Abstract:
A graphic system includes a pipelined graphic engine for generating image frames for display. The pipelined graphic engine includes a geometric processing stage for performing motion extraction, and a rendering stage for generating full image frames at a first frame rate for display at a second frame rate. The second frame rate is higher than the first frame rate. A motion encoder stage receives motion information from the geometric processing stage, and produces an interpolated frame signal representative of interpolated frames. A motion compensation stage receives the interpolated frame signal from the motion encoder stage, and the full image frames from the rendering stage for generating the interpolated frames. A preferred application is in graphic systems that operate in association with smart displays through a wireless connection, such as in mobile phones.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to techniques for pipelining 3D graphics in a graphic engine for rendering some frames and for extracting motion information and applying them to interpolate new frames. In particular, the present invention is applicable to graphic engines that operate in association with smart displays through a wireless or wired connection.  
         [0002]     Exemplary of such an application is the graphic engine in a mobile phone equipped with a wireless (i.e., Bluetooth) or wired connection to a remote display, or within the graphic engine in a mobile phone having an embedded display. However, reference to these preferred applications are in no way to be construed as limiting the scope of the invention.  
       BACKGROUND OF THE INVENTION  
       [0003]     Modern 3D graphic pipelines for graphic engines in graphic cards, like OpenGL and Direct3D pipelines, include a rich set of features for synthesizing interactive tridimensional scenes with a high and realistic quality.  
         [0004]     To output frame-rates ranging from 20/30 to 40/100 frames per second, powerful dedicated graphic cards are required having correspondingly high costs. The number of pictures per time unit (i.e., the frame rate) is usually increased by parallelizing as much as possible the operations required in the frame buffer with respect to the graphic objects that are to be displayed, while at the same time increasing the computational power available by running at higher speeds the operations that cannot be parallelized.  
         [0005]     A generic OpenGL pipeline for 3D interactive graphics is able to implement a set of algorithms that process a tridimensional synthetic scene, which comprises actions and details and is able to present it on a bi-dimensional display. The process to generate and display the scene, from a conceptual point of view, is divided into more consecutive steps or pipeline stages. Each stage has a specific task and provides the input for the next stage. The complexity of each stage varies from one stage to another. Typically, stages that process and affect pixels (at the end of the pipeline) have a higher complexity than those stages that process the 3D scene details. A full description of a graphic pipeline can be found in an Internet publication at URL http://www.extremetech.com/article2/0,3973,9722,00.asp.  
         [0006]     By way of example, approximately 70% of the computational resources are devoted to raster and fragmentation operations while the remaining resources are absorbed by the geometry stages. This happens because the final shape of each object is obtained by applying on its pixels the same steps many times, while other operations are executed only once for each 3D object.  
         [0007]     For a 3D pipeline, it is highly desirable to use as small a number of operations as possible while achieving a good level of detail and ensuring a minimum frame rate. 3D objects that are located and displaced within a tridimensional space of coordinates compose a 3D scene. Each object is composed of a number of graphic primitives (i.e., triangles).  
         [0008]     The appearance of this object depends on the number of primitives. The level of detail perceived from a visual point of view increases with the number of such primitives. A geometric primitive should be a simple entity that can be easily processed by a real pipeline by an algorithm depending on the geometric type of primitive, i.e., points, lines, triangles, squares, polygons and higher-order surfaces.  
         [0009]     Excluding lines and points, a suitable object representation is provided by triangles, and consequently, the use of triangles will be assumed in the following discussions. In fact, a triangle is a simple planar, convex surface that can be processed fairly easily. Its vertices.univocally define each triangle. Each 3D scene can thus be completely defined by a list of vertices. These are tridimensional points located within a reference coordinate system, and such vertices/points are associated to respective primitives.  
         [0010]     Each vertex can be defined by associating the following information: X, Y, Z real coordinates and R, G, B color components. Additional information not needed for the nature of the proposed algorithm are as follows. One or more alpha factors are not needed. Three real coordinates to specify the normal vector associated to the vertex are not needed. The normal vector is used by the lighting stage to apply a luminosity value to the primitive. Two or more coordinates used as addresses of two or three suitable maps are not needed, from which pixel information that is associated to the vertices to contribute to their final color are extracted.  
         [0011]     To locate a 3D object within a scene, certain geometric transformations are needed, that can be based upon simple affine transformations like rotations, translations, scaling, etc. Each object can be displaced independently from the others by transforming its vertices at a certain time. Natural motion is achieved by carefully applying sequences of transformations to obtain a discrete-linear approximation of real continuous motion. Such transformations are not incremental with respect to the previous ones. The position of the object at a certain time is obtained by applying transformations to the object geometry considered at an initial time.  
         [0012]     The viewpoint is also specified, which can be regarded as a window through which the 3D scene is watched. Global motion is a result of the object motion and the motion (if any) of the viewpoint. Alternatively, the viewpoint can be seen as a camera that samples the 3D scene. The 3D scene is displayed on a monitor by a bi-dimensional grid of pixels, each being associated by colors. Certain operations are applied to the pixels before they are displayed. These operations are the most demanding in terms of computational power.  
         [0013]     The pixels compose a frame that is a snapshot from the camera viewpoint. A typical frame-rate of 20-30 frames per second (fps) is needed to achieve a fluid motion perception by the viewer. Different Cartesian reference systems are used in a 3D pipeline. They are as follows: a model space, a world space, a view space, a clip space, and a screen space.  
         [0014]     In the model space, each model is a “local” reference system having for example, the lowest point as its origin to the 3D object. In the world space, all models are arranged within this unique system (OpenGL does not use it). Within the view space (or camera space) the viewpoint is placed at a “world space” point. The “world space” is transformed to have the “camera space” with the camera placed at its origin and directed to the negative z-axis.  
         [0015]     In the clip space, it is possible to detect what primitives are visible using the “clipping” process and send them through the pipeline. The “clip” space is a space obtained due to a perspective transform to have a “view volume”. It projects visible 3D objects on a bi-dimensional plane with a projection center placed at the camera itself (projective transform) or at infinity (orthogonal transform). In OpenGL, the “view volume” is normalized as a unitary cube defined by two vertices of (−1,−1,−1) and (1, 1, 1) coordinates in order to have more efficient clipping operations. A primitive with “clip” space coordinates within the cube is potentially visible.  
         [0016]     In the screen space the 3D primitive coordinates in the “clip” space are re-scaled into 2D screen coordinates depending on the real screen resolution. In  FIG. 1 a  block diagram is shown, illustrating a typical 3D graphic system  100  and its different stages.  
         [0017]     A useful general classification of the processing steps (operations) in such stages is based on the input type that is processed by each stage. Consequently, the pipeline operations can be classified in the following modes: per-vertex operations and per-triangle operations.  
         [0018]     The per-vertex operations are applied on vertices associated to each primitive that composes the scene. Geometric transforms are examples of these operations. The per-triangle operations are applied on the primitives that compose the scene. Exemplary of these are “clipping” and “culling.” The former defines the part of the primitives within the “view volume” and depending on the resulting intersection clipping defines how these are cut while the latter operation determines if they are located outside the “view volume” or back facing the “view point”.  
         [0019]     Per-pixel or per fragment operations operate directly on pixels. Exemplary of these are rendering, per-pixel lighting, per pixel texturing, fragmentation operations where one or more fragments are associated to each pixel. Another difference with respect to the other operations is that “per-pixel” or “per fragment” operations can be applied repeatedly to the same pixel displayed. This is the main reason why highly complex operations reside at this stage. In fact, they will influence also the frame rate.  
         [0020]     On the basis of the above definitions, the 3D graphic system  100  shown in  FIG. 1  can be subdivided in four main stages: an application/scene stage  101 , a geometry stage  111 , a triangle setup stage  112 , and a rendering/rasterization stage  113 . The geometry stage  111 , the triangle setup stage  112  and the rendering/rasterization stage  113  are part of a pipelined graphic engine  110 .  
         [0021]     Lights  107  and textures  108  are the input information regarding 3D objects  106  to the application/scene stage  101 . Operations in the application/scene stage  101  are defined and set by the programmer using API (Application Protocol Interface). OpenGL is an example of API. Typically the operations implemented are database management, motion set-up of 3D objects and camera, description of the content of a 3D animation, controls of primitive visibility (occlusion culling), and level of scene details (LOD, the number of primitives used to render the 3D scene).  
         [0022]     The geometry stage  111  is the first pipeline stage. The associated operations are mainly “per-vertex” operations. It includes operations suitable for moving 3D objects. Motion is obtained by applying geometric transforms to vertices of the primitives in each single object of the scene. Transforms are of the affine type and defined in an affine space where two entities are defined: points and vectors. Results of the transformations are vectors or points.  
         [0023]     The transforms used in a 3D pipeline can be grouped in two main families, i.e., rigid body transforms and project transforms. In rigid body transforms, i.e., roto-traslation plus scaling is where the results are still within the 3D space. In project transforms (prospective, orthogonal etc.), a primitive is moved from the 3D space to the 2D space where those objects are located that will be shown on the screen.  
         [0024]     These transforms use suitable square 4×4 arrays. Each affine transform can be obtained by properly defining each coefficient in such arrays. In the geometry stage  111  other operations such as “culling”, “clipping”, “screen space transform”, “lighting”, and “back-face culling” are also implemented, fully or partly, depending on the kind of implementation.  
         [0025]     The triangle setup stage  112  performs a step that prepares the following rendering stage  113 . In the triangle setup stage  112  operations on data from the geometry stage  111  are organized to compute a new set of data necessary for the next stage. Specifically, a new set of data is generated and associated to each vertex.  
         [0026]     By way of example, an incremental scan conversion process can be implemented in the triangle setup stage  112 . For each item in the list of triangles that are potentially visible and available from the geometry stage  111 , the process locates each triangle over the pixel grid depending also on the Z depth value associated to each vertex.  
         [0027]     The rendering/rasterization stage  113  is among the most complex stages from the computational viewpoint within the 3D graphic engine  110 . In fact, this stage performs “per pixel” computations that are typically iterated many times to provide the final appearance of each pixel actually displayed.  
         [0028]     Operations in the rendering/rasterization stage  113  comprise a shading operation that computes the color of each pixel composing the projected triangle. Different methods exist for implementing 3D shading. Those mostly used are flat shading, gouraud shading and phong shading. These methods span from low (flat) to high (phong) complexity and in the realism achieved.  
         [0029]     Other operations include depth cueing, texture mapping, antialiasing and rasterization. Rasterization draws the current frame with the colors computed during the shading operation by addressing pixels within a frame segment and pixels within a triangle. The order of the operations involved depends on the specific implementation. However, the outcome of the operations performed in the stages from  101  to  113  is finally supplied to a display frame device  130 .  
         [0030]     The description above highlights that the rendering stage  113  operates “per-pixel” and it is the stage in which the most part of the complexity resides. The workload of the rendering stage  113  influences the frame rate that can be achieved at the display  130  side. When the maximum workload that the rendering stage  113  can sustain is fixed, then the complexity of an application in terms of number and type of primitives may temporarily exceed the fixed computational power, thus originating a variable time for rendering a frame and variable frame rate. The same happens if algorithms with different complexities (such as the various shading techniques) are used at different times.  
         [0031]     An approach for obtaining a natural motion, while achieving a sufficient frame rate, is to decrease the number of primitives submitted to the pipeline or simplify the algorithms used. However, this will decrease the level of quality obtained. Allowing the pipeline to vary the frame rate with respect to a minimum value is known as an approach that preserves natural motion, ensures a minimum frame-rate and keeps the quality at good levels.  
         [0032]     If the obtained rate is below such a minimum value, a “frame rate up conversion” technique is applied to increase the frame rate to ensure that minimum rate. For example, if the frame rate is 10 frames per second, the pipeline should render at its output 10 frames per second, or better, one frame per 1/10 of second. If the pipeline can render only an integer number of n frames per second, while a number n 1 &gt;n of frames is required at its output, the frame rate up-conversion factor required is equal to the ratio n 1 /n.  
         [0033]     Methods are known that start from n rendered pictures and interpolate a number n 1  minus n of frames per second to increase the frame rate from n to n 1 . A temporal frame averaging method is one known method. It is a very simple method, but the resulting quality is very poor.  
         [0034]     Assuming that a pipeline is to provide an integer number n of frames, every frame f (with ƒ=1..n) is an image having X by Y pixel resolution, with X indicating the number of horizontal pixels and Y the number of vertical pixels. At each pixel (i,j) with i=0..X−1 and j=0..Y−1 of the f frame, an item of information C (i,j) (ƒ) is associated using P bits. Then each frame f will require (X by Y by P) bits to be stored in the frame buffer.  
         [0035]     Assuming that r is the minimum number of frames to display per second (i.e., the minimum frame-rate required, that typically ranges between 20 and 30 fps), if the pipeline is not able to ensure a minimum frame rate r, then the pipeline would render only a number n 1  frames, with n 1 &gt;n, using the averaging method to generate the remaining (n 1 −n) frames from n.  
         [0036]     For example, the relationship (n 1 −n)=n 1 /2 frames would apply. Even frames ƒ=2,4,6,.. are interpolated using odd frames ƒ−1 and ƒ+1 as follows: C (i,j) (ƒ) is the color of the pixel (i,j) of the frame ƒ, C (i,j) (ƒ−1) is the color of the pixel (i,j) of the frame ƒ−1, and C (i,j) (ƒ+1) is the color of the pixel (i,j) of the frame ƒ+1. Then:  
           C     (     i   ,   j     )       ⁡     (   f   )       =           C     (     i   ,   j     )       ⁡     (     f   -   1     )       +       C     (     i   ,   j     )       ⁡     (     f   +   1     )         2         
 
 which is done per each pixel (i,j) of the frame ƒ, with i=0..X−1 and j=0..Y−1. A major limit of temporal frame averaging lies in that no correction in the motion direction is available, even if possibly needed. 
 
         [0038]     Another known approach uses a motion estimator at the output of the graphic pipeline to estimate per pixel the motion information and correct the result of temporal averaging by using motion compensation techniques. A motion estimator would generate a motion vector per pixel. This however requires more computational power and memory.  
         [0039]     The drawbacks just described regarding 3D pipelines known in the art are particularly relevant when the 3D pipeline is to be included in a graphic card of a device like a mobile phone with an embedded display. It can also be connected to a remote smart display, e.g., for playing 3D games or running various graphic applications using a reduced bitrate wireless or wired transmission channel.  
         [0040]      FIG. 2  shows an application where a graphic system  100  for a mobile phone receives graphic instructions I from the 3D application  101 . On the basis of such instructions, the 3D engine  110  generates at its output fully rendered frames KF at a full rate F 1 . Each frame KF is represented by a bi-dimensional matrix of N rows by M columns, where each intersection between rows and columns defines a color represented by its R, G and B values coded over P bits.  
         [0041]     Such frames KF can now be sent to an embedded display or, as shown in  FIG. 2 , sent to a transmitter stage  120  that, using a wireless or wired connection, transmits them in the form of a bitstream R 1  towards a remote smart display device  130 . The remote smart display device  130  will receive the bitstream R 1  through a receiver stage  135  that outputs the fully rendered frames KF at the full rate F 1 . These represent the bi-dimensional matrix described in the foregoing including NxM colors (RGB) at a rate of F 1  frames per second.  
         [0042]     The bitrate of the bitstream R 1  is then equal to N*M*P*F 1  bits per second. By way of example, for a VGA picture having a resolution of 640×480 pixels the following values are used: N=640, M=480, P=16, F 1 =30, resulting in a bit rate of 140.6 Mbit/s. Such a bitrate is too high to be transmitted by resorting to current wireless or wired transmission standards that use transmission rates from hundreds of kbit/s to Mbit/s. Different architectures have been proposed to obtain more efficient compression schemes.  
         [0043]     Approaches are known to transmit bitstreams at a reduced bitrates using a video encoder, e.g., a MPEG2/4 or JPEG encoder. This can be connected between the 3D engine and the transmitting module to achieve a lower bandwidth during transmission. Of course, an MPEG2/4 or JPEG decoder is needed between the receiving module and the display unit (e.g., a screen) on the display side. These approaches are penalized by their complexity related to the architecture of JPEG/MPEG encoders and decoders. Furthermore, all these blocks process frames at full frame rate, and also introduce a very high latency thus making it difficult to play latency-sensitive application like games.  
         [0044]     Other approaches are known where the 3D engine produces frames to be fed to a motion estimator that considers each even frame. This is done with respect to the order of output from the 3D engine and by predicting the motion with respect to the previous and following odd frame. A plurality of motion vectors associated to each RGB pixel included in the even frames is then produced.  
         [0045]     The motion vectors are then coded using a Mvencoder device and transmitted to the smart display on the wireless connection. The Mvencoder device computes the differences between motion vectors, and then encodes these differences using a variable length code. This technique is widely used in the MPEG2/4 standards.  
         [0046]     The odd frames are also fed to a video encoder that processes them at a lower frame rate. However, to run the task in the frame buffer, the motion estimator should store the above-mentioned frames. While a video encoder can be simpler than an MPEGF2/4 or JPEG encoder, the motion estimator makes the system very expensive in view of the complexity of the functions it performs, the need for a frame buffer, and the need of processing process frames at the full rate output by the 3D engine.  
       SUMMARY OF THE INVENTION  
       [0047]     An object of the present invention is to provide a graphic engine, adapted to permit transmission toward a display unit at a reduced rate, through simpler circuits and at a lower cost.  
         [0048]     According to the present invention, the above object is achieved by a graphic system comprising a pipelined tridimensional graphic engine having the characteristics referred to specifically in the claims that follow. The invention also relates to a corresponding pipelining method, as well as to a computer program product that may be loaded in the memory of a computer and comprising software code portions or data fields for performing the method of the invention when the product is run on a computer.  
         [0049]     Substantially, the approach described herein provides a graphic engine that generates locally fully rendered frames at a reduced frame rate while producing additional motion vector information, without motion estimation, that feeds a motion compensation stage that can be locally or remotely placed with respect to the graphic engine. In the last case, motion information and fully rendered frames are compressed and sent by a wired or wireless connection to a remote smart display unit. There, such information is used along with the fully rendered frames for generating interpolated frames based upon a motion compensation stage.  
         [0050]     As a result, a sensible reduction in terms of complexity is achieved in comparison with the prior art. Also, motion estimation is not required on the graphic engine side. A system architecture to divide the features of the graphic engine and the smart display is also proposed as well as an approach fully local to the graphic engine.  
         [0051]     A display unit may be associated with the system for displaying the image frames at the second frame rate. The graphic system may be at least partially integrated as a self-contained device with the display unit. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0052]     The invention will now be described, purely by way of non-limiting examples, with reference to the attached drawings, wherein:  
         [0053]      FIGS. 1 and 2  are block diagrams of a graphic system and a remote smart display device according to the prior art;  
         [0054]      FIG. 3  represents a block diagram of a graphic system according to the invention;  
         [0055]      FIG. 4  represents in greater detail a portion of the graphic system of  FIG. 3 ;  
         [0056]      FIG. 5  represents a flowchart of the pipelining method according to the invention; and  
         [0057]      FIG. 6  represents motion vectors generated by the pipelining method according to the invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0058]     In the arrangement described herein, the workload of a graphic engine is reduced by generating a set of fully rendered frames at a reduced frame rate. The graphic engine further produces additional motion vector information. The motion vector information is extracted from the graphic pipeline at a point where this information is already directly available, without using motion estimators. A complete sequence of frames at a full frame rate is recreated starting from the fully rendered frames at a reduced frame rate. These frames are received, decoded and then used as base information to recreate the interpolated frames for obtaining a full frame rate. Predictions are obtained using the motion vectors that are used to address them. Predictions are subject to temporal averaging to create frames that, grouped to the reduced ones in the display order, compose the full frame set.  
         [0059]      FIG. 3  shows a graphic system  200 . A graphic application  201  supplies instructions I to a 3D engine  210 . This operates by generating fully rendered frames KF at a reduced frame rate F 2 , lower than the full frame rate F 1  that needs to be achieved at the display side. Thus, interpolated frames IF are needed to achieve a full frame rate.  
         [0060]     Interpolated frames are produced using the information stored in the motion buffers and the rendered frames. Optionally, if the motion compensation stage is placed into the remote smart display, the interpolated frames IF are not produced at the output of the 3D engine  210 , but remotely. A motion buffer encoder  214  is provided in this case to associate each RGB pixel of the future and remotely interpolated frames IF with motion buffer information MB, originated by the 3D engine  210  and sent to the motion buffer encoder  214 .  
         [0061]     The motion buffer encoder  214  computes the difference between incoming motion vectors. The difference is then coded using a variable length code (VLC) in the form of coded motion buffer information in a bitstream R 4  that is sent through a transmitter block  224  on a wireless or wired channel to a remote smart display  230 . A video encoder  215  encodes the fully rendered frames KF output at a full rate F 2  by the 3D engine  210  and sends a bitstream R 3  to a transmitter block  223  that transmits such a bitstream R 3  to the smart display  230 .  
         [0062]     For example, considering a frame comprised of a bi-dimensional matrix of N rows by M columns of RGB colors at a reduced frame rate F 2  and using a compression method adapted to compress 24 bits to 6 bits, the bitstream R 3  has a rate equal to (N*M*6*F 2 ). Consequently for QCIF picture resolution: N=176, M=144, F 2 =15 and R 3  is 2.175 Mbit/s; for QVGA picture resolution N=320, M=240, F 2 =15 and R 3  is 6.59 Mbit/s; and for CIF picture resolution N=352, M=288, F 2 =15 and R 3  is 8.7 Mbit/s.  
         [0063]     Since the bitstream R 4  has a rate typically negligible with respect to the rate of bitstream R 3 , the total bitrate can be transmitted on a wireless connection (such as a Bluetooth or 802.11 standard link) or wired connection, whose bitrate spans from hundreds of kbit/s to some Mbit/s. Furthermore, a suitable compression scheme, like compression schemes described in European Patent applications no. 2003002728 or no. 2003002205, can ensure a low delay, lower for instance than the delay encountered in a MPEG2/4 or JPEG encoder.  
         [0064]      FIG. 3  shows that the graphic engine  210  comprises a geometry stage  211 , a triangle stage  212  and a rasterization stage  213 . Motion buffer information MB is obtained primarily from the geometry stage  211 , as better detailed in the following, without using a motion estimator.  
         [0065]      FIG. 4  shows a block diagram of the smart display  230  comprising two receivers  233  and  234  for the bitstreams R 3  and R 4 , respectively. The receiver  234  is followed by a motion buffer decoder  235  that decodes the motion buffer information MB. For each variable length code, the motion buffer decoder  235  outputs a fixed variable code. This is added to the already decoded, previous code in order to recreate the original motion buffer information MB. The motion buffer information MB is then fed as input to a motion compensation stage  237 .  
         [0066]     The bitstream R 3 , containing the fully rendered frames KF at a frame rate F 2  after the receiving stage  233 , is decoded through a video decoder  236 , corresponding to the video encoder  215 . Then all the fully rendered frames KF originated at the reduced frame F 2  rate are stored in a frame buffer  239 .  
         [0067]     The motion compensation stage  237  receives the motion information MB. Each information stored in the motion information MB is associated to the corresponding pixel in the interpolated frame IF, and point at a space location in the reference frame. The pixel color of the interpolated frame IF is reconstructed by averaging the information of the pixels close to the space location pointed from the motion vector.  
         [0068]     The interpolated frames IF are then mixed to fully rendered frames KF through a multiplexing device  239  and displayed on a remote screen  240 . If a frame rate upconversion process is performed locally between the graphic engine and its display, and not remotely, the same motion compensation procedure described above applies.  
         [0069]     In the following, a description is provided of the methods used by the 3D graphic system shown in  FIG. 3  and  4  to carry out motion vector synthesis and picture motion compensation. These methods extract motion vectors from the geometry stage  111  and use them to compensate temporally the un-rendered frames with respect to those frames that were already rendered, i.e., the fully rendered frames KF.  
         [0070]     Like the temporal averaging technique, this technique uses one or more frames already rendered by the normal 3D pipeline, i.e.., the future and past frames with respect to the frame being interpolated. To perform such an operation, the motion compensation stage  237  is introduced in the 3D pipeline, operating in alternative to the rendering stage  213  at the display side (local or remote smart display).  
         [0071]     As already mentioned, the frames at the output of the pipeline belong to two categories, i.e., the fully rendered frames KF and the interpolated frames IF. The motion information MB concerning the 3D scene extracted from the geometry stage  211  is fed as an input to the motion compensation stage  237 .  
         [0072]     The interpolated frames IF are rendered by the motion compensation stage  237  that uses as predictors the fully rendered frames KF obtained from the video decoder  236 . A frame interpolation index NIF is also introduced to indicate how many interpolated frames IF should be generated by the motion compensation stage.  
         [0073]     The frame interpolation index NIF can be computed in real time by measuring the global motion of a scene. A high value in this measurement leads to a decrease in the number of interpolated frames IF, while a lower value in this measurement dictates an increase. The index NIF can also be set a priori during the pipeline initialization and kept constant during the execution time of the whole application. In a preferred embodiment, the frame interpolation index NIF is set equal to 1, so that the fully rendered frames KF and the interpolated frames IF are in equal numbers and may be sent in an interleaved way to the display  240   
         [0074]     If the motion compensation is local, then it is attached to the rendering stage while if placed remotely at the smart display side the video decoder  236  is coupled to the motion compensation stage  237 . This means that, before using the motion compensation stage  237 , at least one or two fully rendered frames KF should be decoded by the video decoder  236 .  
         [0075]     Specifically, in order to generate the interpolated frames IF in succession, a fully rendered forward frame KFF and a backward frame KFB should be available. A backward frame KFB is a reference frame at a later time in display order, while a forward frame KFF is a reference frame at an earlier time in display order.  
         [0076]     As its input, the motion compensation stage  237  thus receives a fully rendered frame KF, the frame interpolation index and the motion buffer information MB, and comprises a first buffer (designated a forward motion buffer MBF) associated to a forward frame KFF, and a second buffer (designated a backward motion buffer MBB) associated to a backward frame KFB.  
         [0077]     If the index NIF is zero then the pipeline behaves normally, and all the frames are rendered as usual. If the index NIF is equal to a generic value, e.g., n, then for each fully rendered frame KF, n interpolated frames IF should be interpolated by the motion compensation stage  237 . By setting the interpolated frame index NIF to a constant value, it is easy to know when the motion compensation stage  237  will interleave frames at the output of the video decoder  236 .  
         [0078]     Operation of the proposed pipelining arrangement will now be described with reference to the flowchart shown in  FIG. 5 . A block  501  indicates a pipeline initialization operation, in which all parameters, including the index NIF are initialized. The index NIF will then be assumed to be constant for the whole execution time and equal to n.  
         [0079]     Control is subsequently passed to block  502 . There, a motion vector synthesis operation is performed in the geometry stage  211  with a related storage operation  502 A of the results in data structures associated to the vertices. At this point of computation in the pipeline, in a step  503  an evaluation can be made as to whether the frame must be rendered or interpolated. Specifically a triangle setup phase  504 A and  504 B is performed depending on the outcome of step  503 .  
         [0080]     In the case of a fully rendered frame KF a triangle setup step  504 A is performed, carrying out all the operations already described with reference to  FIG. 1 . In the case of an interpolated frame IF, the triangle setup stage  212  computes motion vectors (backward and forward) that are associated to the vertices of potentially visible triangles in the interpolated frame. The triangle-setup stage  212  computes the content of the forward motion buffer MBF and the backward buffer MBB.  
         [0081]     Motion vectors are interpolated to associate information to pixels that form the interpolated frame IF. In general, for each pixel that is different from the interpolated frame IF background, two motion vectors are available. A first one is related to a forward frame KFF, and a second one is related to a backward frame KFB.  
         [0082]     Such interpolated vectors are properly quantized, and stored within the motion buffers MBF and MBB. Irrespective of whether the frame is a fully rendered frame KF or an interpolated frame IF, during the triangle-setup phase a depth buffer ZB is associated to the currently computed frame to divide the pixels in two categories: background pixels and pixels belonging to at least one triangle.  
         [0083]     Two different rendering operations follow, indicated as  505 A and  505 B, depending on the method used to render the frame. Specifically, if the frame is a fully rendered frame KF, in block  505 A the pixel colors are computed as for a normal rendering stage. If the frame is an interpolated frame IF, in block  505 B the pixel colors are computed through operations implemented in the motion compensation stage.  
         [0084]     Assuming the availability of the depth buffer ZB, the forward motion buffer MBF and the backward motion buffer MBB, the pixel color is set to the background value if this pixel belongs to the background. Otherwise, a control is performed depending on the orientations of the two motion vectors. If both vectors are within the forward frame KFF and backward frame KFB, then pixel color is computed by using the information addressed by these motion vectors.  
         [0085]     If only one vector falls in a valid area of a fully rendered forward frame KFF or backward frame KFB, then the pixel color is computed by using the valid information related to the fully rendered frame KF. If both motion vectors fall outside the references frames, then the following strategies can be applied: no operation is performed since there is no valid information about the color; one of the two vectors is truncated to cause it to point into the fully rendered frame KF, and then used for the next coloring phase; and both vectors are truncated and can be used to compute the pixel color.  
         [0086]     Since the motion vectors both being invalid is an unlikely event, it is generally advisable to follow the first strategy, i.e., no operation. In a step  506  the frames KF and IF are stored in the frame buffer  238  and then displayed. Then a jump back to the motion vector synthesis operation  502  is performed to start generation of the next frame.  
         [0087]     Additional details will now be provided on the process for computing motion vector for each vertex during the motion vector synthesis operation  502 . As stated before, a 3D application defines exactly what kind of movement there is at each time instant for each object composing a scene. Motion is obtained by transforming each vertex of each primitive that composes an object composing a scene. In this way, by positioning at each instant the primitives in the scene, the exact position of the respective objects within the scene is known. Such positions are specified by (x, y ,z) coordinates of transformed vertices v.  
         [0088]     These coordinates are specified in different modes depending on the reference system used. Motion vectors are simply computed by tracing the different positions, and motion is not properly estimated but rather traced precisely and so extracted. Such a motion extraction function is performed in the geometry stage  211  of the pipeline, and is properly modified to compute the motion vectors per vertex.  
         [0089]     For example by setting the frame interpolation index NIF=n, it will be sufficient to know and trace subsequent spatial positions of transformed vertices corresponding to the forward frame KFF and the backward frame KFB. In that time range, there will be n+2 spatial positions, n associated to n interpolated frames IF and two associated to the forward and backward frames.  
         [0090]     Basically, (n+2) positions need to be stored for each vertex. The first position stored is the one associated to the forward frame KFF. This position is the endpoint of the motion vector associated to the forward frame KFF vertices. For the next n positions (that are related to the next n time instants “framed” by n interpolated frames IF to be generated) are the application points or start points of the motion vector.  
         [0091]     The same applies to the backward frame KFB. Here the endpoint of the motion vector is associated to the backward frame KFB, while the start points are associated to n positions before. For example if the frame interpolation index NIF is equal to one, then three positions are stored for each vertex, related to interpolation time t 1 , time t 0  related to the forward frame KFF, and time t 2  related to the backward frame KFB.  
         [0092]     In  FIG. 6  an example is shown. v(x t ,y t ,z t ) indicates a motion vector, where the coordinates (x t ,y t ,z t ) are associated to the generic vertex v at a fixed instant. This is the endpoint of the vector itself. Conversely the start point of the vector v related to i-th interpolated frame IF is the position that the vertex has at time t i .  
         [0093]     If the frame interpolation index NIF assumes values between 1 and n, then v(x 0 ,y 0 ,z 0 ) for the generic motion vector will be always related to time instant t o  to which the forward frame KFF refers. Conversely, the position v(x n+1 ,y n+1 ,z n+1 ) of the generic motion vector will always be related to the time instant t n+1  to which the backward frame KFB refers.  
         [0094]     The intermediate positions v(x i ,y i ,z i ) i=1..n, will be the n next spatial positions that such a vertex will take, each related to a specific interpolated frame IF, of index I, to be generated. By adopting this convention and setting the index NIF to 1, then v(x 0 ,y 0 ,z 0 ) is the notation for a generic motion vector that expresses the motion between a vertex v for the (x 1 ,y 1 ,z 1 ) position at the time instant t 1 , related to the only interpolated frame available IF, and the position (x 0 ,y 0 ,z 0 ) of that vertex at the time instant t 0 , related to the forward frame KFF. Also, v(x 2 ,y 2 ,z 2 ) specifies a generic motion vector that synthesizes the motion between a vertex v at the position (x 1 ,y 1 ,z 1 ) at the instant t 1  (again related to the interpolated frame IF) and the position (x 2 ,y 2 ,z 2 ) at the time instant t 2  (again related to the backward frame KFB).  
         [0095]     The next (n+2) transformed coordinates (x,y,z) (i.e., positions) for each visible vertex are stored in the operation  502 A. The storage operation is associated to a time window extending over the n time instants covered by the interpolation process.  
         [0096]     The interpolated frames IF are generated starting from one or more fully rendered frames KF used as references. It is thus straightforward to understand that the coordinate system adopted should be compatible with the bi-dimensional space used for the fully rendered frame KF. x, y and z are coordinates of the generic v vertex after the screen space transform.  
         [0097]     The (n+2) coordinates (x i ,y i ,z i ) with i=0..n+1 stored for each vertex of the scene are obtained as follows. By considering a vertex v of a scene triangle having (x c ,y c ,z c ) as a set of three-dimensional coordinates specified during the execution time of the application, which is a so-called MODELVIEW operation (as well known in the context of OpenGL) which moves objects as the programmer desires.  
         [0098]     Specifically, M i  indicates a 4×4 MODELVIEW matrix associated to the vertex v at the time instant i, while P indicates a 4×4 PROJECTION (OpenGL view orientation) matrix that usually is held to be constant during application execution. S indicates a matrix that implements the screen-space transform, again held to be constant since the screen resolution is fixed.  
         [0099]     The coordinates used to store the motion vertices after (n+2) consecutive instants are designated (x i ,y i ,z i ). Then the relationship between the initial coordinates (x c ,y c ,z c ) of the vertex v and those coordinates (x i ,y i ,z i ) that are actually stored in the vertexes is the following:  
         (           x   i               y   i               z   i           )     =     S   ·   P   ·     M   i     ·     (           x   c               y   c               z   c           )           
 
 with i=0..n+1. 
 
         [0101]     The respective motion information, i.e., (n+2)*(x i ,y i ,z i ) will be stored in a data structure associated to the vertex v in addition to information such as e.g., the vertex source coordinates (x c ,y c ,z c ), the color (r,g,b), texture coordinates (r,g,b)(u,v), the normal (nx,ny,nz) coordinates, the blending factor, and so on.  
         [0102]     In regards to rendering and storing the fully rendered frame KF in the rendering stage  213 , it is important to underline that the frames at the output of the pipelined graphic engine are in a different order with respect to the order required for display.  
         [0103]     Specifically, if the expected display order of frames is f 1 , f 2 , f 3 , . . , f n-1 , f n , assuming that the even frames are rendered by the motion compensation stage  237  when the index NIF is 1, the generation order will be f 1 , f 3 , f 2 , f 5 , f 4 , . . , f n , f n-1 , which is different from the expected presentation order.  
         [0104]     As a consequence, to interpolate a frame IF corresponding to a frame f 2 , fully rendered frames KF corresponding to frames f 1  and f 3  are needed, as the associated forward frame KFF and backward frame KFB. This dictates the need of temporarily storing in an adhoc memory space at least f 1  and f 3  by using auxiliary buffers available in the pipeline.  
         [0105]     When interpolation takes place, the forward frame KFF and the backward frame KFB should be stored until the interpolated frame IF is completely generated. In the following additional details are provided concerning triangle-setup phase  504 B associated with the motion compensation operation  505 B. The forward frame KFF is displayed before the sequence including n interpolated frames IF. The backward frame KFB is displayed after the n-th interpolated frame IF, i.e., after the images of the fully rendered frames KF. The spatial position of the vertex of the 3D scene is thus well known within the temporal window including n+2 frames.  
         [0106]     As already explained (n+2) coordinates (x i ,y i ,z i ) with i=0..n+1 are stored for each visible vertex. Each set of coordinates (x i ,y i ,z i ) defines the endpoint of the motion vector associated to a given frame. Specifically, the first coordinates (i=0) and the last coordinates (i=n+1) correspond to the spatial arrangement of the vertexes related to forward frame KFF and backward frame KFB.  
         [0107]     When generating the i-th interpolated frame IF, the triangle-setup stage  212  is used to associate the vertex coordinate information at the i-th instant (x i ,y i ,z i ) to each pixel of the same i frame. In the arrangement described, the triangle-setup phase  504 B can be taken as a pre-processing phase for the motion information in step  505 B. After being properly transformed, this will be used by the motion compensation stage  237 .  
         [0108]     The motion information stored as the vertex position (x i ,y i ,z i ) at the i-th instant cannot be used directly by the motion compensation stage  237 , as this performs “per-pixel” processing. Consequently, the motion information associated to each pixel should also be calculated. This is required to address fully rendered frame KF data in the motion compensation stage  237 .  
         [0109]     In this way, the exact position of each pixel (i,j) in the forward frame KFF and the backward frame KFB will be known. The input data for each triangle processed during the processing of interpolated frame IF are the following. For v 0 (x i ,y i ,z i ), v 1 (x i ,y i ,z i ) and v 2 (x i ,y i ,z i ); these coordinates are the vertices of a triangle to be rasterized (ordered per increasing y and x), relative to the i-th instant. For v 0 (x 0 ,y 0 ,z 0 ), v 1 (x 0 ,y 0 ,z 0 ) and v 2 (x 0 ,y 0 ,z 0 ); these coordinates are related to the positioning of the same vertex at the instant associated to the forward frame KFF. For v 0 (x n+1 ,y n+1 ,z n+1 ), v 1 (x n+1 ,y n+1 ,z n+1 ) and v 2 (x n+1 ,y n+1 ,z n+1 ); these coordinates are related to the positioning of the same vertex at the instant associated to the backward frame KFB.  
         [0110]     During interpolation of the interpolated frame IF, the depth buffer ZB, the forward motion buffer MBF and the backward motion buffer MBB will store data related to visible triangles. In this way, two sets of useful information items are provided to compute the final color of the pixels within the interpolated frame IF in the subsequent motion compensation stage  237 .  
         [0111]     These information items are respectively stored in the depth buffer ZB, which allow those pixels related to the i-th interpolated frame IF to be divided into sets of visible pixels/objects and background pixels. The motion information is also stored in the forward motion buffer MBF and the backward motion buffer MBB.  
         [0112]     Typically, the location (i,j) of the forward motion buffer MBF includes three coordinates (x 0 ,y 0 ,z 0 ) i,j  related to the (i,j) pixel in the interpolated frame IF that point at the forward frame KFF. Similarly the location (i,j) in the backward motion buffer MBB includes (x n+1 ,y n+1 ,z n+1 ) i,j  coordinates related to the (i,j) pixel in the interpolated frame IF that point at the backward frame KFB.  
         [0113]     When a 3D application uses a perspective projection, the scan-conversion algorithm based on simple linear interpolation of motion vectors is not sufficient to address with the correct accuracy where the pixel (i,j) is located on the forward and backward frames KFF and KFB.  
         [0114]     A modified process with a perspective correction could be adopted. To each vertex two motion vectors are associated. The first is related to the forward frame KFF and is defined by the coordinates (x′ 0l ,y′ 0l ,z′ 0l ) with l=0..2, while the coordinates (x′ (n+1)l ,y′ (n+1)l ,z′ (n+1)l ) with  1 =0..2 specify. the second vector. All of the x′, y′ and z′ coordinates are screen-space.  
         [0115]     To compute the forward vector MVF i,j  the coordinates (x′ 0l ,y′ 0l ,z′ 0l ) are used that are associated to the vertex of a triangle (with l=0..2 indicating the corresponding vertex), while the coordinates (x′ (n+1)l ,y′ (n+1)l ,z′ (n+1)l ) are used for the backward vectors. The resulting process that uses perspective correction is a modified version of the linear process considered in the foregoing. The number of pixels per frame is fixed to (resX·resY), where resX and resY are the horizontal and the vertical resolution, respectively.  
         [0116]     All the items of information associated to a given pixel are stored in the buffer in a group of adjacent storage locations associated to each pixel. Motion buffers store the motion vector components associated to the i-th interpolated frame IF. Each motion vector is comprised of 3 components (x i ,y i ,z i ). z i  is a real coordinate. x i  and y i  are quantized and then stored. Additionally, motion buffers store a fourth coordinate for each pixel, namely z key .  
         [0117]     Specifically, the z pixel coordinate that was in the depth buffer ZB during the rendering phase of the forward frame KFF is stored as z key   pre  in the forward motion buffer MBF. Similarly, the z pixel coordinate that was in the depth buffer ZB during the rendering phase of the backward frame KFB is stored as z key   post  in the backward motion buffer MBB.  
         [0118]     The fourth coordinate z key  will be exploited for the Z-test of visibility in the motion compensation stage  237  described in the following. The two motion buffers MBF and MBB have a number (resX·resY) of locations. Each location stores no more than four coordinates. Two of these are z coordinates (including m bits each), while the two other coordinates are quantized x and y motion vector components (including n bits each). The size for each motion buffer is (resX·resY)·[2·m+2·n] bits.  
         [0119]     To compute the i-th interpolated frame IF, the depth buffer information is needed to distinguish between the pixels that are in the background and the pixels that are visible. Specifically, not-in-background pixels in the depth buffer ZB are pixels belonging to visible objects in the i-th interpolated frame IF.  
         [0120]     A motion vector can address a generic spatial location within a fully rendered frame KF. This location can be different from the (i,j) discrete position. Then the “virtual” pixel that is actually addressed (i.e., pointed to by the vector) may at least partially overlap with other pixels. Subsequently, a quantization procedure of the motion vector components is needed to cause the virtual pixel to coincide with at least one of the sub-pixel associated to each pixel.  
         [0121]     This process, which amounts to rounding the real coordinates (x i ,y i ) to the integer values (└x i ┘,└y i ┘), suggests that the motion vector components should be preferably quantized with a sub-pixel precision. The quantization procedure of the motion vector components having a precision 1/P (with P=1,2,4,..,2 i  where i is a positive integer) operates on a motion vector v(x i ,y i ,z i ). The real coordinates in the screen-space are x i ,y i  and z i .  
         [0122]     The index i is related to the motion buffer that is associated to the i-th interpolated frame IF. Then a quantized vector v(x i   q ,y i   q ,z i   q ) is obtained from vector v, by quantizing it with 1/P pixel precision. The coordinates (x i   q ,y i   q ,z i   q ) are obtained from (x i ,y i ,z i ) by using the following formula:  
             {             x   i   q     =       ⌊         x   i     ·   P     +   0.5     ⌋     P                   y   i   q     =       ⌊         y   i     ·   P     +   0.5     ⌋     P                   z   i   q     =     z   i                   
 
         [0123]     Thus, the quantization moves the vector to a sub-pixel position. If P=1 then the net effect achieved is rounding the (x i ,y i ) components to the nearest integers. This is the case when the motion vector points to the nearest pixel in the screen grid without sub-pixel decomposition.  
         [0124]     With P=2 (half-pixel precision) this operation moves to the center of the pixel to one of adjacent nine sub-pixels in the sub-grid associated with half-pixel definition. With P=4 (quarter-of-pixel precision) up to 25 sub-pixel positions in a respective sub-grid are available to reposition the motion vector. In general, if the quantization uses 1/P pixel precision, then (P+1) 2  sub-pixels are available for repositioning. Selecting P=2 appears to represent a reasonable compromise for most practical applications.  
         [0125]     In the following, additional details will be provided concerning the procedure for computing the color of each pixel in the i-th interpolated frame IF as performed in the moto-compensation operation  505 B. To each pixel a 4-integer value (R,G,B,A) is associated.  
         [0126]     In general, the process for computing the color generates a final pixel color (R,G,B,A) out  starting from n pixels, each one made of values (R,G,B,A) i . To each of these pixel values n weighting coefficients w i  are associated, where:
 
0&lt;w i &lt;1∀i=1..n
 
 Thus, the final color is:  
           (     R   ,   G   ,   B   ,   A     )     out     =       ∑     i   =   1     n     ⁢     [       w   i     ·       (     R   ,   G   ,   B   ,   A     )     i       ]           
 
         [0128]     The motion compensation stage  237  performs a general process for computing colors having as its inputs i) two frames KF (forward frame KFF and backward frame KFB) already rendered by the rendering stage  213 , to be used as references; ii) motion buffer information MB related to the forward and backward frames KFF and KFB, including for each pixel of the i-th interpolated frame IF the coordinates (x i ,y i ,z i ,z Zbuffer ) where x i ,y i  and z i  are the motion vector&#39;s screen coordinates computed at the triangle setup phase  504 B and z Zbuffer  is the buffer ZB pixel value associated to the key frame; and iii) the buffer information ZB i  related to the i-th interpolated frame IF under generation.  
         [0129]     If a pixel (i,j) is not in the background, a check operation is performed to test if the motion vectors are valid or not. A motion vector is valid when its quantized coordinates x and y address an internal location of a related, fully rendered frame KF. Practically, a motion vector is considered valid if:
 
0&lt;x&lt;resX−1
 
0&lt;y&lt;resY−1
 
         [0130]     After such operation if both motion vectors for the pixel (i,j) are valid, the final color is computed using four pixels that overlap the quantized position addressed on the forward frame KFF. The same applies to the backward frame KFB. A total of 8 pixels are used with weighting factors w i  con i=1..8. If only one motion vector is valid, this is used to compute the color of the pixel. Only 4 pixels and weighting factors are needed, related to a fully rendered frame KF. If both motion vectors are invalid (a rare occurrence) different strategies can be used, i.e.,: no action is taken; the pixel is the same as the background; both vectors are made valid by suitable truncation, thus going back to the first case; only one vector is made valid by truncation and then the second case is applied; and the image borders are extended by simple replication of the first/last row/column to cover the space region that make valid the motion vectors. As a result the extension encloses the vector.  
         [0131]     Finding correct values for the weights w i  is important since this has an impact on the final quality. The general scheme is able to compute eight weight coefficients w i  if both motion vectors are valid or if only one is valid and uses four coefficients.  
         [0132]     A procedure to compute the interpolated frame IF using motion compensation information is the following. It uses two motion vectors per pixel from the forward motion buffer MBF, (x pre ,y pre ,z pre ,z ZbufferPre ) associated to the forward frame KFF, and from the backward motion buffer MBB, (x post ,y post ,z post ,z ZbufferPost ) associated to the backward frame KFB. The quantization precision factor P is preferably set to 2.  
         [0133]     Two different criteria to find the weight w i  may be adopted. Assuming that weights w 1 , w 2 , w 3 , w 4  are associated to four pixels addressed by the motion vector on the forward frame KFF, while weights w 5 , w 6 , w 7 , w 8  are associated to four pixels related to the backward frame KFB, the motion vector related to forward frame KFF is considered and the first four weights w i , with i=1..4, are computed on the basis of parameters ca i  and cb i  which are computed using criteria A or B, as detailed in the following.  
         [0134]     By definition w i =ca i ·cb i . The parameters ca i , cb i  are computed starting from (x pre ,y pre ,z pre ,z ZbufferPre ) of a valid motion vector. The criteria referred to in the foregoing are as follows.  
         [0135]     For criteria A, if P=2, then each quantized motion vector has x pre  and y pre  coordinates with decimal portions having values 0 or 0.5. This implies that a quantized pixel can overlap only one of 1, 2 or 4 pixels in the pixel grid of a fully rendered frame KF.  
         [0136]     The number of overlapped pixels influence how ca i  (with i=1..4) is computed:  
         ca   i     =       test   i     NPS         
 
 where NPS indicates the number of pixels overlapped to the quantized motion vector position. test i  is a test variable that can be 0 or 1, if the i-th pixel is (partially) overlapped to “quantized” pixel (test i =1) or not (test i =0). 
 
         [0138]     For criteria B, criteria B uses z pre  and z ZbufferPre  to run a visibility test, while in criteria A only the x pre  and y pre  components are used from each motion vector. The motion vector coordinates x pre  and y pre  address pixels on the forward frame KFF. This may overlap with four pixels of the forward frame KFF.  
         [0139]     This criteria compares z pre  coordinate of the motion vector with each  
         z   i     Zbuffer   ⁢           ⁢   Pre       ,       
 
 with i=1..4 pixels overlapped. If the difference is very low, then a substantial likelihood exists that any overlapped pixel would be very close to the current pixel to be colored in the interpolated frame IF. Otherwise if the difference in the z coordinate is high, the pixels are highly likely to belong to different objects. Pixel color information is not useful and the related weighting factor should be very low. 
 
         [0141]     Then cb i  is defined as follows:  
           Δ   ⁢           ⁢     z   i       =            z   pre     -     z   i     Zbuffer   ⁢           ⁢   Pre                ,       
 
 where i=1..4 indicates which 4 overlapped pixels are addressed. If Δz i &gt;S then cb i =0, otherwise if Δz i ≦S then cb i =1. A forward or backward motion compensation with no Z-test is also possible, thus introducing further simplifications in comparison with the techniques considered before. 
 
         [0143]     For weights w i  with i=1..8, criteria A is the only one used. Criteria B is not applied. Since the z coordinate information is not used, motion vectors MVF and MVB are specified as quantized values (x pre ,y pre ) and (x post ,y post )  
         [0144]     Finally, a forward-only motion compensation procedure can be used. Such procedure uses a single, fully rendered frame KF (e.g., the forward frame KFF), and a single motion vector per pixel to determine the spatial location of that pixel in the forward frame KFF. Since the backward frame KFB is no longer needed, the related memory is free and the processing order is the same as the visualization order on the display side.  
         [0145]     The temporal window in this case includes (n+1) frames. In the place of tracing (n+2) consecutive vertex positions only (n+1) such positions are needed (where n is the frame interpolation index NIF). In this case, triangle setup phase  504 B generates only one motion buffer and is related to the fully rendered frame KF before n interpolated frames IF. The motion compensation stage uses only one motion vector for each pixel in the interpolated frame IF.  
         [0146]     The criteria used for the bi-directional motion compensation procedure can be used in this case as well. If the motion vector is not valid, since e.g., a given detail is not on the fully rendered frame KF, the motion vector must be made valid by truncating the (x,y) components. Another approach is to extend the fully rendered frame KF up to the location addressed by the motion vector. The weights w i  are not as limiting as example four and are computed as previously explained. The arrangements disclosed herein lead to significant advantages over previously known approaches.  
         [0147]     The proposed graphic system and pipelining method generate motion vectors without the need for any motion estimation algorithm and the corresponding hardware resources. Also, the motion compensation stage advantageously uses information in the motion buffer where 4 dimensional information guides the process. Interpolated pictures which are fully rendered are then re-ordered and sent to a display in the right temporal order.  
         [0148]     When a remote smart display is used, the motion compensation stage is placed within it and uses motion information that are transmitted by the modified and proposed graphic engines. Motion information and fully rendered frames are also compressed by the graphic engine and received (via wireless or wired channel) by the smart display, then decoded and sent to the motion compensation stage.  
         [0149]     Additionally, the graphic system disclosed herein is adapted for use within the framework of a very simple video encoder originating a very short processing delay, in particular, when compared to state-of-the-art MPEG2/4 or JPEG encoders.  
         [0150]     Operation of the 3D engine at a reduced frame rate leads to a reduction in terms of power consumption, since this depends linearly on the difference between full and reduced frame rates. It is therefore evident that without prejudice to the underlying principle of the invention, the details and embodiment may vary, also significantly, with respect to what has been disclosed just by way of example without departing from the scope of the invention, and defined by the claims that follow.