Patent Publication Number: US-7212219-B2

Title: Drawing apparatus and method, program and recording medium

Description:
CROSS REFERENCES TO RELATED APPLICATONS 
   The present document is based on Japanese Priority Document JP2003-423003, filed to the Japanese Patent Office on Dec. 19, 2003, the entire content of which being incorporated herein by reference to the extent permitted by law. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a drawing apparatus and method, a program and a recording medium, and more particularly to a drawing apparatus and method, a program and a recording medium wherein accurate drawing is possible by using drawing information shared on a network, irrespective of aspect differences between transmission and reception sides. 
   2. Related Art 
   In drawing applications which make a number of users share drawing information via a network, for example, as drawing information of each user is transmitted to other users via the network, a synchronized screen (image) is displayed at all these users. 
   Image display applications have been known which applications synchronously display still images at a plurality of apparatuses interconnected via a network. 
   For example, MSN Messenger (a registered trademark) of Microsoft Corporation has a whiteboard sharing function. With this whiteboard sharing function, MSN Messenger shares drawing information at a plurality of user terminals (computers) and presents a synchronized screen display. Furthermore, MSN Messenger allows a plurality of terminals to share a screen which displays a pasted still image on which a new image is drawn. It can therefore be said that MSN Messenger is a composite application provided with both the function of a drawing application and the function of a still image display application. 
   Other composite applications provided with both the functions of the drawing application and image display application include, for example, a video conference system described in Japanese Patent Application Publication No. HEI-5-103325, for example. 
   MSN Messenger has a still image displaying function, whereas Windows Media Player (a registered trademark) of Microsoft Corporation has a moving image displaying function. 
   SUMMARY OF THE INVENTION 
   If content, i.e., images and drawing information, are shared by the composite application of the type described above at a plurality of apparatuses, displaying the content relies upon the function of the image display application of the composite application. 
   Namely, if the content is moving images among moving images and still images, in some cases the image display application displays even the same moving image at different aspect ratios on a plurality of apparatuses. Namely, a moving image is displayed on one apparatus at a horizontal/vertical ratio or an aspect ratio of, e.g., 16:9, whereas it is displayed on another apparatus at an aspect ratio of, e.g., 4:3. 
   If only the same moving image is to be synchronously displayed on a plurality of apparatuses, a difference between aspect ratios poses no problem. 
   However, with the above-described composite application sharing the content, i.e., images and drawing information, the position of an image drawn by using drawing information on a screen (image) is displaced in some cases, depending upon the difference of aspect ratios of a plurality of apparatuses. 
     FIG. 1  shows a display example by a composite application. 
   In  FIG. 1 , composite applications  1  and  2  are communicable via a network  3 . 
   The composite applications  1  and  2  exchange sync information via the network  3  so that the same moving image can be displayed synchronously. 
   In this case, the composite application  1  displays the moving image at an aspect ratio of, e.g., 16:9, whereas the composite application  2  displays the same moving image (same content) at an aspect ratio of, e.g., 4:3. 
   In the state that the composite applications  1  and  2  synchronously display the same moving image, as a user of one of the composite applications  1  and  2  draws an image on the displayed moving image (screen), the drawing information of the image is transmitted to the other via the network  3 , and an image corresponding to the drawing information is drawn at the other. 
   In  FIG. 1 , a user of the composite application  1  draws an image on the displayed moving image, the drawing information of the image is transmitted via the network to the composite application  2  which draws an image corresponding to the drawing information. 
   In  FIG. 1 , the moving image including a flower is displayed by using the composite applications  1  and  2 , and the user of the composite application  1  draws a contour line of the flower. 
   In this case, the drawing information of the contour line of the flower is transmitted from the composite application  1  to the composite application  2  via the network  3 . The composite application  2  draws an image in accordance with the drawing information. If the aspect ratios of the moving images displayed by the composite applications  1  and  2  are different, the coordinates of the image displayed by the composite application  1  take (relatively) different values from the coordinates of the image displayed by the composite application  2 . As a result, the position of the image drawn by the composite application  2  is displaced from the position of the image drawn by the composite application  1 . 
   In  FIG. 1 , since the aspect ratios of the composite applications  1  and  2  are different, irrespective of that the composite application  1  draws the contour line of the flower on the moving image, the composite application  2  draws a line at a position displaced from the contour of the flower on the moving image. 
   Displacement of the positions of images hinders comfortable information sharing (good mutual understanding) between the users of the composite applications  1  and  2 . 
   The present invention has been made in consideration of the circumstances described above and enables accurate drawing without position displacement by using drawing information shared on a network, irrespective of an aspect difference between transmission and reception sides. 
   A first drawing apparatus of the present invention is characterized by: first transforming mechanism of transforming position information transmitted from another apparatus into first transformed position information in accordance with an inverse function of a first function for normalizing an aspect ratio of an image displayed on a display apparatus; second transforming mechanism of transforming the first transformed position information into second transformed position information in accordance with an inverse function of a second function corresponding to the aspect ratio of the image and being different from the first function; and drawing mechanism of drawing an image on a screen of the display apparatus. 
   The first drawing apparatus may further have: third transforming mechanism of transforming drawing input position information representative of a position, on the screen of the display apparatus, of a drawing input by a user into third transformed position information in accordance with the second function; fourth transforming mechanism of transforming the third transformed position information into fourth transformed position information in accordance with the first function; and transmitting mechanism of transmitting the fourth transformed position information to the other apparatus via a network. 
   A first drawing method of the present invention is characterized by: a first transforming step of transforming position information transmitted from another apparatus into first transformed position information in accordance with a first function for normalizing an aspect ratio of an image displayed on a display apparatus; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with a second function corresponding to the aspect ratio of the image and being different from the first function; and a drawing step of drawing an image on a screen of the display apparatus. 
   A first program of the present invention is characterized by: a first transforming step of transforming position information transmitted from another apparatus into first transformed position information in accordance with a first function for normalizing an aspect ratio of an image displayed on a display apparatus; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with a second function corresponding to the aspect ratio of the image and being different from the first function; and a drawing step of drawing an image on a screen of the display apparatus. 
   A program recorded in a first recording medium of the present invention is characterized by: a first transforming step of transforming position information transmitted from another apparatus into first transformed position information in accordance with a first function for normalizing an aspect ratio of an image displayed on a display apparatus; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with a second function corresponding to the aspect ratio of the image and being different from the first function; and a drawing step of drawing an image on a screen of the display apparatus. 
   A second drawing apparatus of the present invention is characterized by: first transforming mechanism of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on a display apparatus and being different from a first function for normalizing the aspect ratio of the image; second transforming mechanism of transforming the first transformed position information into second transformed position information in accordance with the first function; and transmitting mechanism of transmitting the second transformed position information to another apparatus via a network. 
   A second drawing method of the present invention is characterized by: a first transforming step of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on a display apparatus and being different from a first function for normalizing the aspect ratio of the image; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with the first function; and a transmitting step of transmitting the second transformed position information to another apparatus via a network. 
   A second program of the present invention is characterized by: a first transforming step of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on a display apparatus and being different from a first function for normalizing the aspect ratio of the image; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with the first function; and a transmitting step of transmitting the second transformed position information to another apparatus via a network. 
   A program recorded in a second storage medium of the present invention is characterized by: a first transforming step of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on a display apparatus and being different from a first function for normalizing the aspect ratio of the image; a second transforming step of transforming the first transformed position information into second transformed position information in accordance with the first function; and a transmitting step of transmitting the second transformed position information to another apparatus via a network. 
   In the first drawing apparatus and drawing method, program and recording medium of the present invention, the position information transmitted from the other apparatus is transformed into the first transformed position information in accordance with the first function for normalizing the aspect ratio of the image displayed on the display apparatus, and the first transformed position information is transformed into the second transformed position information in accordance with the second function corresponding to the aspect ratio of the image. In accordance with the second transformed position information, an image is drawn on the screen of the display apparatus. 
   In the second drawing apparatus and drawing method, program and recording medium of the present invention, the drawing input position information representative of the position of the drawing input by the user is transformed into the first transformed position information in accordance with the second function corresponding to the aspect ratio of the image displayed on the display apparatus and being different from the first function for normalizing the aspect ratio of the image, and the first transformed position information is transformed into the second transformed information. The second transformed position information is transmitted via the network to the other apparatus. 
   According to the preferred embodiments of the present invention, it is possible to prevent displacement of a drawing position in order to establish a desirable mutual understanding between communicating parties. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects, features and advantages of the present invention will become more apparent from the following description of the presently preferred exemplary embodiments of the invention taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  is a diagram illustrating drawing by a conventional composite application; 
       FIG. 2  is a block diagram showing an example of the structure of a drawing sharing system according to a preferred embodiment of the present invention; 
       FIG. 3  is a block diagram showing an example of the hardware structure of a computer  11 ; 
       FIG. 4  is a diagram showing a display example of a window  11 A; 
       FIG. 5  is a block diagram showing an example of the structure of drawing apparatuses  50  and  54 ; 
       FIG. 6  is a diagram showing display examples of windows  12 A and  12 A; 
       FIG. 7  is a block diagram showing an example of the structure of a drawing sharing section  53 ; 
       FIG. 8  is a diagram illustrating a front coordinate system; 
       FIG. 9  is a diagram illustrating a rear coordinate system; 
       FIG. 10  is a diagram illustrating a front coordinate system; 
       FIG. 11  is a diagram illustrating a rear coordinate system; 
       FIG. 12  is a diagram illustrating a normalized coordinate system; 
       FIG. 13  is a diagram illustrating a normalized coordinate system; 
       FIG. 14  is a diagram illustrating the process to be executed by drawing sharing sections  53  and  57 ; 
       FIG. 15  is a flow chart illustrating the process to be executed by the drawing sharing section  53 ; and 
       FIG. 16  is a flow chart illustrating the process to be executed by the drawing sharing section  53 ; 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE PRESENT INVENTION 
   In the following description of the preferred embodiments of the present invention, the correspondence between the disclosed inventions and the embodiments is as follows. The description is used for confirming that the embodiments supporting the inventions described in this specification are described in the specification. Therefore, the embodiments described in this specification as not corresponding to some invention are not intended to mean that the embodiments do not correspond to an invention. Conversely, an embodiment described in this specification as corresponding to some invention is not intended to mean that the embodiment does not correspond to an invention other than some other invention, its variation, combinations of inventions, sub combinations, etc. 
   Further, the description is not intended to cover all the inventions described in the specification. In other words, it is not intended to deny the presence of inventions described in this specification but not claimed in this application, i.e., to deny the presence of inventions which may be divisionally submitted in the future and inventions emerging through corrections or amendments and additionally submitted in the future. 
   A drawing apparatus described herein is characterized in that in a drawing apparatus (e.g., a drawing apparatus  50  of  FIG. 5 ) for drawing an image on a screen of a display apparatus (e.g., a display  27 A of  FIG. 3 ) for displaying an image, in accordance with position information representative of a drawing position transmitted from another apparatus (e.g., a drawing apparatus  54  of  FIG. 5 ) via a network (e.g., a network  3  of  FIG. 5 ), the drawing apparatus includes: first transforming mechanism (e.g., a normalized coordinate transformation section  62  of  FIG. 7 ) for transforming the position information (e.g., (x 3 , y 3 ) of  FIG. 14 ) transmitted from the other apparatus into first transformed position information (e.g., (x 2 , y 2 ) of  FIG. 14 ) in accordance with an inverse function of a first function (e.g., an inverse function g 1   −1  of a function g 1  of  FIG. 14 ) for normalizing an aspect ratio of an image displayed on the display apparatus; second transforming mechanism (e.g., a rear coordinate transformation section  63  of  FIG. 7 ) for transforming the first transformed position information into second transformed position information (e.g., (x 1 , y 1 ) of  FIG. 14 ) in accordance with an inverse function of a second function (e.g., an inverse function f 1   −1  of a function f 1  of  FIG. 14 ) corresponding to the aspect ratio of the image and being different from the first function; and drawing means (a drawing section  67  of  FIG. 7 ) for drawing an image on a screen of the display apparatus. 
   The drawing apparatus according to another aspect of the present invention is characterized by: third transforming mechanism (e.g., a front coordinate transformation section  64  of  FIG. 7 ) for transforming drawing input position information (e.g., (x 1 , y 1 ) of  FIG. 12 ) representative of a position, on the screen of the display apparatus, of a drawing input by a user into third transformed position information (e.g., (x 2 , y 2 ) of  FIG. 12 ) in accordance with the second function; fourth transforming mechanism (e.g., a normalizing section  65  of  FIG. 7 ) for transforming the third transformed position information into fourth transformed position information (e.g., (x 3 , y 3 ) of  FIG. 12 ) in accordance with the first function; and transmitter (e.g., a transmission section  66  of  FIG. 7 ) for transmitting the fourth transformed position information to the other apparatus via a network. 
   A drawing method according to another aspect of the present invention is characterized in that in a drawing method of drawing an image on a screen of a display apparatus (e.g., the display  27 A of  FIG. 3 ) for displaying an image, in accordance with position information representative of a drawing position transmitted from another apparatus (e.g., the drawing apparatus  54  of  FIG. 5 ) via a network (e.g., the network  3  of  FIG. 5 ), the drawing method includes: a first transforming step (e.g., Step S 12  of  FIG. 16 ) of transforming position information transmitted from another apparatus into first transformed position information in accordance with a first function for normalizing an aspect ratio of an image displayed on a display apparatus; a second transforming step (e.g., Step S 13  of  FIG. 16 ) of transforming the first transformed position information into second transformed position information in accordance with a second function corresponding to the aspect ratio of the image and being different from the first function; and a drawing step (e.g., Step S 14  of  FIG. 16 ) of drawing an image on a screen of the display apparatus. 
   A program and a program recorded in a recording medium according to another aspect of the present invention are characterized in that in a program for making a computer execute a drawing process of drawing an image on a screen of a display apparatus (e.g., the display  27 A of  FIG. 3 ) for displaying an image, in accordance with position information representative of a drawing position transmitted from another apparatus (e.g., the drawing apparatus  54  of  FIG. 5 ) via a network (e.g., the network  3  of  FIG. 5 ), the program having: a first transforming step (e.g., Step S 12  of  FIG. 16 ) of transforming position information transmitted from another apparatus into first transformed position information in accordance with a first function for normalizing an aspect ratio of an image displayed on a display apparatus; a second transforming step (Step S 13  of  FIG. 16 ) of transforming the first transformed position information into second transformed position information in accordance with a second function corresponding to the aspect ratio of the image and being different from the first function; and a drawing step (e.g., Step S 14  of  FIG. 16 ) of drawing an image on a screen of the display apparatus. 
   A drawing apparatus according to another aspect of the present invention is characterized in that in a drawing apparatus (e.g., the drawing apparatus  50  of  FIG. 5 ) for drawing an image on a screen of a display apparatus (e.g., the display  27 A of  FIG. 3 ) for displaying an image in accordance with a drawing input by a user, the drawing apparatus includes: first transforming mechanism (e.g., the front coordinate transformation section  64  of  FIG. 7 ) for transforming drawing input position information (e.g., (x 1 , y 1 ) of  FIG. 14 ) representative of a position of a drawing input by a user into first transformed position information (e.g., (x 2 , y 2 ) of  FIG. 14 ) in accordance with a second function (e.g., the function f 1  of  FIG. 12 ) corresponding to an aspect ratio of an image displayed on the display apparatus and being different from a first function (e.g., the function g 1  of  FIG. 12 ) for normalizing the aspect ratio of the image; second transforming mechanism (e.g., the normalizing section  65  of  FIG. 7 ) for transforming the first transformed position information into second transformed position information (e.g., (x 3 , y 3 ) of  FIG. 14 ) in accordance with the first function; and transmitter (e.g., the transmission section  66  of  FIG. 7 ) for transmitting the second transformed position information to another apparatus (e.g., a drawing apparatus  54  of  FIG. 5 ) via a network (e.g., the network  3  of  FIG. 5 ). 
   A drawing method according to another aspect of the present invention is characterized in that in a drawing method of drawing an image on a screen of a display apparatus for displaying an image in accordance with a drawing input by a user on the screen of the display apparatus, the drawing method includes: a first transforming step (e.g., Step S 1  of  FIG. 15 ) of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on a display apparatus and being different from a first function for normalizing the aspect ratio of the image; a second transforming step (e.g., Step S 2  of  FIG. 15 ) of transforming the first transformed position information into second transformed position information in accordance with the first function; and a transmitting step (e.g., Step S 3  of  FIG. 15 ) of transmitting the second transformed position information to another apparatus via a network. 
   A program and a program recorded in a recording medium according to another aspect of the present invention are characterized in that in a program for making a computer execute a drawing process of drawing an image on a screen of a display apparatus for displaying an image in accordance with a drawing input by a user on the screen of the display apparatus, the program includes: a first transforming step (e.g., Step S 1  of  FIG. 15 ) of transforming drawing input position information representative of a position of a drawing input by a user into first transformed position information in accordance with a second function corresponding to an aspect ratio of an image displayed on the display apparatus and being different from a first function for normalizing the aspect ratio of the image; a second transforming step (e.g., Step S 2  of  FIG. 15 ) of transforming the first transformed position information into second transformed position information in accordance with the first function; and a transmitting step (e.g., Step S 3  of  FIG. 15 ) of transmitting the second transformed position information to another apparatus via a network. 
   An example of preferred embodiment of the present invention will be described herein below. 
     FIG. 2  is a block diagram showing an example of the structure of a drawing sharing system according to a preferred embodiment of the present invention. 
   In  FIG. 2 , a computer  11  and a computer  12  are interconnected via a network  3  and can bidirectionally communicate with each other. 
   The computers  11  and  12  are each installed with a composite application (program) provided with both functions of a drawing application for drawing and an image display application for synchronously displaying an image, as will be later described. 
   For example, as the users of the computers  11  and  12  activate the composite application, predetermined windows are displayed on the computers  11  and  12 . Sync information (e.g., such as time code) for synchronously displaying a moving image is exchanged between the computers  11  and  12 . The same moving image is therefore displayed synchronously on the windows of the computers  11  and  12 . 
   It is assumed herein that the moving image to be displayed on the computers  11  and  12  is stored, for example, in the computers  11  and  12 , respectively. However, for example, a moving image may be stored in one of the computers  11  and  12 , and the moving image is transmitted from one to the other via the network  3  so that the same moving image can be displayed synchronously on the computers  11  and  12 . The computers  11  and  12  may receive a moving image from an unrepresented server on the network  3  to display the synchronous images. 
   For example, as a user of the computer  11  draws characters, figures or the like on the window displaying a moving image, the computer  11  transmits the drawing information of the drawn characters, figures or the like to the computer  12  via the network  3 . The computer  12  receives the drawing information transmitted from the computer  11  via the network  3  and draws an image corresponding to the drawing information (displays the same characters, or figures drawn on the window of the computer  11 ). 
   Similarly, as a user of the computer  12  draws characters, figures or the like on the window displaying a moving image, the computer  12  transmits the drawing information of the drawn characters, figures or the like to the computer  11  via the network  3 . The computer  11  receives the drawing information transmitted from the computer  12  via the network  3  and draws an image corresponding to the drawing information (displays the same characters, or figures drawn on the window of the computer  12 ). 
   The network  3  may be the Internet, a LAN (Local Area Network) or the like. The network  3  may either wired or wireless. 
     FIG. 3  is a block diagram showing an example of the hardware structure of the computer  11  shown in  FIG. 2 . The computer  12  of  FIG. 2  has a similar hardware structure to that of the computer  11 . 
   A CPU (Central Processing Unit)  21 , a ROM (Read Only Memory)  22  and a RAM (Random Access Memory)  23  are interconnected via a bus  24 . An input/output interface  25  is also connected to the bus  24 . 
   Connected to the input/output interface  25  are an input section  26  constituted of a keyboard, a mouse and the like, an output section  27  constituted of a display  27 A, a speaker  27 B and the like, a storage section  28  constituted of a hard disk and the like, and a communication section  29 . 
   When necessary, a drive  30  is also connected to the input/output interface  25 . A magnetic disk  31 , an optical disk  32 , a magneto optical disk  33  or a semiconductor memory  34  is mounted on the drive when appropriate, and a program read from the media is installed in the storage section  28  when necessary. 
   A program storage medium for storing a program to be installed in the computer  11  and being executable by the computer  11  is constituted of a package medium, ROM  22  for temporarily or permanently storing the program, a hard disk constituting the storage section  28  or the like. The package medium is the magnetic disk (including a floppy disk)  31 , the optical disk (including a CD-ROM (Compact Disk-Read Only Memory) and a DVD (Digital Versatile Disc))  32 , the magneto optical disk (MD (Mini-Disc) (a registered trademark))  33 , the semiconductor memory  34  or the like. Storing the program in the program storage medium is performed by utilizing wired or wireless communication media such as a local network, the Internet and digital satellite broadcasting, if necessary, via an interface such as a router and a modem. 
   The computer  11  executes various processes as CPU  21  executes the program installed in the storage section  28 . 
   In  FIG. 3 , a composite application (program)  40  is installed in the storage section  28 , the composite application  40  being provided with both functions of a drawing application for drawing by sharing drawing information and an image display application for synchronously displaying an image. The composite application  40  is constituted of an image display program (module)  41  for synchronously displaying an image (still image, moving image) and a drawing sharing program (module)  42  for sharing drawing information. 
   The storage section  28  also stores an image (of a moving image and a still image, the moving image is assumed to be used herein) to be displayed by the image display program  41 . 
   In response to an instruction from, e.g., a user, CPU  21  loads the composite application  40  in RAM  23  as shown in  FIG. 3  and executes it. The computer  11  functions therefore as a drawing apparatus for displaying a moving image synchronous with the other computer and drawing an image. 
     FIG. 4  shows a display example of a window  11 A displayed on the display  27 A when CPU  21  shown in  FIG. 3  executes the composite application  40 . 
   As the composite application  40  is executed, the window  11 A is displayed on the display  27 A. 
   As the composite application  40  is executed, a moving image stored in the storage section  28  is reproduced and displayed on the window  11 A. 
   Further, as a user of the computer  11  operates the input section (mouse or the like)  26  to draw a circle on the moving image displayed on the window  11 A and draw an arrow directing toward the circle, for example, the circle and arrow corresponding to this operation (drawing) are displayed on the window  11 A, as shown in  FIG. 4 . 
     FIG. 5  shows an example of the structure of a drawing apparatus functionally realized as CPU  21  shown in  FIG. 3  executes the composite application  40 . 
   In  FIG. 5 , a drawing apparatus  50  corresponds to the computer  11  of  FIG. 2 , and a drawing apparatus  54  corresponds to the computer  12  of  FIG. 2 . 
   The drawing apparatus  50  corresponding to the computer  11  is constituted of a user interface  51 , an image display section  52  and a drawing sharing section  53 . 
   In the drawing apparatus  50 , the user interface  51  corresponds to, e.g., the input section  26  and output section  27  of  FIG. 3 . 
   The image display section  52  exchanges sync information with an image display section  56  of the drawing apparatus  54  via the network  3  so that the content of a moving image stored in the storage section  28  ( FIG. 3 ) are displayed synchronously with the drawing apparatus  54  on the window  11 A of the display  27 A of the output section  27  as the user interface  51 . 
   As the user operates the input section  26  ( FIG. 3 ) as the user interface  51  and draws an image on the window  11 A, the drawing sharing section  53  draws characters, figures or the like (displays characters, figures or the like) corresponding to the user operation, on the window  11 A of the display  27 A of the output section  27  as the user interface  51 . Further, the drawing sharing section  53  transmits drawing information of the image to the drawing apparatus  54  via the network  3 . 
   The drawing sharing section  53  receives drawing information transmitted from the drawing apparatus  54  via the network  3  and draws characters, figures or the like (displays characters, figures or the like) on the window  11 A of the display  27 A of the output section  27  as the user interface  51 . 
   The image display section  52  and drawing sharing section  53  correspond to the image display program  41  and drawing sharing program  42  of  FIG. 3 , respectively. 
   The drawing apparatus  54  corresponding to the computer  12  is constituted of a user interface  55 , an image display section  56  and a drawing sharing section  57 . The user interface  55 , image display section  56  and drawing sharing section  57  are structured in a manner similar to that of the above-described user interface  51 , image display section  52  and drawing sharing section  53 , and the description thereof is therefore omitted. 
     FIG. 6  shows a display example of the windows displayed on the drawing apparatuses  50  and  54  of  FIG. 5 . 
   The drawing apparatus  50  displays the window  11 A on the display  27 A of the output section  27  as the user interface  51 . Similarly, the drawing apparatus  54  displays the window  12 A on the display  27 A of the output section  27  as the user interface  55 . 
   The image display section  52  of the drawing apparatus  50  of  FIG. 5  exchanges sync information with the image display section  56  of the drawing apparatus  54  via the network  3 , so that the same moving image is synchronously displayed on the window  11 A of the drawing apparatus  50  and on the window  12 A of the drawing apparatus  54 . 
   The aspect ratios of the moving image displayed on the windows  11 A and  12 A are dependent upon, for example, the drawing apparatuses  50  and  54  and the like. Therefore, the aspect ratios of the moving image displayed on the windows  11 A and  12 A are the same in one case and different in the other case. 
   In  FIG. 6 , a user of the drawing apparatus  50  draws a circle on the window  11 A and an arrow directing toward the circle, for example. In this case, the drawing sharing section  53  of the drawing apparatus  50  transmits the drawing information of the drawn circle and arrow to the drawing apparatus  54  via the network  3 . 
   The drawing sharing section  57  of the drawing apparatus  54  receives the drawing information transmitted from the drawing sharing section  53  of the drawing apparatus  50  via the network  3 . The drawing sharing section  57  displays on the window  12 A the same circle and arrow as those drawn on the window  11 A by the user of the drawing apparatus  50 , synchronously with the drawing by the user of the drawing apparatus  50 . 
   As the user of the drawing apparatus  54  draws an image on the window  12 A, the drawing sharing section  57  transmits the drawing information of the image to the drawing sharing section  53  via the network  3 . The drawing sharing section  53  receives the drawing information from the drawing sharing section  57  and draws the image on the window  11 A in accordance with the drawing information. 
   In the manner described above, synchronized images are drawn on the windows  11 A and  12 A. 
     FIG. 7  is a block diagram showing an example of the structure of the drawing sharing section  53 . 
   The drawing sharing section  57  of  FIG. 5  is structured in a similar manner. 
   A reception section  61  is supplied with drawing information transmitted from the drawing apparatus  54  via the network  3 . The reception section  61  receives the drawing information transmitted via the network  3  and supplies normalized coordinates (x 3 , y 3 ) contained in the drawing information to be described later to a normalized coordinate transformation section  62 . 
   The normalized coordinate transformation section  62  transforms the normalized coordinates (x 3 , y 3 ) supplied from the reception section  61  into rear coordinates (x 2 , y 2 ) to be described later, and supplies them to a rear coordinate transformation section  63 . 
   The rear coordinate transformation section  63  is supplied with the rear coordinates (x 2 , y 2 ) from the normalized coordinate transformation section  62  and also with rear coordinates (x 2 , y 2 ) from a front coordinate transformation section  64  to be described later. The rear coordinate transformation section  63  transforms the rear coordinates (x 2 , y 2 ) supplied from the normalized coordinate transformation section  62  or front coordinate transformation section  64  into front coordinates (x 1 , y 1 ) to be described later, and supplies them to a drawing section  67 . 
   The front coordinate transformation section  64  is supplied via the user interface  51  with input data (x 1 , y 1 ), as the front coordinates representative of a position where the user drew an image. The front coordinate transformation section  64  transforms the input data (x 1 , y 1 ) supplied from the user interface  51  into the rear coordinates (x 2 , y 2 ) and supplies them to a normalizing section  65  and the rear coordinate transformation section  63 . 
   The normalizing section  65  transforms the rear coordinates (x 2 , y 2 ) supplied from the front coordinate transformation section  64  into the normalized coordinates (x 3 , y 3 ) and supplies them to a transmission section  66 . 
   The transmission section  66  transmits drawing information containing the normalized coordinates (x 3 , y 3 ) supplied from the front coordinate transformation section  64  to the drawing apparatus  54  via the network  3 . 
   The drawing section  67  writes a predetermined value (draws an image) in a drawing memory  68  at a corresponding address, in accordance with the front coordinates (x 1 , y 1 ) supplied from the rear coordinate transformation section  63 . The drawing memory  68  stores the predetermined value in response to the writing by the drawing section  67 . 
   The display control section  69  displays the image corresponding to the stored value in the drawing memory  68  on the window  11 A of the display  27 A. 
   Since the content (an image corresponding to the written value) drawn relative to the drawing memory  68  by the drawing section  67  is displayed on the window  11 A, it can be said that the drawing section  67  operates to draw an image on the screen of the display  27 A. 
   Next, description will be made on front coordinates, rear coordinates, and normalized coordinates. 
   The front coordinates are the coordinates in a front coordinate system, and the rear coordinates are the coordinates in a rear coordinate system. 
     FIG. 8  is a diagram illustrating the front coordinate system. 
   The front coordinate system is a coordinate system using as a reference the window  11 A displayed on the computer  11  (window  12 A displayed on the computer  12 ). 
   Namely, in  FIG. 8 , the front coordinate system uses the upper left corner of the window  11 A (display area) as its origin (0, 0), a direction from left to right as an abscissa direction, and a direction from up to down as a ordinate direction. 
   In  FIG. 8 , the horizontal length (along the abscissa direction) of the display area of the window  11 A is represented by w 1  and the vertical length (along the ordinate direction) is represented by h 1 . This display area is an area where a user can draw an image, and its size changes as the window  11 A is resized. 
   In  FIG. 8 , an image (moving image)  71  as the content is displayed in the window  11 A. The image  71  is displayed by the image display section  52  ( FIG. 5 ), and has a rectangle shape having a horizontal length of b 1  and a vertical length of a 1  as shown in  FIG. 8 . Namely, the aspect ratio (horizontal:vertical) of the image  71  is b 1 :a 1 . The aspect ratio b 1 :a 1  of the image  71  depends on the function of the image display program  41  ( FIG. 3 ) corresponding to the image display section  52  ( 56 ), and may change with a computer in some cases. It is herein assumed that the horizontal length b 1  and vertical length a 1  of the image  71  will not change even if the window  11 A is resized. However, the horizontal length b 1  and vertical length a 1  of the image  71  may be changed so as to match resizing the window  11 A, for example, while the aspect ratio b 1 :a 1  is maintained. 
   The image  71  is displayed on the window  11 A, for example, in such a manner that the center of gravity of the rectangle of the window  11 A becomes coincident with the center of gravity of the rectangle of the image  71 . 
   Therefore, the coordinates of the upper left corner of the image  71  is represented by the front coordinates ((w 1 −b 1 )/2, (h 1 −a 1 )/2). A vector from the origin (0, 0) of the front coordinate system to the point ((w 1 −b 1 )/2, (h 1 −a 1 )/2) is represented by a vector u. A vector from the upper left corner of the image  71  to a point (x 1 , y 1 ) in the display area of the window  11 A is represented by a vector v. 
   In this case, the vector v in the front coordinate system can be expressed by equation (1) by using the vector u. 
   
     
       
         
           
             
               
                 v 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               x 
                               1 
                             
                           
                         
                         
                           
                             
                               y 
                               1 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     u 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               x 
                               1 
                             
                           
                         
                         
                           
                             
                               y 
                               1 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   1 
                                 
                                 - 
                                 
                                   b 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   1 
                                 
                                 - 
                                 
                                   a 
                                   1 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
     FIG. 9  is a diagram illustrating a rear coordinate system. 
   The rear coordinate system is a coordinate system using as a reference a rear screen  80 . 
   Assuming that a user draws a point in the display area of the window  11 A, the drawing sharing section  53  does not draw this point directly on the window  11 A, but draws it once in a rear screen  80 . 
   The rear screen  80  is a screen common to all the drawing apparatuses, and in the example shown in  FIG. 9 , has a rectangular shape having a horizontal length of w 2  and a vertical length of h 2 . The entity of the rear screen  80  is a predetermined storage area of, for example, RAM  23  ( FIG. 3 ). 
   In  FIG. 9 , the rear coordinate system is defined by using the upper left corner of the rear screen as an origin (0, 0), a direction from left to right as an abscissa direction and a direction from up to down as an ordinate direction. 
   In  FIG. 9 , a rear content screen (area)  81  is shown on the rear screen  80 . The rear content screen  81  corresponds to the area where the image  71  of  FIG. 8  is shown. The rear content screen  81  has a rectangle shape having a horizontal length of kb 1  and a vertical length of ka 1 . Namely, the rear content screen  81  is a rectangle similar to the image at a similarity ratio of k. For example, the similarity ratio k may by 0.6. 
   In the rear screen  80 , the rear content screen  81  is disposed, for example, in such a manner that the center of gravity of the rectangle of the rear screen  80  becomes coincident with the center of gravity of the rectangle of the rear content screen  81 . 
   Therefore, the coordinates of the upper left corner of the rear content screen  81  are represented by ((w 2 −kb 1 )/2, (h 2 −ka 1 )/2)) in the rear coordinate system. A vector from the origin (0, 0) of the rear screen  80  to the point ((w 2 −kb 1 )/2, (h 2 −ka 1 )/2)) is represented by a vector t. A vector from the upper left corner of the rear content screen  81  to a point (x 2 , y 2 ) on the rear screen  80  corresponding to the point (x 1 , y 1 ) in  FIG. 8  is represented by a vector s. 
   Since the point (x 1 , y 1 ) in  FIG. 8  is in the image  71  and the rectangle of the image  71  and the rectangle of the rear content screen  81  are similar at the similarity ratio k, the vector s from the upper left corner of the rear content screen  81  to the point (x 2 , y 2 ) can be represented by a vector kv by using a vector v from the upper left corner of the image  71  of  FIG. 8  to the point (x 1 , y 1 ). 
   The point (x 2 , y 2 ) in the rear coordinate system corresponding to the point (x 1 , y 1 ) in the front coordinate system is expressed by a sum t+kv of the vector t from the origin (0, 0) of the rear coordinate system to the upper left corner of the rear content screen  81  and the vector s (=kv) from the upper left corner of the rear content screen  81  to the point (x 2 , y 2 ). Therefore, the point (x 2 , y 2 ) in the rear coordinate system is expressed by the following equation (2) by using the vector v using the corresponding point (x 1 , y 1 ) in the front coordinate system. 
   
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         
                           x 
                           2 
                         
                       
                     
                     
                       
                         
                           y 
                           2 
                         
                       
                     
                   
                   ) 
                 
                 = 
                 
                   
                     t 
                     + 
                     kv 
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   2 
                                 
                                 - 
                                 
                                   kb 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   2 
                                 
                                 - 
                                 
                                   ka 
                                   1 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       k 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 1 
                               
                             
                           
                           
                             
                               
                                 y 
                                 1 
                               
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         k 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   1 
                                 
                                 - 
                                 
                                   b 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   1 
                                 
                                 - 
                                 
                                   a 
                                   1 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   Equation (2) is a function (mapping) f for transforming the point (front coordinates) (x 1 , y 1 ) in the front coordinate system into the corresponding point (rear coordinates) (x 2 , y 2 ) in the rear coordinate system. 
   Equation (2) is the function f for transforming the front coordinates (x 1 , y 1 ) into the rear coordinates (x 2 , y 2 ) in accordance with the aspect ratio of b 1 :a 1  of the image  71  displayed on the computer  11 , and the function f is described as a function f 1  in order to distinguish this function f from a function f for transforming the front coordinates into the rear coordinates in accordance with an aspect ratio of b 2 :a 2  of an image displayed on the computer  12  to be described later. 
   The front coordinate transformation section  64  ( FIG. 7 ) transforms the input data (x 1 , y 1 ) as a point in the front coordinate system into the point (x 2 , y 2 ) in the rear coordinate system, by using the function f 1    63  of  FIG. 7  transforms. 
   The rear coordinate transformation section the point (x 2 , y 2 ) in the rear coordinate system into the point (x 1 , y 1 ) in the front coordinate system, by using an inverse function f 1   −1  of the function f 1 . Namely, the rear coordinate transformation section  63  transforms the rear coordinates (x 2 , y 2 ) into the front coordinates (x 1 , y 1 ) in accordance with the inverse function f 1   −1  represented by the following equation (3) obtained by solving equation (2) relative to (x 1 , y 1 ) 
   
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         
                           x 
                           1 
                         
                       
                     
                     
                       
                         
                           y 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 = 
                 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 w 
                                 1 
                               
                               - 
                               
                                 b 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 1 
                               
                               - 
                               
                                 a 
                                 1 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       1 
                       k 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                         - 
                         
                           
                             1 
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       w 
                                       2 
                                     
                                     - 
                                     
                                       kb 
                                       1 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       h 
                                       2 
                                     
                                     - 
                                     
                                       ka 
                                       1 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
   
   The values of w 2  and h 2  of the rear screen  80  of  FIG. 9  are set so that a point in the front coordinate system corresponding to an optional point is positioned in a range of the rear screen  80 , at least when the size of the window  11 A ( FIG. 8 ) is maximized. 
   The front and rear coordinate systems described above can be defined in a similar manner for the window  12 A displayed on the computer  12 . 
     FIG. 10  is a diagram illustrating the front coordinate system using as a reference the window  12 A displayed on the computer  12 . 
   In  FIG. 10 , similar to the case of  FIG. 8 , the front coordinate system is defined by using an upper left corner of the window  12 A (in the display area) as an origin (0, 0), a direction from left to right as an abscissa direction and a direction from up to down as an ordinate direction. 
   In  FIG. 10 , a horizontal (along the abscissa direction) length of the display area of the window  12 A is set to w 3  and the vertical (along the ordinate direction) length is set to h 3 . This display area is also an area where a user can draw an image, and its size changes as the window  12 A is resized. 
   In  FIG. 10 , an image (moving image)  121  as content is displayed in the window  12 A. The image  121  is displayed by the image display section  56  ( FIG. 5 ) and in the example shown in  FIG. 10 , has a rectangle shape having a horizontal length of b 2  and a vertical length of a 2 . Namely, the aspect ratio (horizontal:vertical) of the image  121  is b 2 :a 2 . 
   The image display sections  52  and  56  of  FIG. 5  display the same moving image as the image  71  ( FIG. 8 ) and the image  121  on the windows  11 A and  12 A, respectively, at different aspect ratios if b 1 :a 1  is different from b 2 :a 2 . If b 1 :a 1  is not equal to b 2 :a 2 , it is assumed that b 1 &lt;a 1  and b 2 &lt;a 2  are satisfied or b 1 &gt;a 1  and b 2 &gt;a 2  are satisfied. 
   In the window  12 A, the image  121  is displayed, for example, in such a manner that the center of gravity of the rectangle of the window  12 A becomes coincident with the center of gravity of the rectangle of the image  121 . 
   Therefore, the coordinates of the upper left corner of the image  121  are represented by ((w 3 −b 2 )/2, (h 3 −a 2 )/2) in the front coordinate system. A vector of the origin (0, 0) of the front coordinate system to the point ((w 3 −b 2 )/2, (h 3 −a 2 )/2) is represented by a vector u. A vector from the upper left corner of the image  121  to a point (x 5 , y 5 ) in the display area of the window  12 A is represented by a vector v. 
   In this case, the vector v in the front coordinate system is expressed by the following equation corresponding to equation (1), by using the vector u. 
   
     
       
         
           
             
               
                 v 
                 = 
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               x 
                               5 
                             
                           
                         
                         
                           
                             
                               y 
                               5 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     u 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               x 
                               5 
                             
                           
                         
                         
                           
                             
                               y 
                               5 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   3 
                                 
                                 - 
                                 
                                   b 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   3 
                                 
                                 - 
                                 
                                   a 
                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   Similar to the drawing sharing section  53  described above, as a user draws a point in the display area of the window  12 A, the drawing sharing section  57  of  FIG. 5  does not draw the point on the window  12 A directly, but draws it once on the rear screen. 
     FIG. 11  shows the rear screen  110  for the drawing sharing section  57 . 
   In this embodiment, the rear screen  110  is common to (the same as) the rear screen  80  of  FIG. 9 , and as described with  FIG. 9 , has the rectangle shape having the horizontal length of w 2  and the vertical length h 2 . 
   In  FIG. 11 , the rear coordinate system is defined by using the upper left corner of the rear screen  110  as an origin (0, 0), a direction from left to right as an abscissa direction and a direction from up to down as an ordinate direction. 
   Similar to the rear screen  80  of  FIG. 9 , a rear content screen (image)  111  is shown on the rear screen  110 . The rear content screen  111  corresponds to the area where the image  121  of  FIG. 10  is displayed. The rear content screen  111  has a rectangle shape having a horizontal length of kb 2  and a vertical length of ka 2 . Namely, the rear content screen  111  has a rectangle shape similar to the image  121  at a similarity ratio of k. The similarity ratio can be, for example 0.6, as described earlier. 
   In the rear screen  110 , similar to the rear content screen  81  of  FIG. 9 , the rear content screen  111  is disposed, for example, in such a manner that the center of gravity of the rectangle of the rear screen  110  becomes coincident with the center of gravity of the rectangle of the rear content screen  111 . 
   Therefore, the coordinates of an upper left corner of the rear content screen  111  are represented by ((w 2 −kb 2 )/2, (h 2 −ka 2 )/2) in the rear coordinate system. A vector from an origin (0, 0) of the rear screen  110  to the point ((w 2 −kb 2 )/2, (h 2 −ka 2 )/2) is represented by a vector t. A vector from the upper left corner of the rear content screen  111  to a point (x 4 , y 4 ) on the rear screen  110  corresponding to the point (x 5 , y 5 ) of  FIG. 5  is represented by a vector s. 
   Since the point (x 5 , y 5 ) in  FIG. 10  is in the image  121  and the rectangle of the image  121  and the rectangle of the rear content screen  111  are similar at the similarity ratio k, the vector s from the upper left corner of the rear content screen  111  to the point (x 4 , y 4 ) can be represented by a vector kv by using a vector v from the upper left corner of the image  121  of  FIG. 10  to the point (x 5 , y 5 ). 
   The point (x 4 , y 4 ) in the rear coordinate system corresponding to the point (x 5 , y 5 ) in the front coordinate system is expressed by a sum t+kv of the vector t and the vector s (=kv). Therefore, the point (x 4 , y 4 ) in the rear coordinate system is expressed by the following equation (5) corresponding to equation (2) by using the vector v using the corresponding point (x 5 , y 5 ) in the front coordinate system. 
   
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         
                           x 
                           4 
                         
                       
                     
                     
                       
                         
                           y 
                           4 
                         
                       
                     
                   
                   ) 
                 
                 = 
                 
                   
                     t 
                     + 
                     kv 
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   2 
                                 
                                 - 
                                 
                                   kb 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   2 
                                 
                                 - 
                                 
                                   ka 
                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       k 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 x 
                                 5 
                               
                             
                           
                           
                             
                               
                                 y 
                                 5 
                               
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         k 
                         2 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   w 
                                   3 
                                 
                                 - 
                                 
                                   b 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   h 
                                   3 
                                 
                                 - 
                                 
                                   a 
                                   2 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   Similar to equation (2), equation (5) is a function (mapping) f for transforming the front coordinates (x 5 , y 5 ) in the front coordinate system into the corresponding rear coordinates (x 4 , y 4 ) in the rear coordinate system. 
   Equation (5) is the function f for transforming the front coordinates into the rear coordinates in accordance with the aspect ratio of b 2 :a 2  of the image  121  displayed on the computer  12 , and the function f is described as a function f 2  in order to distinguish this function f from the function f 1  of equation (2) for transforming the front coordinates into the rear coordinates in accordance with the aspect ratio of b 1 :a 1  of the image  71  displayed on the computer  11 . 
   The rear coordinates (x 4 , y 4 ) can be transformed into the front coordinates (x 5 , y 5 ) by using an inverse function f 2−1  of the function f 2  of equation (5), i.e., the inverse function f 2   −1  expressed by the following equation (6) obtained by solving equation (5) relative to the front coordinates (x 5 , y 5 ). 
   
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         
                           x 
                           5 
                         
                       
                     
                     
                       
                         
                           y 
                           5 
                         
                       
                     
                   
                   ) 
                 
                 = 
                 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 w 
                                 3 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 3 
                               
                               - 
                               
                                 a 
                                 2 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       1 
                       k 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   x 
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   4 
                                 
                               
                             
                           
                           ) 
                         
                         - 
                         
                           
                             1 
                             2 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       w 
                                       2 
                                     
                                     - 
                                     
                                       kb 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       h 
                                       2 
                                     
                                     - 
                                     
                                       ka 
                                       2 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   The image  71  shown in  FIG. 8  is, as described above, similar to the rear content screen  81  corresponding to the image  71  and shown in  FIG. 9 , and the rear content screen  81  maintains the aspect ratio of b 1 :a 1  of the image  71 . The function f 1  of equation (2) for transforming the front coordinates (x 1 , y 1 ) into the rear coordinates (x 2 , y 2 ) for the computer  11  (drawing apparatus  50 ) transforms therefore the front coordinates (x 1 , y 1 ) into the rear coordinates (x 2 , y 2 ) by maintaining the aspect ratio of b1:a1 of the image  71  ( FIG. 8 ) displayed on the window  11 A. It can therefore be said that the function f 1  of equation (2) (also the inverse function f 1   −1  of equation (3)) is in a sense a function corresponding to the aspect ratio of b 1 :a 1  of the image  71 . 
   From the same reason, the function f 2  of equation (5) transforms the front coordinates (x 5 , y 5 ) into the rear coordinates (x 4 , y 4 ) by maintaining the aspect ratio of b 2 :a 2  of the image  121  ( FIG. 10 ) displayed on the window  12 A. It can therefore be said that the function f 2  of equation (5) (also the inverse function f 2   −1  of equation (6)) is in a sense a function corresponding to the aspect ratio of b 2 :a 2  of the image  121 . 
   Assuming now that in  FIG. 5  synchronous images are drawn on the windows  11 A and  12 A by exchanging the rear coordinates (x 2 , y 2 ) ((x 4 , y 4 )) between the drawing apparatuses  50  and  54 , for example as a user of the drawing apparatus  50  draws a point represented by the front coordinates (x 1 , y 1 ) on the window  11 A, the drawing apparatus  50  transforms the front coordinates (x 1 , y 1 ) into the rear coordinates (x 2 , y 2 ) by using the function f 1  of equation (2) and transmits the rear coordinates to the drawing apparatus  54 . 
   The drawing apparatus  54  receives the rear coordinates (x 2 , y 2 ) from the drawing apparatus  50  and transforms the rear coordinates into the front coordinates (x 5 , y 5 ) by the inverse function f 1   −1  of equation (6), by using the rear coordinates (x 2 , y 2 ) as the rear coordinates (x 4 , y 4 ) of equation (6). The drawing apparatus  54  draws (displays) the point on the window  12 A at the position represented by the front coordinates (x 5 , y 5 ). 
   The rear coordinates (x 2 , y 2 ) transmitted from the drawing apparatus  50  to the drawing apparatus  54  are the same as the rear coordinates (x 4 , y 4 ) received by the drawing apparatus  54  from the drawing apparatus  50  and transformed into the front coordinates (x 5 , y 5 ) by the inverse function f 2   −1  of equation (6). Namely, the rear coordinates (x 2 , y 2 ) on the rear screen  80  ( FIG. 9 ) transmitted from the drawing apparatus  50  to the drawing apparatus  54  are the same as the rear coordinates (x 4 , y 4 ) on the rear screen  110  ( FIG. 11 ) received by the drawing apparatus  54  from the drawing apparatus  50  and transformed into the front coordinates (X 5 , y 5 ) by the inverse function f 1   −1  of equation (6). 
   However, the rear coordinates (x 2 , y 2 ) are the coordinates obtained by the drawing apparatus  50  by transforming the front coordinates (x 1 , y 1 ) by the function f 1  of equation (2) corresponding to the aspect ratio of b 1 :a 1  of the image  71 . Further, the rear coordinates (x 4 , y 4 ) same as the rear coordinates (x 2 , y 2 ) are transformed into the front coordinates (x 5 , y 5 ) by the drawing apparatus  54  by using the inverse function f 1   −1  of equation (6) corresponding to the aspect ratio of b 2 :a 2  of the image  121 . 
   Therefore, if the aspect ratio of b 1 :a 1  of the image  71  displayed by the drawing apparatus  50  is different from the aspect ratio of b 2 :a 2  of the image  121  displayed by the drawing apparatus  54 , the front coordinates (x 1 , y 1 ) at the drawing apparatus  50  are not coincident with the front coordinates (x 5 , y 5 ) at the drawing apparatus  54 , so that there is a position displacement between the point drawn by the user at the drawing apparatus  50  and the point drawn by the drawing apparatus  54 . 
   To avoid the above-described position displacement, the drawing apparatuses  50  and  54  (drawing sharing sections  53  and  57 ) of  FIG. 5  each transform the rear coordinates by a function g for normalizing the aspect ratio of an image to be displayed on the display  27 A (windows  11 A and  12 A) and transmit/receive the transformed coordinates. 
   The coordinates obtained by transforming the rear coordinates by the function g for normalizing the aspect ratio of an image, is herein called normalized coordinates. 
   The normalized coordinates are coordinates in a normalized coordinate system, and the normalized coordinate system is a coordinate system using as a reference a virtual normalized screen. 
     FIGS. 12 and 13  are diagrams illustrating the normalized coordinate system. 
     FIG. 12  shows the window  11 A, the rear screen  80  and a normalized screen  90  respectively displayed by the drawing apparatus  50  (drawing sharing section  53 ), and  FIG. 13  shows the window  12 A, the rear screen  110  and a normalized screen  100  respectively displayed by the drawing apparatus  54  (drawing sharing section  57 ). 
   Since the window  11 A and rear screen  80  in  FIG. 12  are similar to the window  11 A shown in  FIG. 8  and the rear screen  80  shown in  FIG. 9 , the description thereof is omitted. Since the window  12 A and rear screen  110  in  FIG. 13  are also similar to the window  12 A shown in  FIG. 10  and the rear screen  110  shown in  FIG. 11 , the description thereof is omitted. 
   As shown in  FIG. 12 , in the drawing sharing section  53  of the drawing apparatus  50 , as a user draws an image on the window  11 A at the front coordinates (x 1 , y 1 ), the front coordinates (x 1 , y 1 ) are transformed into the rear coordinates (x 2 , y 2 ) by the function f 1  of equation (1). Further, in the drawing apparatus  50 , the rear coordinates (x 2 , y 2 ) are transformed into the normalized coordinates (x 3 , y 3 ) in the normalized coordinate system by a function g 1  for normalizing the aspect ratio of the image  71  to be displayed by the drawing apparatus  50 , and the normalized coordinates are transmitted to the drawing apparatus  54 . 
   In the drawing apparatus  50 , as shown in  FIG. 12 , the normalized coordinate system is a coordinate system using as a reference the virtual normalized screen  90 . 
   In  FIG. 12 , the normalized screen  90  has, for example, the same rectangle shape as the rear screen  80 , i.e., the rectangle shape having the horizontal length of w 2  and the vertical length of h 2 . The normalized screen  90  may be different from the rear screen  80 . 
   In  FIG. 12 , the normalized coordinate system is defined by using an upper left corner of the normalized screen  90  as an origin (0, 0), a direction from left to right as an abscissa direction and a direction from up to down as an ordinate direction. 
   In  FIG. 12 , a normalized content screen (area)  91  is shown on the normalized screen  90 . The normalized content screen  91  is a region having the same horizontal and vertical length and obtained by normalizing, for example, at an aspect ratio of 1:1 the aspect ratio b 1 :a 1  of the area (rear content screen  81  of the rear screen  80 ) where the image  71  on the window  11 A is displayed. 
   Namely, in  FIG. 12  the normalized content screen  91  has, for example, a square shape having the vertical length of ka 1  same as that of the rear content screen  81  and the horizontal length of ka 1 . The aspect ratio of the normalized content screen  91  is therefore 1:1. However, the aspect ratio of the normalized content screen  91  is not limited to 1:1 (also for a normalized content screen  100  to be described later). 
   In the normalized screen  90 , the normalized content screen  91  is disposed, for example, in such a manner that the center of gravity of the rectangle of the normalized screen  90  becomes coincident with the center of gravity of the square of the normalized content screen  91 . 
   In  FIG. 12 , the vertical length ka 1  of the normalize content screen  91  is the same as the vertical length ka 1  of the rear content screen  81 , and the horizontal length ka 1  of the normalized content screen  91  is different from the horizontal length kb 1  of the rear content screen  81 . Therefore, the rear coordinates (x 2 , y 2 ) on the center line equally dividing the rear content screen  81  into right and left halves are coincident with the normalized coordinates (x 3 , y 3 ) on the center line equally dividing the normalized content screen  91  into right and left haves. 
   The right or left area obtained by dividing the rear content screen  81  at the center line into right and left halves corresponds to the right or left area obtained by dividing the normalized content screen  91  at the center line into right and left halves. It is therefore necessary to transform a point in the left area of the rear content screen  81  into a point in the left area of the normalized content screen  91 , and to transform a point in the right area of the rear content screen  81  into a point in the right area of the normalized content screen  91 . 
   In  FIG. 12 , the normalized content screen  91  has the vertical length of ka 1  same as the vertical length of ka 1  of the rear content screen  81 , and the horizontal length of ka 1  is different from the horizontal length of kb 1  of the rear content screen  81 . The normalized content screen  91  has therefore an area obtained by expanding/compressing the rear content screen  81  in the horizontal direction. 
   In order to transform the point (x 2 , y 2 ) in the right or left area of the rear content screen  81  into the point (x 3 , y 3 ) in the right or left area of the normalized content screen  91 , by maintaining the y coordinates as they are, the x coordinates are moved (expanded/compressed) in accordance with the ratio b 1 :a 1  of the x-direction lengths (horizontal lengths) of the rear content screen  81  and normalized content screen. 
   Namely, the point (rear coordinates) (x 2 , y 2 ) on the rear screen  80  can be transformed into the point (normalized coordinates) (x 3 , y 3 ) on the normalized screen  90  by the function g 1  of the following equation (7). 
   
     
       
         
           
             
               
                 
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   The normalized coordinates (x 3 , y 3 ) on the normalized screen  90  can be transformed into the rear coordinates (x 2 , y 2 ) on the rear screen  80  by an inverse function g 1   −1  obtained by solving equation (7) relative to (x 2 , y 2 ), i.e., the following equation (8). 
   
     
       
         
           
             
               
                 
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   Similar to the drawing sharing section  53  of the drawing apparatus  50 , as shown in  FIG. 13 , in the drawing sharing section  57  of the drawing apparatus  54 , as a user draws an image on the window  11 A at the front coordinates (x 5 , y 5 ), the front coordinates (x 5 , y 5 ) are transformed into the rear coordinates (x 4 , y 4 ) by the function f 2  of equation (5). Further, in the drawing apparatus  54 , the rear coordinates (x 4 , y 4 ) are transformed into the normalized coordinates (x 3 , y 3 ) in the normalized coordinate system by a function g 2  for normalizing the aspect ratio of the image  121  to be displayed by the drawing apparatus  54 , and the normalized coordinates are transmitted to the drawing apparatus  50 . 
   In the drawing apparatus  54 , as shown in  FIG. 13 , the normalized coordinate system is a coordinate system using as a reference the virtual normalized screen  100 . 
   In  FIG. 13 , the normalized screen  100  has the same rectangle shape as the rear screen  110 , for example, i.e., the rectangle shape having the horizontal length of w 2  and the vertical length of h 2 . The normalized screen  100  may be different from the rear screen  110 . 
   In  FIG. 13 , the normalized coordinate system is defined by using an upper left corner of the normalized screen  100  as an origin (0, 0), a direction from left to right as an abscissa direction and a direction from up to down as an ordinate direction. 
   In  FIG. 13 , a normalized content screen (area)  101  is shown on the normalized screen  100 . Similar to  FIG. 12 , the normalized content screen  101  is a region having the same horizontal and vertical length and obtained by normalizing at an aspect ratio of 1:1 the aspect ratio b 2 :a 2  of the area (rear content screen  111  of the rear screen  110 ) where the image  121  on the window  12 A is displayed. 
   Namely, in  FIG. 13  the normalized content screen  101  has, for example, a square shape having the vertical length of ka 2  same as that of the rear content screen  111  and the horizontal length of ka 2 . The aspect ratio of the normalized content screen  101  is therefore 1:1. 
   In the normalized screen  100 , the normalized content screen  101  is disposed, for example, in such a manner that the center of gravity of the rectangle of the normalized screen  100  becomes coincident with the center of gravity of the square of the normalized content screen  101 . 
   The vertical length ka 2  of the normalized content screen  101  is the same as the vertical length ka 2  of the rear content screen  111 , and the horizontal length ka 2  is different from the horizontal length kb 2  of the rear content screen  111 . Therefore, similar to the normalized content screen  91  shown in  FIG. 12 , the normalized content screen  101  has also an area obtained by expanding/compressing the rear content screen  111  in the horizontal direction. 
   The point (rear coordinates) (x 4 , y 4 ) on the rear screen  110  can be transformed into the point (normalized coordinates) (x 3 , y 3 ) on the normalized screen  100  by a function g 2  of the following equation (9) derived in a manner similar to equation (7). 
   
     
       
         
           
             
               
                 
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   The normalized coordinates (x 3 , y 3 ) on the normalized screen  100  can be transformed into the rear coordinates (x 4 , y 4 ) on the rear screen  110  by an inverse function g 2   −1  obtained by solving equation (9) relative to (x 4 , y 4 ), i.e., the following equation (10). 
   
     
       
         
           
             
               
                 
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   The drawing apparatuses  50  and  54  draw an image without position displacement by exchanging the above-described normalized coordinates (x 3 , y 3 ). 
     FIG. 14  is a diagram illustrating the process to be executed by the drawing sharing section  53  of the drawing apparatus  50  and the drawing sharing section  57  of the drawing apparatus  54  respectively of  FIG. 5 . 
   In  FIG. 14 , for the purposes of description simplicity, the vertical length ka 1  of the rear content screen  81  on the rear screen  80  is set equal to the vertical length ka 2  of the rear content screen  111  on the rear screen  110 . Therefore, in  FIG. 14 , the normalized content screen  91  corresponding to the rear content screen  81  is the same as the normalized content screen  101  corresponding to the rear content screen  111 . 
   For example, at the drawing apparatus  50  as the user draws an image on the window  11 A at the point indicated by the front coordinates (x 1 , y 1 ), the drawing sharing section  53  transforms the front coordinates (x 1 , y 1 ) into the rear coordinates (x 2 , y 2 ) by the function f 1  of equation (2). Then, the drawing sharing section  53  transforms the rear coordinates (x 2 , y 2 ) into the normalized coordinates (x 3 , y 3 ) by the function g 1  of equation (7) and transmits the drawing information containing the normalized coordinates (x 3 , y 3 ) to the drawing apparatus  54 . 
   The drawing sharing section  57  of the drawing apparatus  54  receives the drawing information from the drawing sharing section  53  and transforms the normalized coordinates (x 3 , y 3 ) contained in the drawing information into the rear coordinates (x 4 , y 4 ) by the inverse function g 2   −1  of equation (10). Then, the drawing sharing section  57  transforms the rear coordinates (x 4 , y 4 ) into the front coordinates (x 5 , y 5 ) by the inverse function f 2   −1  of equation (6) and draws a point on the window  12 A at the position indicated by the front coordinates (x 5 , y 5 ). 
   On other hand, for example, at the drawing apparatus  54  as the user draws an image on the window  12 A at the point indicated by the front coordinates (x 5 , y 5 ), the drawing sharing section  57  transforms the front coordinates (x 5 , y 5 ) into the rear coordinates (x 4 , y 4 ) by the function f 2  of equation (5). Then, the drawing sharing section  57  transforms the rear coordinates (x 4 , y 4 ) into the rear normalized coordinates (x 3 , y 3 ) by the function g 2  of equation (9) and transmits the drawing information containing the normalized coordinates (x 3 , y 3 ) to the drawing apparatus  50 . 
   The drawing sharing section  53  of the drawing apparatus  50  receives the drawing information from the drawing sharing section  57  and transforms the normalized coordinates (x 3 , y 3 ) contained in the drawing information into the rear coordinates (x 2 , y 2 ) by the inverse function g 1   −1  of equation (8). Then, the drawing sharing section  53  transforms the rear coordinates (x 2 , y 2 ) into the front coordinates (x 1 , y 1 ) by the inverse function f 1   −1  of equation (3) and draws a point on the window  11 A at the position indicated by the front coordinates (x 1 , y 1 ). 
   Next, with reference to the flow chart of  FIG. 15 , description will be made on the process to be executed by the drawing sharing section  53  of  FIG. 7  to transmit drawing information to the drawing apparatus  54 . 
   The process of  FIG. 15  starts when the input data (coordinates) (x 1 , y 1 ) representative of the position in the front coordinate system where the image was drawn is supplied from the user interface  51 , in response to that the user of the drawing apparatus  50  (computer  11 ) draws some image on the window  11 A. 
   At Step S 1 , the front coordinate transformation section  64  coordinate-transforms the input data (x 1 , y 1 ) supplied from the user interface  51  into the rear coordinates (x 2 , y 2 ) by the function f 1  corresponding to the aspect ratio b 1 :a 1  of the image  71  displayed on the window  11 A, i.e., equation (2), and supplies the rear coordinates to the rear coordinate transformation section  63  and normalizing section  65  to thereafter advance to Step S 2 . 
   As the rear coordinates (x 2 , y 2 ) are supplied from the front coordinate transformation section  64 , the rear coordinate transformation section  63  coordinate-transforms the rear coordinates (x 2 , y 2 ) into the front coordinates (x 1 , y 1 ) by the inverse function f 1   −1  of the function f 1 , i.e., equation (3), and supplies the front coordinates to the drawing section  67 . In accordance with the front coordinates (x 1 , y 1 ) supplied from the rear coordinate transformation section  63 , the drawing section  67  writes (draws) a predetermined value in the drawing memory  68  at a corresponding address. The display control section  69  displays an image corresponding to the stored value in the drawing memory  68  on the window  11 A of the display  27 A ( FIG. 3 ). In this manner, the point corresponding to the input data (x 1 , y 1 ) is displayed on the window  11 A. 
   In this case, the front coordinates (x 1 , y 1 ) obtained at the rear coordinate transformation section  63  are the same as the input data (x 1 , y 1 ). 
   At Step S 2 , the normalizing section  65  coordinate-transforms the rear coordinates (x 2 , y 2 ) supplied from the front coordinate transformation section  64  into the normalized coordinates (x 3 , y 3 ) by the function g 1  for normalizing the aspect ratio of b 1 :a 1  of the image  71  displayed on the window  11 A, i.e., equation (7), and transmits the normalized coordinates to the transmission section  66  to thereafter advance to Step S 3 . 
   At Step S 3 , the transmission section  66  transmits the drawing information containing the normalized coordinates (x 3 , y 3 ) supplied from the normalizing section  65  to the drawing apparatus  54  (drawing sharing section  57 ) ( FIG. 5 ) via the network  3  to thereafter terminate the process. 
   The process conforming to the flow chart of  FIG. 15  is also executed by the drawing sharing section  57  of the drawing apparatus  54 , in addition to the drawing sharing section  53 . 
   Next, with reference to the flow chart of  FIG. 16 , description will be made on the process to be executed by the drawing sharing section  53  of  FIG. 7  in accordance with the drawing information transmitted from the drawing sharing section  57  of the drawing apparatus  54 . 
   As the drawing information is transmitted from the drawing sharing section  57  of the drawing apparatus  54  via the network  3 , at Step S 11  the reception section  61  receives the drawing information and supplies the normalized coordinates (x 3 , y 3 ) contained in the drawing information to the normalized coordinate transformation section  62  to thereafter advance to Step S 12 . 
   Namely, since the drawing sharing section  57  of the drawing apparatus  54  executes a process similar to that described with  FIG. 15  and transmits the drawing information containing the normalized coordinates (x 3 , y 3 ) corresponding to the drawing made by the user of the drawing apparatus  54  (computer  12 ), at Step S 11  the reception section  61  receives the drawing information transmitted in this manner. 
   At Step S 12  the normalized coordinate transformation section  62  coordinate-transforms the normalized coordinates (x 3 , y 3 ) from the reception section  61  into the rear coordinates (x 2 , y 2 ) by the inverse function g 1   −1  of the function g 1  for normalizing the aspect ratio of b 1 :a 1  of the image  71  displayed on the window  11 A, i.e., equation (8), and supplies the rear coordinates to the rear coordinate transformation section  63  to thereafter advance to Step S 13 . 
   At Step S 13 , the rear coordinate transformation section  63  coordinate-transforms the rear coordinates (x 2 , y 2 ) from the normalized coordinate transformation section  62  into the front coordinates (x 1 , y 1 ) by the inverse function f 1   −1  of the function f 1 , i.e., equation (3), and supplies the front coordinates to the drawing section  67  to thereafter advance to Step S 14 . 
   At Step S 14 , in accordance with the front coordinates (x 1 , y 1 ) supplied from the rear coordinate transformation section  63 , the drawing section  67  writes (draws) a predetermined value in the drawing memory  68  at a corresponding address. The display control section  69  displays the image corresponding to the stored value in the drawing memory  68  on the window  11 A of the display  27 A ( FIG. 3 ) to thereafter terminate the process. 
   As described above, in the drawing apparatus  50 , the normalized coordinates (x 3 , y 3 ) transmitted from the drawing apparatus  54  via the network  3  is transformed into the rear coordinates (x 2 , y 2 ) by the inverse function g 1   −1  of the function g 1  for normalizing the aspect ratio of b 1 :a 1  of the image  71  displayed on the display  27 A, the rear coordinates (x 2 , y 2 ) are transformed into the front coordinates (x 1 , y 1 ) by the inverse function f 1   −1  of the function f 1  corresponding to the aspect ratio b 1 :a 1  of the image  71  and being different from the function g 1 , and an image is drawn on the screen of the display  27 A in accordance with the front coordinates (x 1 , y 1 ). Accordingly, accurate drawing without position displacement can be performed irrespective of different aspect ratios of the drawing apparatus  54  on the transmission side of drawing information and the drawing apparatus  50  on the reception side. 
   In the drawing apparatus  50 , the front coordinates (x 1 , y 1 ) as the input data representative of the position of the drawing made by the user is transformed into the rear coordinates (x 2 , y 2 ) by the function f 1  corresponding to the aspect ratio of b 1 :a 1  and being different from the function g 1  for normalizing the aspect ratio of b 1 :a 1  of the image  71  displayed on the display  27 A, the rear coordinates (x 2 , y 2 ) are transformed into the normalized coordinates (x 3 , y 3 ) by the function g 1 , and the normalized coordinates (x 3 , y 3 ) are transmitted to the drawing apparatus  54  via the network  3 . Accordingly, accurate drawing without position displacement is possible also in the case that the drawing apparatus  50  becomes the transmission side of drawing information and the drawing apparatus  54  becomes the reception side. 
   Therefore, the users of the drawing apparatuses  50  and  54  can have comfortable information sharing (mutual understanding). 
   In this embodiment, in the drawing apparatus  50 , the input data (x 1 , y 1 ) drawn by a user is once coordinate-transformed into the rear coordinates (x 2 , y 2 ) and thereafter further coordinate-transformed into the front coordinates (x 1 , y 1 ), and the drawing section  67  draws an image in accordance with the front coordinates (x 1 , y 1 ). Instead, the drawing section  67  may draw an image directly in accordance with the input data (x 1 , y 1 ). 
   Further, in this embodiment although two users of the drawing apparatuses  50  and  54  share drawing information via the network  3 , drawing information may be shared by three or more users via the network. 
   Furthermore, the transmission methods of transmitting drawing information via the network  3  to be shared by a plurality of users may be a so-called bucket relay method, for example, wherein drawing information is sequentially transmitted from one user to another repetitively or a method wherein a computer of one user operates as a server, and this server transfers drawing information to and from client computers of other users. 
   Still further, in the examples of preferred embodiments present herein, although the rear screens  80  and  110  have a common size (same size), the rear screens  80  and  110  may have different sizes. This also applies to the normalized screens  90  and  100 .