Patent Publication Number: US-7212215-B2

Title: Apparatus and method for rendering an antialiased image

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefits of Japanese Patent Application Numbers: 2000-252148, filed Aug. 23, 2000; and 2001-241292, filed Aug. 8, 2001, the entire disclosures of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention relates to an apparatus and method for rendering an antialiased image, which are suitable for use in an entertainment system, such as a game machine, and a computer system. 
     Nowadays, the advent of highly-integrated, high-speed processors and memories has enabled real-time generation of three-dimensional images, which has hitherto been difficult to achieve. Thus, for example, a video-game machine is enabled to display three-dimensional images with realism. 
     When a three-dimensional image is displayed, the three-dimensional image is resolved into a plurality of polygons (that is, unit figures). Then, the entire three-dimensional image is rendered by rendering each of these polygons. 
     Practically, the displaying of this three-dimensional image is performed by performing geometry processing, such as coordinate transformation, clipping processing and lighting processing, on data representing the polygons which constitute the three-dimensional image, and then performing perspective projection conversion processing on resultant data obtained by such geometry processing to thereby convert three-dimension space data into data representing pixels arranged on a two-dimensional plane. 
     When such a three-dimensional image is rendered, the position of each of the polygons, which is represented by a floating or fixed point number, is converted into an integer number so as to be made to correspond to a pixel located at a fixed position on the screen of a display apparatus. Thus, aliasing occurs. Further, stair-step-like distortions called “jaggies” of a display image are caused owing to this aliasing. An occurrence of such aliasing or a jaggy may give a sense of incongruity to a user watching the three-dimensional image. Especially, in the case that this three-dimensional image is a dynamic image, flicker may be caused in this image. 
     Thus, a conventional image rendering apparatus reduces jaggies by virtually dividing each pixel into finer units called “sub-pixels” and then calculating the intensity of light of each of the sub-pixels according to a ray tracing method and thereafter averaging the calculated intensities of light of the sub-pixels of each pixel. 
     Further, another conventional image rendering apparatus reduces the jaggies by first generating a high-resolution image and then performing filtering on the image thereby to decrease the number of pixels and to antialias the image. 
     However, generally, a dynamic image comprises 20 to 30 frames or so per second. Thus, the rendering of a dynamic image needs to perform the calculation of the intensity of light of each of the sub-pixels according to the ray tracing method 20 to 30 times per second. Therefore, the former conventional image rendering apparatus, has drawbacks in that such calculations take time and that a dynamic image cannot be antialiased in real time. 
     Furthermore, the latter conventional image rendering apparatus, which is adapted to antialias (that is, reduce jaggies) by first generating a high-resolution image and then performing filtering on the image thereby to decrease the number of pixels, has drawbacks in that a buffer memory and a Z-buffer, each of which has large capacity and operates at a high speed, are needed when a dynamic image is displayed, and, thus, increasing the manufacturing cost and size of the apparatus increase. 
     SUMMARY OF THE INVENTION 
     The invention is accomplished in view of the aforementioned drawbacks of the conventional apparatuses. Accordingly, an object of the invention is to provide an image rendering apparatus of a low-cost small-sized configuration, which is enabled to reduce jaggies in real-time, and to provide an image rendering method enabled to reduce jaggies in real-time, a storage medium for storing a image rendering program enabled to reduce jaggies in real-time, and a server apparatus for distributing such an image rendering program. 
     To achieve the foregoing object, according to an aspect of the present invention, there is provided an image rendering apparatus that comprises an image rendering means for rendering an image, an antialiased image forming means for forming a partially antialiased image by extracting data corresponding to a predetermined line part of the rendered image and performing antialiasing processing on the extracted data, and overwriting means for overwriting the formed partially antialiased image onto the image rendered by the image rendering means. 
     Thus, according to the invention, data corresponding to, for example, a predetermined line part of an edge portion of a rendered image is extracted. Subsequently, antialiasing is performed on the extracted data. Thus, a partial antialiased image is formed. Then, this partial antialiased image is overwritten onto the rendered image. 
     Consequently, an image, in which jaggies are reduced by performing partially antialiasing thereon, is obtained. Further, because the image is partially antialiased, jaggies in the image are reduced at a high speed even when low-speed and low-cost devices are used. Thus, it is possible to make the apparatus of a low-cost simple configuration perform an operation of reducing jaggies on a dynamic image in real time. 
     Further, according to another aspect of the invention, there is provided an image rendering method that comprises the steps of rendering an image by an image rendering means, forming a partially antialiased image by extracting data corresponding to a predetermined line part of the rendered image and performing antialiasing processing on the extracted data, and overwriting the partially antialiased image onto the rendered image. 
     Thus, according to the invention, data corresponding to, for example, a predetermined line part of an edge portion of a rendered image is extracted. Subsequently, antialiasing is performed on the extracted data. Thus, a partial antialiased image is formed. Then, this partial antialiased image is overwritten onto the rendered image. 
     Consequently, an image, in which jaggies are reduced by performing partially antialiasing thereon, is obtained. Further, because the image is partially antialiased, jaggies in the image are reduced at a high speed even when low-speed and low-cost devices are used. Thus, it is possible to make the apparatus of a low-cost simple configuration perform an operation of reducing jaggies on a dynamic image in real time. 
     Furthermore, according to another aspect of the invention, there is provided a storage medium for storing a computer program. This program comprises the steps of rendering an image by an image rendering means, forming a partially antialiased image by extracting data corresponding to a predetermined line part of the rendered image and performing antialiasing processing on the extracted data, and overwriting the partially antialiased image onto the rendered image. 
     Thus, according to the invention, data corresponding to, for example, a predetermined line part of an edge portion of a rendered image is extracted by executing the computer program stored on the storage medium. Subsequently, antialiasing is performed on the extracted data. Thus, a partial antialiased image is formed. Then, this partial antialiased image is overwritten onto the rendered image. 
     Consequently, an image, in which jaggies are reduced by performing partially antialiasing thereon, is obtained. Further, because the image is partially antialiased, jaggies in the image are reduced at a high speed even when low-speed and low-cost devices are used. Thus, it is possible to make the apparatus of a low-cost simple configuration perform an operation of reducing jaggies on a dynamic image in real time. 
     Further, according to another aspect of the invention, there is provided a server apparatus that comprises a storage medium for storing a computer program. This program comprises the steps of rendering an image by an image rendering means, forming a partially antialiased image by extracting data corresponding to a predetermined line part of the rendered image and performing antialiasing processing on the extracted data, and overwriting the partially antialiased image onto the rendered image. This server apparatus further comprises distributing means for distributing a computer program stored on the storage medium. 
     The distributing means includes, for example, means for distributing the computer program in a wireless manner, in addition to means for distribution of the computer program in a wired way through a communication network, such as the Internet. 
     Thus, according to the invention, data corresponding to, for example, a predetermined line part of an edge portion of a rendered image is extracted by executing the computer program distributed by the server. Subsequently, antialiasing is performed on the extracted data. Thus, a partial antialiased image is formed. Then, this partial antialiased image is overwritten onto the rendered image. 
     Consequently, an image, in which jaggies are reduced by performing partially antialiasing thereon, is obtained. Further, because the image is partially antialiased, jaggies in the image are reduced at a high speed even when low-speed and low-cost devices are used. Thus, it is possible to make the apparatus of a low-cost simple configuration perform an operation of reducing jaggies on a dynamic image in real time. 
     Further, according to another aspect of the invention, there is provided a computer program that comprises a step of performing, when an image is rendered, antialiasing on at least a limited portion including a predetermined line part of the image. Thus, an image, in which aliasing and jaggy are reduced partially, is obtained. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block view illustrating a video-game machine that is an embodiment of the invention; 
         FIG. 2  is a block view illustrating a graphic memory provided in the video-game machine; 
         FIG. 3  is a flowchart illustrating an operation of reducing jaggies, which is performed in the video-game machine that is the embodiment of the invention; 
         FIG. 4  is a view illustrating contours and contour candidates extracted from an image to be rendered in the operation of reducing jaggies; 
         FIG. 5  is a view illustrating an image to be written to a frame buffer of the graphic memory without performing antialiasing thereon; 
         FIGS. 6A and 6B  are views illustrating an antialiasing operation to be performed on the extracted contours and contour candidates; 
         FIG. 7  is a view illustrating the antialiased contours and contour candidates; and 
         FIG. 8  is a view illustrating an image obtained by overwriting the antialiased contours and contour candidates onto the image written to the frame buffer. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       FIG. 1  illustrates a video-game machine to which an image rendering apparatus of the present invention is applied. This video-game machine has two kinds of bus lines, that is, a main bus  1  and a sub-bus  2 , which serve as bus lines for performing data transmission in each block. The main bus  1  and the sub-bus  2  are connected to each other through a bus controller  3 . The main bus  1  is used as a bus line for high-speed data transmission, while the sub-bus  2  is used for low-speed data transmission. The rapidity of the main bus  1  is ensured by transmitting data, which may be transmitted at a low speed, by using the sub-bus  2 . 
     The main bus  1  is connected to a main CPU (Central Processing Unit)  4  comprising, a microprocessor for example, a main memory  5  including, a RAM (Random Access Memory) for example, a main DMAC (Direct Memory Access Controller)  6 , an MDEC (MPEG (Moving Picture Experts Group) Decoder)  7 , and a GPU (Graphic Processor Unit)  8 , in addition to the bus controller  3 . 
     The sub-bus  2  is connected to the GPU  8 , a sub-CPU  9  similar to the main CPU  4  for example, a sub-memory  10  similar to the main memory  5  for example, a sub-DMAC  11 , a ROM (Read-Only Memory)  12  for storing an operating system etc., an SPU (Sound Processing Unit)  13 , an ATM (Asynchronous Transmission Mode) communication portion  14 , an auxiliary storage unit  15 , and an input device I/F (interface)  16 , in addition to the bus controller  3 . 
     The bus controller  3  performs a connection control operation of either disconnecting the main bus  1  from the sub-bus  2  or connecting the main bus  1  to the sub-bus  2  according to circumstances. 
     When the main bus  1  is disconnected from the sub-bus  2 , devices connected to the main bus  1  cannot access devices connected to the sub-bus  2  and vice versa. 
     In contrast, when the sub-bus  2  is connected to the main bus  1 , devices connected to main bus  1  can access devices connected to the sub-bus  2 , and vice versa. 
     In an initial state (just after power-up of this video-game machine), the bus controller  3  is adapted to perform a control operation in such a way as to connect the main bus  1  to the sub-bus  2  (that is, bring the main bus  1  and the sub-bus  2  into an open state). 
     The main CPU  4  performs various kinds of control operations according to a program stored in the main memory  5 . Practically, for example, when this video-game machine is booted, the main CPU  4  reads a boot program from the ROM  12  connected to the sub-bus  2  through the bus controller  3 , and boots the video-game machine. Then, the main CPU  4  loads application programs (in this case, game programs and an image rendering program (to be described later)) and necessary data into the main memory  5  and the sub-memory  10  from the auxiliary storage unit  15  such as a disk drive unit, and executes the application programs. 
     Furthermore, a GTE (Geometry Transfer Engine)  17  is provided in the main CPU  4 . This GTE  17  has a parallel processing system for simultaneously performing a plurality of operations. Further, the GTE  17  performs arithmetic operations for geometry processing, such as coordinate transformation, light source calculation, matrix operations, and vector operations, at a high speed in response to requests from the CPU  4 . Moreover, the GTE  17  generates polygon data representing polygons, which constitute a three-dimensional image to be displayed, and supplies the generated polygon data to the main CPU  4 . 
     When receiving the polygon data from the GTE  17 , the CPU  4  obtains two-dimensional space data by performing perspective projection conversion on the received data. Subsequently, the main CPU  4  transfers the generated data to the GPU  8  through the main bus  1  at a high speed. 
     Furthermore, a cache memory (or cache)  18  is provided in the main CPU  4 . Thus, the main CPU  4  can speed up data processing by accessing this cache memory  18  instead of the main memory  5 . 
     The main memory  5  stores the programs, as described above, and the data which is needed for the data processing in the main CPU  4 . 
     The main DMAC  6  performs a DMA transfer control operation on devices on the main bus  1 . Further, when the bus controller  3  is in the open state, the main DMAC  5  performs the DMA transfer control operation on the devices on the sub-bus  2  in addition to the devices on the main bus  1 . 
     The MDEC  7  is an I/O device that can operate concurrently with the main CPU  4 . Further, the MDEC  7  functions as an image expansion engine and reproduces image data compression-coded by utilizing, for example, MPEG techniques. 
     The GPU  8  functions as a rendering processor. That is, the GPU  8  calculates pixel data representing pixels of the polygons according to the color data of the vertices of the polygons and the Z-values representing the depth thereof from a viewpoint. Thereafter, the GPU  8  writes (or renders) the calculated pixel data to the graphic memory  19 . Thus, an image rendering operation is performed. Moreover, the GPU  8  reads pixel data rendered onto the graphic memory  19  and outputs the pixel data in the form of a video signal. 
     Incidentally, the GPU  8  fetches polygon data from the main DMAC  6  and the devices on the sub-bus  2 . Then, the GPU  8  performs rendering according to the polygon data. 
     The graphic memory  19  comprises a DRAM etc. for example, and has a frame buffer  25 , a Z-buffer  26  and a texture memory  27 , as illustrated in  FIG. 2 . 
     The frame buffer  25  has (what is called) a dual buffer configuration and has a storage capacity of two frames. That is, the frame buffer  25  has first and second frame buffers (sub-buffers), each of which has a storage capacity that is sufficient to store pixel data of one frame. The frame buffer  25  is constructed so that pixel data written to the second frame sub-buffer is read while pixel data is written to the first frame sub-buffer, and that pixel data written to the first frame sub-buffer is read during pixel data is written to the second frame sub-buffer. That is, the frame sub-buffers are alternately assigned to a buffer used for displaying pixel data, that is, a buffer used for reading pixel data therefrom corresponding to each frame, and the other frame sub-buffer is assigned to a buffer used for writing pixel data thereto. In other words, sub-buffers respectively assigned to the buffer used for reading pixel data therefrom, and the buffer used for writing pixel data thereto are switched between the first and second frame sub-buffers every frame. 
     The Z-buffer  26  has storage capacity sufficient to store Z-values of one frame. This Z-buffer  26  is adapted to store a Z-value of a frontmost polygon, which is located nearest to a user watching the screen, of an image to be displayed on the screen. The texture memory  27  is adapted to store data of textures to be attached to the polygons. 
     The GPU  8  is adapted to perform rendering by using the frame buffer  25 , the Z-buffer  26 , and the texture memory  27 . That is, the GPU  8  causes the Z-buffer  26  to store a Z-value of a frontmost one of the polygons constituting a three-dimensional image, and determines according to the stored Z-value whether or not pixel data is rendered onto the frame buffer  25 . When the pixel data is rendered thereonto, the GPU  8  reads data representing the texture from the texture memory  27  and then obtains the pixel data by using the read data. Subsequently, the GPU  8  renders the pixel data to the frame buffer  25 . 
     As illustrated in  FIG. 1 , the sub-CPU  9  performs various kinds of processing by reading the programs stored in the sub-memory  10  and executing the read programs. Like main memory  5 , the sub-memory  10  is adapted to store the programs and data needed by the sub-CPU  9 . 
     The sub-DMAC  11  performs a DMA transfer control operation on the devices on the sub-bus  2  only when the main bus  1  is disconnected from the sub-bus  2  by the bus controller  3  (that is, only in a closed state). 
     The ROM  12  stores boot programs for both the main CPU  4  and the sub-CPU  9 , and an operating system, etc. 
     The SPU  13  receives packets transferred from the sub-CPU  9  or the sub-DMAC  11 , and reads audio data from the sound memory  20 , which stores the audio data, according to a sound command included in the packet. Subsequently, the SPU  13  supplies the audio data to a speaker unit, and causes the speaker unit to generate corresponding sounds. 
     The ATM communication portion  14  controls communication operations (that is, ATM communication operations) to be performed through a network (NW), such as a public line. Thus, a user of the video-game machine may transmit data directly to and receive data directly from a user of another video-game machine or may transmit data to and receive data from the latter user through the Internet or the center office of what is called a personal computer communication system. This enables a user of a video-game machine to play a game (for example, a battle game) on the network with a user of another video-game machine. 
     The auxiliary storage unit  15  is an optical disk drive unit, and enabled to reproduce (or read) information like programs and data recorded on optical disks, such as a CD-ROM, a CD-RW, a DVD-ROM, and a DVD-RW. 
     The input device I/F  16  is an interface for taking in signals corresponding to operations to be performed on an operation unit serving as a control pad and an external input image (video input) and audio signals (audio input) reproduced by other devices. Further, the input device I/F  16  outputs the external input signal onto the sub-bus  2 . 
     When a main power supply is turned on, the main CPU  4  reads and executes the boot program from the ROM  12  in the video-game machine. Further, programs and data are read from a CD-ROM set in the auxiliary storage unit  15 . Such programs and data are loaded into the main memory  5  and the sub-memory  10 . Then, by executing the program in the main CPU  4  or the sub-CPU  9 , the dynamic image and sounds of a game are reproduced. 
     Practically, the main CPU  4  generates polygon data for rendering polygons, which constitute a predetermined three-dimensional image, according to the data stored in the main memory  5 . Then, the main CPU  4  encodes this polygon data into packets and supplies the packets to the GPU  8  through the main bus  1 . 
     When receiving the polygon data, which is encoded into the packets, from the main CPU  4 , the GPU  8  renders the polygons in the frame buffer  25  in sequence from the polygon according to an object to which the main CPU  4  issued an output instruction, by simultaneously performing Z-buffering by using the Z-buffer  26  illustrated in  FIG. 2 . The image rendered in the frame buffer  25  is suitably read by the GPU  8  and then outputted in the form of a video signal. Thus, the three-dimensional image for the game is displayed on the two-dimensional screen of a display apparatus. 
     On the other hand, the sub-CPU  9  generates a sound command, in response to which the generation of sounds is performed, according to the data stored in the sub-memory  10 . Subsequently, the sub-CPU  10  encodes this sound command into packets and supplies the packets to the SPU  13  through the sub-bus  2 . The SPU  13  reads sound data, which is stored in the sound memory  20 , according to the sound command issued from the sub-CPU  9 , and supplies this sound data to a speaker unit. Thus, sounds of BGM (Background Music) of the game and other kinds of sounds are radiated through the speaker unit. 
     When a three-dimensional image is rendered, the position of each of the polygons, which is represented by a floating or fixed decimal point number, is converted into an integer number so as to be made to correspond to a pixel located at a fixed position on the screen of the display apparatus. Thus, aliasing occurs by entailing stair-step-like distortions called “jaggies”. 
     The video-game machine performs an operation of reducing jaggies, according to an antialiasing program. This antialiasing program is reproduced (or read) from a CD-ROM or DVD-ROM, etc. in the auxiliary storage unit  15  shown in  FIG. 1 . Alternatively, this program is downloaded by the ATM communication portion  14  from a storage medium  22  (such as a hard disk (HDD)) provided in the predetermined server apparatus  21  through the communication network NW such as the Internet. 
     This antialiasing program includes routines illustrated in the flowchart of  FIG. 3 . The execution of the antialiasing program illustrated in this flowchart is started when the program is loaded into the main memory  5  and put into an executable state after the main power supply is turned on and the program is received from the auxiliary storage unit  15  or the server apparatus  21  shown in  FIG. 1 . 
     Incidentally, it is assumed that data needed for rendering the polygon, such as data representing the shape of the polygon and data concerning the light source, are stored in the main memory  5  at that time. 
     At step S 1 , the main CPU  4  reads the polygon data, which is needed for rendering polygons that constitute a three-dimensional image of 1 frame, from the main memory  5  through the main bus  1  and then supplies or transfers the read polygon data to the GTE  17 . Subsequently, the main CPU  4  extracts contours and contour candidates of the three-dimensional image to be rendered, if necessary, as line data or line strip data according to this polygon data. The extracted data is temporarily stored in the cache memory  18 . 
       FIG. 4  illustrates an example of the three-dimensional image for describing the contours and the contour candidates thereof. Referring to  FIG. 4 , the “contour” is an outline that becomes the outward form of an object independently of a direction from which the contour is seen in the three-dimensional space. In contrast, the “contour candidate” may be employed as such an outline that becomes or does not become the outward form of an object depending upon a direction from which the contour candidate is seen in the three-dimensional space. Such contours and contour candidates are “visually important lines” representing the parts of three-dimensional images such as edge portions of an object. It is preliminarily determined according to the three-dimensional image, which includes such lines, and the viewpoint what parts of the object respectively correspond to the “visually important lines”, that is, what polygons respectively correspond to these lines. Consequently, the main CPU  4  extracts contours and contour candidates, if necessary, of the three-dimensional image as line (or curve) data or line strip data according to this polygon data, when transferring the polygon data to the GTE  17 . 
     At step S 1 , the extraction of the “visually important lines” is performed. Thus, data representing lines, which have a low probability that these lines are the outlines of the object (that is, these lines are visually unimportant lines), are not extracted as line data or as line strip data. 
     Thus, at step S 1 , only necessary minimum line data or line strip data representing visually important portions are extracted. Further, as will be described later, antialiasing processing is performed on the extracted line data or line strip data. Therefore, the time required to perform antialiasing processing is reduced. Consequently, the speed, at which the entire three-dimensional image is rendered, is increased. 
     Next, at step S 2 , the main CPU  4  performs rendering processing. Practically, when supplied with the polygon data for rendering the polygons, the GTE  17  of the main CPU  4  performs geometry processing on each of the polygons in the three-dimensional space according to the position of the viewpoint. Moreover, the GTE  17  performs perspective projection conversion processing on the data having undergone the geometry processing. The “viewpoint” serving as a reference point for the geometry processing is given by the operation unit via the user. 
     Further, the main CPU  4  obtains the polygon data by calculating luminance and texture addresses corresponding to each of the polygons in a screen coordinate system upon completion of this perspective projection conversion. The main CPU  4  then supplies the polygon data to the GPU  8  through the main bus  1 . 
     When supplied with the polygon data of 1 frame from the main CPU  4 , the GPU  8  divides each of the pixels located at the coordinates of each of the vertices of the polygons into 16 sub-pixels (that is, one pixel is divided into a 4×4 matrix of sub-pixels). Then, the GPU  8  obtains RGB values of the sub-pixels of the sides and inner portions of the polygons by performing a DDA (Digital Differential Analyzer) operation with sub-pixel accuracy. 
     This DDA operation is a linear interpolation to be performed between two points so as to obtain the RGB value of each of pixels constituting a segment that connects the two points with each other. That is, according to this DDA operation, one of the two points is set as a starting point. The other point is set as an ending point. In addition, a certain value is preliminarily set at each of the starting point and the ending point. Then, a change in the value (or a rate of change thereof) at each of the pixels of the segment is obtained by dividing the difference between the values respectively set at the starting point and the ending point by the number of the pixels of the segment drawn between the starting point and the ending point. Then, the value of this rate of change is sequentially added (that is, accumulated) to each pixel between the starting point and the ending point. Thus, the values of the pixels of the segment drawn between the starting point and the ending point are obtained. 
     Consider the following example for providing values to sub-pixels p 1 , p 2 , and p 3  of the three vertices apexes of a triangular polygon. First, such a DDA operation is performed on each of a set of the sub-pixels p 1  and p 2 , and a set of the sub-pixels p 2  and p 3  and a set of the sub-pixels p 1  and p 3  with sub-pixel accuracy. Thus, the polygon data Z, R, G, B, S, T, and Q corresponding to the sub-pixels located on the three sides of this polygon, and the polygon data Z, R, G, B, S, T, and Q corresponding to the sub-pixels located in this polygon are obtained, by using X-coordinates and Y-coordinates thereof as variables. 
     The polygon data X, Y, and Z represent sets of X-coordinates, Y-coordinates and Z-coordinates of three vertices of the triangular polygon, respectively. Further, the polygon data R, G, and B represent the luminance values of red, green and blue colors at the three vertices of the polygon, respectively. Furthermore, the polygon data S, T, and Q represent texture coordinates (that is, homogeneous coordinates corresponding to the textures) at the three vertices of the triangular polygon. 
     The video-game machine of this embodiment is adapted so that a pattern (or material: a texture) is added to the surface of an object by texture mapping. Thus, the polygon data S, T, and Q are used in this texture mapping. The texture addresses are obtained by multiplying each of the values S/Q and T/Q by a texture size. 
     Subsequently, the GPU  8  writes the RGB values of the pixels of the polygon to the frame buffer  25  by using the Z-buffer  26 . Practically, the GPU  8  obtains final RGB values to be written to this frame buffer  25  as follows. 
     That is, the GPU  8  calculates the texture addresses U (S/Q) and V (T/Q) by dividing the polygon data S and T by the polygon data Q when performing the texture mapping according to the polygon data X, Y, Z, R, G, B, S, T, and Q (obtained as a result of performing the DDA operation) of a prime sub-pixel of the sub-pixels which is allocated at the central of the polygons. Moreover, if necessary, the GPU  8  performs various kinds of filtering processing. Thus, the color data of textures at the X-coordinate and the Y-coordinate of each of the sub-pixels are calculated. Then, texture color data corresponding to the texture addresses U and V are read from the texture memory  27 . 
     Subsequently, the GPU  8  calculates final RGB values of each of the sub-pixels by performing filtering processing by mixing the RGB values of this texture color data and those obtained as a result of performing the DDA operation at a predetermined mixture ratio. Thus, polygons are constituted. Then, the GPU  8  writes the final RGB values to the frame buffer  25 . Incidentally, the GPU  8  writes the RGB values to the frame buffer  25  by simultaneously performing Z-buffering by the use of the Z-buffer  26 . 
       FIG. 5  shows an example of an image rendered in the frame buffer  25  in this manner. This image shown in  FIG. 5  is rendered by pasting three triangle polygons (triangle strips)  31  to  33  together so that the entire resultant polygon has a triangular shape. 
     In  FIG. 5 , each square “□” corresponds to one pixel. A filtering operation is performed on each pixel by mixing the RGB value of the texture color data and that obtained as a result of performing the DDA operation at a predetermined mixture ratio. Thus, an image of a triangle is rendered by the entire polygon formed by performing such a filtering operation on each pixel. 
     For readily seeing the boundaries between the triangle polygons  31 ,  32  and  33 , each of the pixels of the straight edges (or lines) of the polygons  31  to  33  is indicated by a black square “▪” in  FIG. 5 . Further, the image rendered in the frame buffer  25  in this stage does not undergo the antialiasing processing. It follows that aliasing occurs in the image. 
     When a predetermined image is rendered in the frame buffer  25  in this way, control advances to step S 3  of this flowchart. At this step S 3 , the CPU  8  performs antialiasing process according to the contours and contour candidates extracted at step S 1 . 
     As described above, when transferring the polygon data to the GTE  17 , the main CPU  4  extracts the contours, together with the contour candidates if necessary, according to this polygon data as line (or curve) data or line strip data. The extracted data is stored in the cache memory  18 . Subsequently, when control advances to step S 3 , the main CPU  4  reads the line data or the line strip data stored in the cache memory  18  and supplies the read data to the GPU  8 . Then, the GPU  8  obtains the ratio (that is, an occupancy rate) of the area occupied by a straight line to that of the area of each of pixels, through which the straight line passes, as an α-value (α) of each of such pixels. Furthermore, the GPU  8  calculates the pixel value of each of the pixels according to the following equation by using the α-value thereof:
 
(Pixel Value)=(Source Color)×α+(Destination Color)×(1−α)
 
That is, a “Pixel Value” is obtained by adding the “Source Color” multiplied by an “α-value” and the “Destination Color” multiplied by the value “1−α-value”. Then, an a-blending processing (to be described later) is performed by obtaining the pixel value according to this equation.
 
       FIG. 6A  shows the occupancy rate of each of the pixels in the case that an angle, which a straight line to be rendered forms with the X-axis, is equal to or more than a predetermined value (in this case, 45 degrees).  FIG. 6B  shows the occupancy rate of each of the pixels in the case that an angle, which a straight line to be rendered forms with the X-axis, is less than the predetermined value (in this case, 45 degrees). In  FIGS. 6A and 6B , for readily understanding of the invention, an ideal straight line to be rendered is illustrated as a hollow straight line. Further, in the case that an ideal line to be rendered is a curved line, the angle, which the line to be rendered forms with the X-axis, is evaluated by approximating this curved line to be a straight line in each of the pixels. 
     As is understood from  FIG. 6A , in the case that an angle, is equal to or more than 45 degrees, objects to be rendered are pixels that each include a part of the line and adjoin with each other in the direction of the X-axis. That is, the range of pixels, in which the straight line (that is, to which antialiasing process is performed) is rendered, is expanded and obtained along the direction of the X-axis. Similarly, as is understood from  FIG. 6B , in the case that an angle, is less than 45 degrees, objects to be rendered are pixels that each include a part of the line and adjoin with each other in the direction of the Y-axis. That is, the range of pixels, in which the straight line is rendered, is expanded and obtained along the direction of the Y-axis. Further, the GPU  8  calculates the occupancy rate of the straight line corresponding to each of the pixels to be rendered and obtains values, such as 20%, 40%, 60%, and 80%, as the calculated occupancy rate. Moreover, the GPU  8  performs the operation based on the aforementioned equation (that is, performs the α-blending processing) on the pixel values by using the calculated occupancy rate as the α-value. 
     The α-values of the pixels to be rendered, which adjoin with each other in the direction of the X-axis or Y-axis), are set so that a total of the α-values of such pixels is 100%. 
     Furthermore, in the case of this example, for simplicity of description, the foregoing description of calculation of the pixel values has been given by employing only four kinds of values, that is, 20%, 40%, 60%, and 80% as the values of the occupancy rates. However, the actual occupancy rate is set according to the resolution of sub-pixels. For instance, in the case of calculating the pixel values by dividing each of the pixels into 16 sub-pixels (that is, a 4×4 matrix of sub-pixels), the occupancy rate is set by employing a 16-level resolution so that the number of resolution levels, which are, for instance, 6.25%, 12.5%, 18.75%, . . . , is equal to the number of the sub-pixels of each pixel. 
       FIG. 7  illustrates only the contours (or contour candidates), which are rendered by calculating the pixel values, such as RGB values, according to the occupancy rates of the ideal line and extracted from the aforementioned example. As shown in  FIG. 7 , a gradational image of each of the contours (or contour candidates) is thus obtained by performing the α-blending processing on the contours (or contour candidates). Consequently, antialiased less-jaggy smooth contours (or contour candidates) are rendered. 
     As described above, the video-game machine of this embodiment is adapted in such a way as to calculate the occupancy rate with sub-pixel accuracy. Thus, the video-game machine of this embodiment is enabled to calculate the occupancy rate with finer accuracy, as compared with the conventional machine that calculates the occupancy rate correspondingly to each of the pixels. Consequently, in the case of this embodiment, the contours (or contour candidates) are rendered according to more suitable pixel values. Hence, much-less-jaggy smooth contours (or contour candidates) to be rendered are obtained. 
     Subsequently, when the antialiased contours (or contour candidates) are thus formed, the GPU  8  advances to step S 4  shown in the flowchart of  FIG. 3 , whereupon overwriting of the pixel values is performed. Practically, the GPU  8  overwrites the pixel values, which are calculated by performing the α-blending processing, onto the pixel values of the pixels corresponding to the contours (or contour candidates) in the image written to the frame buffer  25 . That is, an image to finally be rendered is obtained by performing antialiasing on a part of an original image. This overwriting processing is performed by simultaneously referring to the Z-values of the contours (or contour candidates), which are stored in the Z-buffer  26 . 
     Thus, data representing an image having the antialiased contours (or contour candidates) as shown in  FIG. 8  are written onto the frame buffer  2 . The GPU  8  reads data representing the image of 1 frame written to the frame buffer  25  and supplies a signal representing the read data to the display apparatus as a video signal. Consequently, a three-dimensional image having antialiased smooth contours (or contour candidates) is displayed on the screen of the display apparatus. 
     The routines illustrated in the flowchart of  FIG. 3  are continuously executed correspondingly to each frame during a game. Thus, all the three-dimensional images displayed during the game are less-jaggy images. 
     Although the video-game machine according to this embodiment employs what is called a Z-buffer method according to which the image is rendered in the frame buffer  25  by using the Z-buffer  26  and performing Z-buffering, the video-game machine may be adapted to perform Z-sorting at step S 4  before the data representing the antialiased contours (or contour candidates) is overwritten onto the data stored in the frame buffer  25 . That is, a much-less-jaggy high-picture-quality three-dimensional image is formed by performing, after the Z-sorting is performed on the contours (or contour candidates), antialiasing thereon and then overwriting the data representing the antialiased contours (or contour candidates) onto the data stored in the frame buffer  25 . 
     As is apparent from the foregoing description, the video-game machine of this embodiment first extracts visually important portions, such as contours or contour candidates, of an image to be rendered. Then, this machine performs antialiasing processing on the extracted contours or contour candidates. Subsequently, this machine overwrites data representing the antialiased contours or contour candidates onto the data representing the original image. Thus, jaggies are reduced by performing antialiasing processing partially on the visually important portions, such as the contours or contour candidates, of the image. Consequently, a less-jaggy high-picture-quality image is obtained. 
     Further, because this embodiment is adapted so that the antialiasing processing is performed only on the visually important limited portion of the entire image, the antialiasing processing is performed on the image at a very high speed even when inexpensive hardware is employed. Therefore, antialiasing processing can be performed on a dynamic image to be displayed, which is composed of, for example, 20 to 30 frames per second, in realtime. Moreover, inexpensive hardware may be employed in the video-game machine. Thus, the invention provides a video-game machine of a low-cost simple configuration, which is enabled to perform antialiasing processing on a dynamic image. 
     Furthermore, even when the video-game machine according to this embodiment does not have a large-capacity, high-speed frame buffer and Z-buffer, this machine is enabled to perform antialiasing processing on a dynamic image. Thus, such a vide-game machine is realized by having a low-cost, small-sized configuration. 
     Furthermore, this embodiment is adapted to selectively perform only on the visually important portions of the entire image. Thus, this embodiment eliminates the necessity for a grouping operation, such as a sorting operation, which is needed for performing antialiasing on triangle polygons in the conventional machine. 
     This embodiment is illustrative, and the invention is not limited thereto. For example, in the foregoing description of this embodiment, the case, in which the invention is applied to a video-game machine, has been described. However, the invention may be applied to an effector for providing special effects for an image, and to a computer graphic system such as a CAD system. 
     Further, the invention may be applied to a recording/reproducing apparatus for recording and reproducing an image, which is taken by a video camera, by coding the image so that the image is represented by polygons, and to a transmission system for transmitting and receiving an image coded in such a way as to be represented by polygons. In this case, an antialiased high-picture-quality reproduction image is obtained by employing the techniques according to the invention when the image coded in such a way as to be represented by polygons is decoded. 
     Furthermore, although it has been described in the foregoing description of the aforementioned embodiment that rendering is performed in units of frames, the rendering processing may be performed in units of fields. Additionally, the invention may be applied to the case of rendering any of a dynamic image, a static image, and three-dimensional and two-dimensional graphics. 
     Besides, although it has been described in the foregoing description of the aforementioned embodiment that the rendering processing is performed by executing a computer program for reducing jaggies in a processor, the rendering processing may be performed by providing hardware dedicated to the rendering processing and using this hardware. 
     Further, although it has been described in the foregoing description of the aforementioned embodiment that the antialiased three-dimensional image is displayed on the screen of the display apparatus by being outputted thereto, such an image may be outputted to a two-dimensional output apparatus, such as a printer apparatus, and then printed therein. 
     Furthermore, although it has been described in the foregoing description of the aforementioned embodiment that the antialiasing processing is achieved by performing the α-blending processing, other antialiasing techniques may be employed instead of such a technique of the embodiment. Further, the apparatus of the invention is adapted to form an antialiasing image at a high speed by selectively performing antialiasing processing on a visually important portion of the image. Thus, even in the case of employing other antialiasing techniques, advantageous effects similar to those of the embodiment are obtained as long as an antialiased image is formed at a high speed by selectively performing the antialiasing processing. 
     Needless to say, various other modifications may be made without departing from the spirit and scope of the invention. 
     As described above, the apparatus of the invention has a low-cost, small-sized configuration and is, however, enabled to form an antialiased high-picture-quality image at a high speed. Consequently, the apparatus of the invention is enabled to perform antialiasing processing on a dynamic image in real time.