
               
               
                 0x1022 
                 ProjectionC 
                 C parameter in projection equations 
               
               
                 0x1023 
                 ProjectionD 
                 D parameter in projection equations 
               
               
                 0x1024 
                 ProjectionE 
                 E parameter in projection equations 
               
               
                 0x1025 
                 ProjectionF 
                 F parameter in projection equations 
               
               
                 0x1026 
                 ProjectOrtho 
                 If set selects orthographic otherwise non- 
               
               
                   
                   
                 orthographic (Zh or 1.0 select) 
               
               
                 0x103f 
                 NumTex 
                 Number of active textures 
               
               
                 0x1040 
                 Tex0 
                 B0: Reserved 
               
               
                   
                   
                 B1: texture projection 
               
               
                   
                   
                 0: (s,t): texmul is 2x4 
               
               
                   
                   
                 1: (s,t,q): texmul is 3x4 
               
               
                   
                   
                 B2: input form (format of source input data for 
               
               
                   
                   
                   regular textures) 
               
               
                   
                   
                 0: (A, B, 1.0, 1.0) (used for regular texture 
               
               
                   
                   
                   source) 
               
               
                   
                   
                 1: (A, B, C, 1.0) (used for geometry or normal 
               
               
                   
                   
                  source) 
               
               
                   
                   
                 B3: Reserved 
               
               
                   
                   
                 B[6,4]: texgen type 
               
               
                   
                   
                 0: Regular transformation (transform incoming 
               
               
                   
                   
                  data) 
               
               
                   
                   
                 1: texgen bump mapping 
               
               
                   
                   
                 2: Color texgen: (s,t)=(r.g:b) (g and b are 
               
               
                   
                   
                  concatenated), color0 
               
               
                   
                   
                 3: Color texgen: (s,t)=(r,g:b) (g and b are 
               
               
                   
                   
                  concatenated). color 1 
               
               
                   
                   
                 B[11:7]: regular texture source row: 
               
               
                   
                   
                  Specifies location of incoming textures in 
               
               
                   
                   
                  vertex (row specific) (i.e.: geometry is row0, 
               
               
                   
                   
                  normal is row1, etc . . .) for regular 
               
               
                   
                   
                  transformations (refer to the table below) 
               
               
                   
                   
                 B[14:12]: bump mapping source texture: 
               
               
                   
                   
                 n: use regular transformed tex(n) for bump 
               
               
                   
                   
                  mapping source 
               
               
                   
                   
                 B[17:15]: Bump mapping source light: 
               
               
                   
                   
                 n: use light #n for bump map direction 
               
               
                   
                   
                   source (10 to 17) 
               
               
                 0x1041 
                 Tex1 
                 SeeTex0 
               
               
                 0x1042 
                 Tex2 
                 SeeTex0 
               
               
                 0x1043 
                 Tex3 
                 SeeTex0 
               
               
                 0x1044 
                 Tex4 
                 SeeTex0 
               
               
                 0x1045 
                 Tex5 
                 SeeTex0 
               
               
                 0x1046 
                 Tex6 
                 SeeTex0 
               
               
                 0x1047 
                 Tex7 
                 SeeTex0 
               
               
                 0x1050 
                 Dual Tex0 
                 B[5:0]: Indicates which is the base row of the 
               
               
                   
                   
                   the dual transform matrix for regular 
               
               
                   
                   
                   texture coordinate0. 
               
               
                   
                   
                 B[7:6]: Not used. 
               
               
                   
                   
                 B[8]: specifies if texture coordinate should be 
               
               
                   
                   
                   normalized before send transform. 
               
               
                 0x1051 
                 DualTex1 
                 See DualTex0 
               
               
                 0x1052 
                 DualTex2 
                 See DualTex0 
               
               
                 0x1053 
                 DualTex3 
                 See DualTex0 
               
               
                 0x1054 
                 DualTex4 
                 See DualTex0 
               
               
                 0x1055 
                 DualTex5 
                 See DualTex0 
               
               
                 0x1056 
                 DualTex6 
                 See DualTex0 
               
               
                 0x1057 
                 DualTex7 
                 See DualTex0 
               
               
                   
               
            
           
         
       
     
     Example API Calls 
     The following are example relevant application programmer interface calls that can be used to control stitching: 
     
       
         
           
               
               
               
             
               
                   
               
               
                 Function 
                 Parameters 
                 Description 
               
               
                   
               
             
            
               
                 GXLoadPosMtxImm 
                 matrix 
                 different matrix sent down for 
               
               
                   
                   
                 each tube segment 
               
               
                   
                 matrix 
                 GX_PNMTX0-GX_PNMTX9 
               
               
                   
                 destination 
               
               
                 GXLoadNrmMtxImm 
                 matrix 
                 different matrix sent down for 
               
               
                   
                   
                 each tube segment 
               
               
                   
                 matrix 
                 GX_PNMTX0-GX_PNMTX9 
               
               
                   
                 destination 
               
               
                 GXMatrixIndex1u8 
                 matrix source 
                 GX_PNMTX0-GX_PNMTX9 
               
               
                   
               
            
           
         
       
     
     GXLoadPosMtxImm 
     Description 
     This function is used to load a 3×4 model view matrix mtxPtr into matrix memory at location id. This matrix can be used to transform positions in model space to view space, either by making the matrix the current one (see GXSetCurrentMtx), or by setting a matrix id for each vertex. The parameter mtxPtr is a pointer to a 3×4 (row×column) matrix. The parameter id is used to refer to the matrix location, enumerated by GXPosNrmiMtx, in matrix memory. 
     You can also load a normal matrix (GXLoadkNrmMtxImm or GXLoadNrmMtxIndx) to the same id. Generally, the normal matrix will be the inverse transpose of the position matrix. The normal matrix is used during vertex lighting. In cases where the modelview and inverse transpose of the modelview (excluding translation) are the same, you can load the same matrix for both position and normal transforms. 
     The matrix is copied from DRAM through the CPU cache into the Graphics FIFO, so matrices loaded using this function are always coherent with the CPU cache. 
     Arguments 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 mtxPtr 
                 Specifies a pointer to the matrix data. 
               
               
                 id 
                 Specifies the matrix name. Accepted values are enumerated by 
               
               
                   
                 GXPosNrmMtx. 
               
               
                   
               
            
           
         
       
     
     Example usage: 
     void GXLoadPosMtxImm( 
     f 32  mtxPtr[ 3 ] [ 4 ], 
     u 32  id) 
     GXLoadNrmMtxImm 
     Description 
     This function is used to load a 3×3 normal transform matrix into matrix memory at location id from the 3×4 matrix mtxPtr. This matrix is used to transform normals in model space to view space, either by making it the current matrix (see GXSetCurrentMtx), or by setting a matrix id for each vertex. The parameter mtxPtr is a pointer to a 3×4 (row×column) matrix. The translation terms in the 3×4 matrix are not needed for normal rotation and are ignored during the load. The parameter id, enumerated by GXPosNrmMtx, is used to refer to the estimation matrix location in matrix memory. 
     You can also load a position matrix (GXLoadPosMtxImm) to the same id. Normally, the normal matrix will be the inverse transpose of the position (modelview) matrix and is used during vertex lighting. In cases where the modelview and the inverse transpose of the modelview matrix (excluding translation) are the same, the same matrix can be loaded for both normal and position matrices. 
     To load a normal matrix from a 3×3 matrix, use GXLoadNrmMtxImm3×3. 
     The matrix data is copied from main memory or the CPU cache into the Graphics FIFO, so matrices loaded by this function are always coherent with the CPU cache. 
     Arguments 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 mtxPtr 
                 Specifies a pointer to the matrix data. 
               
               
                 id 
                 Specifies the matrix name. Accepted values are enumerated by 
               
               
                   
                 GKPosNrmMtx. 
               
               
                   
               
            
           
         
       
     
     Example usage: 
     void GXLoadPosMtxImm( 
     f 32  mtxPtr[ 3 ] [ 4 ], 
     u 32  id) 
     GXMatrixIndex 
     Description 
     This function is used to specify matrix index data for a vertex. It can only be called between GXBegin and GXEnd. The matrix index specifies which matrix (previously loaded into matrix memory, see GXLoadPosMtxImm, GXLoadNrmMtxImm and GXLoadTexMtxImm) to use to transform this vertex&#39;s data. 
     To use this function for a vertex, you first enable a matrix index in the current vertex descriptor. The current vertex descriptor is set using GXSetVtxDesc. There is no need to set a vertex attribute format (GXSetVtxAttrFmt) because the index must be an unsigned 8-bit number. Both GXMatrixIndex1u8 and GXMatrixIndex1×8 are identical. 
     The order in which vertex functions must be called is specified by GXSetVtxDesc. Each vertex must send attributes (positions, colors, normals, etc.) in the specified order to guarantee proper interpretation by the graphics hardware. 
     The GXMatrixIndex1u8 (GXMatrixIndex1×8) is implemented as an inline function for optimal performance. The GXMatrixIndex1u8 (GXMatrixIndex1×8) is implemented as a regular function so the library can verify the correct order of vertex function calls between GXBegin/GXEnd (a common source of errors). 
     Arguments 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 index 
                 An unsigned 8-bit index into matrix memory. This number 
               
               
                   
                 indicates the first row of matrix memory where the matrix was 
               
               
                   
                 loaded. 
               
               
                   
               
            
           
         
       
     
     Example usage: 
     void GXMatrixIndex1u8 (u8 index); 
     void GXMatrixIndex1×8 (u8 index); 
     Supported Functions: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                   
                 GX_INDEX8, 
               
               
                   
                 GX_Direct 
                 GX_INDEX16 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 GXPosition3f32, GXPosition3u8 
                   
               
               
                   
                 GXPosition3s8, GXPosition3u16, 
               
               
                 GX 
                 GXPosition3s16 
                 GXPosition1x16, 
               
               
                 Position 
                 GXPosition2f32, GXPosition2u8 
                 GXPosition1x8 
               
               
                   
                 GXPosition2s8, GXPosition2u16, 
               
               
                   
                 GXPosition2s16 
               
               
                 GXColor 
                 GXColor4u8, GXColor3u8, 
                 GXColor1x16, 
               
               
                   
                 GXColor1u32. 
                 GXColor1x8 
               
               
                   
                 GXColor1u16 
               
               
                 GX 
                 GXNormal3f32, GXNormal3s16, 
                 GXNormal1x16 
               
               
                 Normal 
                 GXNormal3s8 
                 GXNormal1x8 
               
               
                 GXTex 
                 GXTexCoord2f32, GXTexCoord2s16, 
                 GXTexCoord1x16, 
               
               
                 Coord 
                 GXTexCoord2u16, GXTexCoord2s8, 
                 GXTexCoord1x8 
               
               
                   
                 GXTexCoord2u8 
               
               
                   
                 GXTexCoord1f32, GXTexCoord1s16, 
               
               
                   
                 GXTexCoord1u16, GXTexCoord1s8, 
               
               
                   
                 GXTexCoord1u8 
               
               
                 GXMatrix 
                 GXMatrixIndex1u8/ 
                 None 
               
               
                 Index 
                 GXMatrixIndex1x8 
               
               
                 GXVertex 
                 None 
                 None 
               
               
                   
               
            
           
         
       
     
     GXSetVtxDesc 
     Example Usage: 
     void GXSetVtxDesc(GXAttr attr, GXAttrType type); 
     Description 
     This function sets the type of a single attribute (attr) in the current vertex descriptor. The current vertex descriptor defines which attributes are present in a vertex and how each attribute is referenced. The current vertex descriptor is used by the Graphics Processor (GP) to interpret the graphics command stream produced by the GX API. In particular, the current vertex descriptor is used to parse the vertex data that is present in the command stream. 
     Attributes 
     GX_VA_POSMTXIDX 
     The attr parameter names the attribute. The attribute GX_VA_POSMTXIDX is used to specify a matrix index (8 bits) per vertex. This index will be used to index a position (and normal, if lighting) matrix in matrix memory. Providing a matrix index per vertex allows character skinning. 
     GX_VA_TEX0MTXIDX-GX_VA_TEX7MTXIDX 
     You may also specify a texture matrix index per vertex, using GX_VA_TEX0MTXIDX-GX_VA_TEX7MTXIDX. Each matrix index is an 8-bit value that is the row address of the texture matrix in matrix memory. The matrix index number corresponds to the generated texture coordinate used in GXSetTexCoordGen. For example, GX_VA_TEX3MTXIDX inicates the matrix to use when generating GX_TEXCOORD3. You provide texture matrix indices in sequential order, but it is possible to skip matrix indices. For example, you can provide GX_VA_TEX0MTXIDX and GX_VA_TEX2MTXIDX. The texture coordinate GX_TEXCOORD1 will use the matrix specified in GXSetTexCoordGen. In other words, the default texture matrix index provided by GXSetTexCoordGen will be overridden by a per-vertex matrix index if one is provided. Providing texture matrix indices per vertex may be used when generating texture coordinates from a skinned (stitched) model, for example, when reflection-mapping a skinned model. 
     GX_VA_POS 
     The GX_VA_POS attribute is used for position. Position is the only attribute that is required for each vertex. 
     GX_VA_NRM, GX_VA_NBT 
     The GX_VA_NRM attribute is used for 3 element normals. GX_VA_NBT is enabled when three normals are needed (normal, binormal, and tangent), such as for bump mapping. GX_VA_NRM and GX_VA_NBT should not be enabled at the same time. GX_VA_NRM and GX_VA_NBT will share the same format in the vertex attribute format, see GXSetVtxAttrFmt. 
     Attribute Types 
     The attribute type GX_NONE indicates that no data or index will be sent for this attribute. The attribute type GX_DIRECT indicates that the data for this attribute will be passed directly in the graphics command stream (as opposed to being indexed). The attribute type GX_INDEX8 indicates that an 8-bit index will be sent in the command stream. The 8-bit index 0xff is a reserved value. It is used to disable the vertex in the graphics processor. You can use this to “turn off” certain triangles in a display list, without having to regenerate a new display list. The graphics processor will use the index, along with the attribute&#39;s array base pointer and stride (see GXSetArray), to look up the attribute&#39;s data. The GX_INDEX16 attribute type indicates a 16-bit index is present in the vertex data. The 16-bit index 0xffff is a reserved value used to disable the vertex in the graphics processor. 
     GXInit clears the current vertex descriptor using GXClearVtxDesc. 
     Arguments 
     
       
         
           
               
               
               
             
               
                   
               
               
                   
                 As- 
                   
               
               
                   
                 cending 
                   
               
               
                   
                 order in 
                   
               
               
                 Attribute 
                 a vertex 
                 Description 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 GX_VA_PNMTXIDX 
                 0 
                 Position/Normal Matrix Index 
               
               
                 GX_VA_TEX0MTXIDX 
                 1 
                 GX_TEXCOORD0 matrix index 
               
               
                 GX_VA_TEX1MTXIDX 
                 2 
                 GX_TEXCOORD1 matrix index 
               
               
                 GX_VA_TEX2MTXIDX 
                 3 
                 GX_TEXCOORD2 matrix index 
               
               
                 GX_VA_TEX3MTXIDX 
                 4 
                 GX_TEXCOORD3 matrix index 
               
               
                 GX_VA_TEX4MTXIDX 
                 5 
                 GX_TEXCOORD4 matrix index 
               
               
                 GX_VA_TEX5MTXIDX 
                 6 
                 GX_TEXCOORD5 matrix index 
               
               
                 GX_VA_TEX6MTXIDX 
                 7 
                 GX_TEXCOORD6 matrix index 
               
               
                 GX_VA_TEX7MTXIDX 
                 8 
                 GX_TEXCOORD7 matrix index 
               
               
                 GX_VA_POS 
                 9 
                 Position 
               
               
                 GX_VA_NRM or 
                 10 
                 Normal or 
               
               
                 GX_VA_NBT 
                   
                 Normal/Binormal/Tangent 
               
               
                 GX_VA_CLR0 
                 11 
                 Color 0 
               
               
                 GX_VA_CLR1 
                 12 
                 Color 1 
               
               
                 GX_VA_TEX0 
                 13 
                 Texture Coordinate 0 
               
               
                 GX_VA_TEX1 
                 14 
                 Texture Coordinate 1 
               
               
                 GX_VA_TEX2 
                 15 
                 Texture Coordinate 2 
               
               
                 GX_VA_TEX3 
                 16 
                 Texture Coordinate 3 
               
               
                 GX_VA_TEX4 
                 17 
                 Texture Coordinate 4 
               
               
                 GX_VA_TEX5 
                 18 
                 Texture Coordinate 5 
               
               
                 GX_VA_TEX6 
                 19 
                 Texture Coordinate 6 
               
               
                 GX_VA_TEX7 
                 20 
                 Texture Coordinate 7 
               
               
                   
               
            
           
         
       
     
     Example Image Results 
     FIG. 9 shows an example stitched image result provided by an example implementation. 
     Other Example Compatible Implementations 
     Certain of the above-described system components  50  could be implemented as other than the home video game console configuration described above. For example, one could run graphics application or other software written for system  50  on a platform with a different configuration that emulates system  50  or is otherwise compatible with it. If the other platform can successfully emulate, simulate and/or provide some or all of the hardware and software resources of system  50 , then the other platform will be able to successfully execute the software. 
     As one example, an emulator may provide a hardware and/or software configuration (platform) that is different from the hardware and/or software configuration (platform) of system  50 . The emulator system might include software and/or hardware components that emulate or simulate some or all of hardware and/or software components of the system for which the application software was written. For example, the emulator system could comprise a general purpose digital computer such as a personal computer, which executes a software emulator program that simulates the hardware and/or firmware of system  50 . 
     Some general purpose digital computers (e.g., IBM or Macintosh personal computers and compatibles) are now equipped with 3D graphics cards that provide 3D graphics pipelines compliant with DirectX or other standard 3D graphics command APIs. They may also be equipped with stereophonic sound cards that provide high quality stereophonic sound based on a standard set of sound commands. Such multimedia-hardware-equipped personal computers running emulator software may have sufficient performance to approximate the graphics and sound performance of system  50 . Emulator software controls the hardware resources on the personal computer platform to simulate the processing, 3D graphics, sound, peripheral and other capabilities of the home video game console platform for which the game programmer wrote the game software. 
     FIG. 10A illustrates an example overall emulation process using a host platform  1201 , an emulator component  1303 , and a game software executable binary image provided on a storage medium  62 . Host  1201  may be a general or special purpose digital computing device such as, for example, a personal computer, a video game console, or any other platform with sufficient computing power. Emulator  1303  may be software and/or hardware that runs on host platform  1201 , and provides a real-time conversion of commands, data and other information from storage medium  62  into a form that can be processed by host  1201 . For example, emulator  1303  fetches “source” binary-image program instructions intended for execution by system  50  from storage medium  62  and converts these program instructions to a target format that can be executed or otherwise processed by host  1201 . 
     As one example, in the case where the software is written for execution on a platform using an IBM PowerPC or other specific processor and the host  1201  is a personal computer using a different (e.g., Intel) processor, emulator  1303  fetches one or a sequence of binary-image program instructions from storage medium  1305  and converts these program instructions to one or more equivalent Intel binary-image program instructions. The emulator  1303  also fetches and/or generates graphics commands and audio commands intended for processing by the graphics and audio processor  114 , and converts these commands into a format or formats that can be processed by hardware and/or software graphics and audio processing resources available on host  1201 . As one example, emulator  1303  may convert these commands into commands that can be processed by specific graphics and/or or sound hardware of the host  1201  (e.g., using standard DirectX, OpenGL and/or sound APIs). 
     An emulator  1303  used to provide some or all of the features of the video game system described above may also be provided with a graphic user interface (GUI) that simplifies or automates the selection of various options and screen modes for games run using the emulator. In one example, such an emulator  1303  may further include enhanced functionality as compared with the host platform for which the software was originally intended. 
     FIG. 10B illustrates an emulation host system  1201  suitable for use with emulator  1303 . System  1201  includes a processing unit  1203  and a system memory  1205 . A system bus  1207  couples various system components including system memory  1205  to processing unit  1203 . System bus  1207  may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. System memory  1207  includes read only memory (RONM)  1252  and random access memory (RAM)  1254 . A basic input/output system (BIOS)  1256 , containing the basic routines that help to transfer information between elements within personal computer system  1201 , such as during start-up, is stored in the ROM  1252 . System  1201  further includes various drives and associated computer-readable media. A hard disk drive  1209  reads from and writes to a (typically fixed) magnetic hard disk  1211 . An additional (possible optional) magnetic disk drive  1213  reads from and writes to a removable “floppy” or other magnetic disk  1215 . An optical disk drive  1217  reads from and, in some configurations, writes to a removable optical disk  1219  such as a CD ROM or other optical media. Hard disk drive  1209  and optical disk drive  1217  are connected to system bus  1207  by a hard disk drive interface  1221  and an optical drive interface  1225 , respectively. The drives and their associated computer-readable media provide nonvolatile storage of computer-readable instructions, data structures, program modules, game programs and other data for personal computer system  1201 . In other configurations, other types of computer-readable media that can store data that is accessible by a computer (e.g., magnetic cassettes, flash memory cards, digital video disks, Bernoulli cartridges, random access memories (RAMs), read only memories (ROMs) and the like) may also be used. 
     A number of program modules including emulator  1303  may be stored on the hard disk  1211 , removable magnetic disk  1215 , optical disk  1219  and/or the ROM  1252  and/or the RAM  1254  of system memory  1205 . Such program modules may include an operating system providing graphics and sound APIs, one or more application programs, other program modules, program data and game data. A user may enter commands and information into personal computer system  1201  through input devices such as a keyboard  1227 , pointing device  1229 , microphones, joysticks, game controllers, satellite dishes, scanners, or the like. These and other input devices can be connected to processing unit  1203  through a serial port interface  1231  that is coupled to system bus  1207 , but may be connected by other interfaces, such as a parallel port, game port Fire wire bus or a universal serial bus (USB). A monitor  1233  or other type of display device is also connected to system bus  1207  via an interface, such as a video adapter  1235 . 
     System  1201  may also include a modem  1154  or other network interface means for establishing communications over a network  1152  such as the Lnternet. Modem  1154 , which mav be internal or external, is connected to system bus  123  via serial port interface  1231 . A network interface  1156  may also be provided for allowing system  1201  to communicate with a remote computing device  1150  (e.g., another system  1201 ) via a local area network  1158  (or such communication may be via wide area network  1152  or other communications path such as dial-up or other communications means). System  1201  will typically include other peripheral output devices, such as printers and other standard peripheral devices. 
     In one example, video adapter  1235  may include a 3D graphics pipeline chip set providing fast 3D graphics rendering in response to 3D graphics commands issued based on a standard 3D graphics application programmer interface such as Microsoft&#39;s DirectX 7.0 or other version. A set of stereo loudspeakers  1237  is also connected to system bus  1207  via a sound generating interface such as a conventional “sound card” providing hardware and embedded software support for generating high quality stereophonic sound based on sound commands provided by bus  1207 . These hardware capabilities allow system  1201  to provide sufficient graphics and sound speed performance to play software stored in storage medium  62 . 
     All documents referenced above are hereby incorporated by reference. 
     While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.