Abstract:
An image display method for displaying an image of a character in a virtual space configures a computer to execute steps of, a parameter setting step for setting parameters concerning movement of the character, a reference unit time setting step for setting a reference unit time of stepwise change of the parameters, a minimal unit time setting step for setting a minimal unit time of a equally divided time of reference unit time, a basic setting step of parameters, for setting the parameters for each reference unit time, and for allocating the parameters for each minimal unit time, a smoothing step for setting a smoothed parameters for each said minimal unit time, the parameters being allocated to the minimal unit time, and a display step for displaying the object according to said parameters set in the smoothing step for each minimal unit time.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to an image display Program and an image display apparatus for displaying an image of objects existing within a virtual space. 
         [0003]    2. Prior Art 
         [0004]    When movement is to be expressed of an object such as a character on a game machine etc., calculation of fine movement of each portions of the object is unpractical because the data volume to be processed and the calculation load are immense. 
         [0005]    The Japanese Patent Publication of Unexamined Application 2001-160150 discloses a “Motion Display Method of a Game Character” in which interpolation frames are prepared beforehand for interpolating motions between motions A and B of different reference posture when the motion of the object is changed from the motion A to the motion B. The interpolation frames are generated by Affine transformation of polygons of the object. Then, number n of interpolation frames is set according to correlation between the motions A and B. And n frames from the first frames of the motion B are substituted by the interpolating frames. A lot of calculation load is needed. 
         [0006]    The Japanese Patent Gazette No. 3618298 discloses a “Motion Display Method” in which frames of motions A and B are composed when the motion A is transferred to the motion B. The composing ratio of the motion A is high first and the composing ration of the motion B is gradually increased so as to interpolating composed motion is generated. A smooth interpolation is realized. However, the displayed image is not always natural. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    The present invention is invented so as to solve the conventional problems above and has an object to realize clear and natural motion display. 
         [0008]    The present invention is an image display program for displaying an image of a character in a virtual space, said program letting a computer execute steps of, a parameter setting step for setting parameters concerning movement of said character, a reference unit time setting step for setting reference unit time of stepwise change of the parameters, a minimal unit time setting step for setting a minimal unit time of a equally divided time of said reference unit time, a parameter allocating step for allocating said parameters to each reference unit time, and for allocating said parameters to each said minimal unit time, a smoothing step for setting a smoothed parameters for each said minimal unit time, said parameters being allocated to said minimal unit time, and a display step for displaying said object according to said parameters set in said smoothing step for each minimal unit time. 
         [0009]    Therefore, a clear and natural movement can easily realized. A clear and natural rotational movement is displayed by a hardware of rather small size. 
         [0010]    The present invention is an image display apparatus for displaying an image of a character in a virtual space comprising a parameter setting means for setting parameters concerning movement of said character, a reference unit time setting means for setting a reference unit time of stepwise change of the parameters, a minimal unit time setting means for setting a minimal unit time of a time equally divided said reference unit time, a parameter allocating means for allocating said parameters to each reference unit time, and for allocating said parameters to each said minimal unit time, a smoothing means for setting a smoothed parameters for each said minimal unit time, said parameters being allocated to said minimal unit time, and a display means for displaying said object according to said parameters set by said smoothing means for each minimal unit time. 
         [0011]    Therefore, a clear and natural movement can easily realized. A clear and natural rotational movement is displayed by a hardware of rather small size. 
         [0012]    In the image display program and image display apparatus, the parameters includes, for example, a rotational angular velocity (ωx, ωy, ωz) around three dimensional coordinate axes (X-, Y- and Z-coordinate) in said virtual space, said rotational angular velocity ωx being rightward rotation around said X-axis viewing toward plus direction of said X-axis, said rotational angular velocity ωy being rightward rotation around said Y-axis viewing toward plus direction of said Y-axis, and said rotational angular velocity ωy being rightward rotation around said Z-axis viewing toward plus direction of said Z-axis. 
         [0013]    Therefore, any three dimensional rotational movement may be clearly and naturally expressed. 
         [0014]    In the image display program and image display apparatus, said parameters includes a posture parameter indicative of posture of said character. 
         [0015]    Therefore, any three dimensional rotational movement may be clearly and naturally expressed. 
         [0016]    In the image display program and image display apparatus, said reference unit time is for example 0.5 sec. Said smoothing step and smoothing means sets a smoothed parameters of said successive minimal unit time. Said smoothing is executed for example by a weighted addition of a plurality of successive parameters. Weights of said weighted addition may be equal to one another. Said minimal unit time is for example a quarter of said reference unit time. 
         [0017]    Therefore, movement is displayed utmost clearly and naturally according to experiences. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1  is an elevation view showing an embodiment of a game machine (image processing apparatus) according to the present invention. 
           [0019]      FIG. 2  is a block diagram showing the apparatus of  FIG. 1 . 
           [0020]      FIG. 3  is a figure showing a virtual space displayed on the game machine in  FIG. 1 . 
           [0021]      FIG. 4  is an elevation view showing a situation of a character object of  FIG. 3  standing upright, which moves in the virtual space. 
           [0022]      FIG. 5  is a right side view of  FIG. 4 . 
           [0023]      FIG. 6  is an elevation view showing a situation of the object of  FIG. 4  raising one hand. 
           [0024]      FIG. 7  is a right side view of  FIG. 6 . 
           [0025]      FIG. 8  is a left side view of  FIG. 6 . 
           [0026]      FIG. 9  is an elevation view showing a situation of the object of  FIG. 4  holding by arms knees drawn up, 
           [0027]      FIG. 10  is a right side view of  FIG. 9 , 
           [0028]      FIG. 11  is a table showing posture parameters and change in rotational angular velocity of the character for each reference unit time, 
           [0029]      FIG. 12  is a table showing posture parameters and change in rotational angular velocity of the character for each maximal unit time, 
           [0030]      FIG. 13  is a table showing a smoothed result of posture parameters and change in rotational angular velocity in  FIG. 12 , 
           [0031]      FIG. 14  is a table showing a rotational angle in  FIG. 13  for each maximal unit time, 
           [0032]      FIG. 15  is a table showing a total rotational angle obtained by an integration of the rotational angle in  FIG. 14 , 
           [0033]      FIG. 16  is a graph showing the posture parameters in  FIG. 13  and the total rotational angle in  FIG. 15 , 
           [0034]      FIG. 17  is a perspective view showing the character of  FIG. 4  simplified for explaining composition of posture and rotation of the character, 
           [0035]      FIG. 18  is a perspective view showing the character of  FIG. 9  simplified for explaining composition of posture and rotation of the character, 
           [0036]      FIG. 19  is a perspective view showing a situation of the character in  FIGS. 17 and 18  with composed posture and rotation, 
           [0037]      FIG. 20  is a perspective view showing another situation of the character in  FIGS. 17 and 18  with composed posture and rotation, 
           [0038]      FIG. 21  is a perspective view showing further another situation of the character in  FIGS. 17 and 18  with composed posture and rotation, 
           [0039]      FIG. 22  is a figure showing a skeleton of the character in  FIG. 4  for the posture composition, 
           [0040]      FIG. 23  is a figure showing a skeleton of the character in  FIG. 5  for the posture composition, 
           [0041]      FIG. 24  is a figure showing a skeleton of the character in  FIG. 6  for the posture composition, 
           [0042]      FIG. 25  is a figure showing a skeleton of the character in  FIG. 7  for the posture composition, 
           [0043]      FIG. 26  is a figure showing a skeleton of the character in  FIG. 8  for the posture composition, 
           [0044]      FIG. 27  is a figure showing a skeleton of the character in  FIG. 9  for the posture composition, 
           [0045]      FIG. 28  is a flowchart showing a processing of the first embodiment of an image processing program according to the present invention, 
           [0046]      FIG. 29  is a table showing posture parameters composed by smoothing. 
           [0047]      FIG. 30  is a graph showing posture parameters composed by smoothing, and 
           [0048]      FIG. 31  is a flowchart showing a processing of the second embodiment of an image processing program according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0049]    Preferred embodiments are described of an image display program and an image display apparatus according to the present invention, hereafter. 
       First Embodiment 
     [Image Display Apparatus] 
       [0050]    In  FIG. 1 , a game machine (image display apparatus)  2000  includes a controller  2100 , a display apparatus  2200  such as a TV monitor and a keyboard  2300 . 
         [0051]    On the display apparatus  2200 , an image of character objects CH (shown by CH 1  to CH 3 ) moving in a virtual space. The characters CH 1  to CH 3  perform diving from an object OB of diving platform. 
         [0052]    For example, the character CH jumps backward from the diving platform OB with left hand raised and rotating rightward (shown by an arrow R 1 ). The character drops along a parabolic orbit G as shown by an image CH 2 . Then, the character changes its posture to a posture of holding knees (shown by CH 3 ) and drops further. According to this embodiment, these movements can be clearly and naturally expressed by a hardware of rather low performance. 
         [0053]    The above movement display of the character CH is executed by an input signal from the controller  2100  or by cooperation of a CPU  1000 , a system memory  1020 , a video processor and a graphic memory  1040 , according to a predetermined program. The CPU  1000 , system memory  1020 , video processor and graphic memory  1040  are described later with reference to  FIG. 2 . 
         [0054]    However, there are other various objects in the virtual space, only the character CH is described, here, for easy understanding of the present invention. 
         [0055]    In  FIG. 2 , the game machine (image display apparatus)  2000  includes the CPU  1000  for controlling the total component of the game machine, a boot ROM  1010  for storing a program which starts the game machine up, and the system memory  1020  for storing a program executed by the CPU  1000  and data. 
         [0056]    The game machine  2000  is provided with a video processor  1030  for generating and controlling images to be displayed, and a graphic memory  1040  for storing material images for the generated images and for storing the generated images. The video processor  1030  displays the generated images on the display apparatus  2200 . 
         [0057]    The game machine  2000  is provided with an audio processor  1070  for generating sound and an audio memory  1080  for storing sound data. The audio processor  1070  generates digital signal of sound according to the data stored in the audio memory  1080  and outputs the sound from a speaker or headphone (not shown). 
         [0058]    The game machine  2000  is provided with a CD-ROM drive  1090  etc. of a memory device for program data and others. In the memory device, a game program, data etc. are read into the system memory  1020 , graphic memory  1040  or audio memory  1080 . 
         [0059]    The game machine is provided with a memory interface  1130  by which players can read and write their own memory cards A and B. The players can register result of a game, situation of an interrupted game etc. 
         [0060]    The game machine  2000  is provided with a modem  1150  connected through a communication interface  1160 . A network game can be executed by a plurality of game machines  2000  through a network. A statistics of the game result, a ranking of the players, various events and other various information concerning games can be obtained from a server (not shown). 
         [0061]    The game machine  2000  is provided with a controller interface  1140  having terminals  1  to  4  to which a controller  2100  is connected. 
       [Image Display Algorithm] 
       [0062]    Next, an image display algorithm executed by the game machine  2000  is described. 
         [0063]    In  FIG. 3 , three dimensional coordinates of X, Y and Z-coordinates is defined in a virtual space VS. For example, a rightward rotational angle a around the X-axis, a rightward rotational angle β around the Y-axis and a rightward rotational angle γ around the Z-axis, and rotational angular velocities ωx, ωy and ωz of the rotational angles a, β and γ are defined. 
         [0064]    The character CH and other objects are arranged in the virtual space VS at any positions, in any postures and with any rotational anguler velocity by setting these parameters, that is, the coordinates (X, Y, Z), rotational angles (a, β, γ) and rotational anguler velocity (ωx, ωy, ωz). 
         [0065]    As shown in  FIGS. 4 to 10 , a plurality of postures, for example, of standing upright ( FIGS. 4 and 5 ), with raising hand ( FIGS. 6 to 8 ) and with knees drawn up and held by arms ( FIGS. 9 and 10 ) are defined for the character CH. Any of the postures can be selected and be continuously changed. 
         [0066]    In order to rotate the character CH with changing the posture, the posture and the rotational angular velocity are set for each reference unit time (0.5 sec, for example), as shown in  FIG. 11 , for example. 
       [Parameter, Reference Unit Time and Minimal Unit Time] 
       [0067]    In  FIG. 11 , the rotational angular velocity (ωx, ωy, ωz) changes (0, 0, 0)[deg], (720, 0, 0)[deg], (0, 720, 0)[deg], (720, 720, 0)[deg], (720, 0, 720)[deg] and (0, 0, 0)[deg]. In  FIG. 11 , six postures are set. The posture is expressed by posture parameter (described later) Pa, Pb, Pc, Pd, Pe and Pf, and changes from Pa to Pb, then to Pc, then to Pd, then to Pe, and then to Pf. 
         [0068]    In order to clarify the dynamic change of the rotation and the posture, the reference unit time (T, hereafter) is divided into minimal unit times (t, hereafter), the rotational angular velocity (ωx, ωy, ωz) and the posture parameter (Pa, Pb, Pc, Pd, Pe, Pf) are allocated to each minimal unit time. 
         [0069]    In  FIG. 12 , the reference unit time T=1 is divided into minimal unit times of 0≦t&lt;0.125 [sec], 0.125≦t&lt;0.250 [sec], 0.250≦t&lt;0.375 [sec] and 0.375≦t&lt;0.500 [sec]. 
         [0070]    The reference unit time T=2 is divided into minimal unit times of 0.500≦t&lt;0.625 [sec], 0.625≦t&lt;0.750 [sec], 0.750≦t&lt;0.875 [sec] and 0.875≦t&lt;1.000 [sec]. 
         [0071]    The reference unit time T=3 is divided into minimal unit times of 1.000≦t&lt;1.125 [sec], 1.125≦t&lt;1.250 [sec], 1.250≦t&lt;1.375 [sec] and 1.375≦t&lt;1.500 [sec]. 
         [0072]    The reference unit time T=4 is divided into minimal unit times of 1.500≦t&lt;1.625 [sec], 1.625≦t&lt;1.750 [sec], 1.750≦t&lt;1.875 [sec] and 1.875≦t&lt;2.000 [sec]. 
         [0073]    The reference unit time T=5 is divided into minimal unit times of 2.000≦t&lt;2.125 [sec], 2.125≦t&lt;2.250 [sec], 2.250≦t&lt;2.375 [sec] and 2.375≦t&lt;2.500 [sec]. 
         [0074]    The reference unit time T=6 is divided into minimal unit times of 2.500≦t&lt;2.625 [sec], 2.625≦t&lt;2.750 [sec], 2.750≦t&lt;2.875 [sec] and 2.875≦t&lt;3.000 [sec]. 
       [Posture Parameter] 
       [0075]    The posture parameter is described concerning the characters CH shown in  FIGS. 4 to 10 . 
         [0076]    The character CH is modeled to be a construction (called “skeleton”) consisting of moving components of links (called “arc”). The posture is defined by relative angles at conjunction points (called “node”) of arcs. As shown in  FIG. 22  corresponding to  FIG. 4 , the character CH consists of, for example, a skeleton of a plurality of arcs E 1  to E 20  covered with a head, a torso, arms, feet etc. An end N 0  (node at parietal point) of the uppermost arc E 1  is defined as a reference point. 
         [0077]      FIGS. 22 to 27  shows skeletons corresponding to the character of  FIGS. 4 to 9 , for the posture composition. 
         [0078]    In order to clarify the expression, references are shown in  FIGS. 24 and 25  for different portions relative to  FIGS. 22 and 23 , and references for arcs are omitted in  FIGS. 24 and 25 . 
         [0079]    The arc E 1  is rotatably connected with the arc E 2  (at the neck) by a node N 1 . The arc E 2  is rotatably connected with the arc E 3 , E 4  (at the shoulder) and E 6  (at the chest) by a node N 3 . 
         [0080]    The arc E 3  is rotatably connected with the arc E 5  (at the upper right hand) by a node N 2 . The arc E 5  is rotatably connected with the arc E 8  (at the right forearm) by a node N 5 . The arc E 8  is rotatably connected with the arc E 11  (at the right hand) by a node N 8 . 
         [0081]    The arc E 4  is rotatably connected with the arc E 7  (at the upper left hand) by a node N 4 . The arc E 7  is rotatably connected with the arc E 10  (at the left forearm) by a node N 7 . The arc E 10  is rotatably connected with the arc E 14  (at the left hand) by a node N 10 . 
         [0082]    The arc E 6  is rotatably connected with the arc E 9  (at the belly) by a node N 6 . The arc E 9  is rotatably connected with the arc E 12  and E 13  (at the pelvis) by a node N 9 . 
         [0083]    The arc E 12  is rotatably connected with the arc E 15  (at the right femul) by a node N 11 . The arc E 15  is rotatably connected with the arc E 17  (at the right leg) by a node N 15 . The arc E 17  is rotatably connected with the arc E 19  (at the right foot) by a node N 17 . 
         [0084]    The arc E 13  is rotatably connected with the arc E 16  (at the left femul) by a node N 13 . The arc E 16  is rotatably connected with the arc E 18  (at the left leg) by a node N 18 . The arc E 18  is rotatably connected with the arc E 20  (at the left foot) by a node N 20 . 
         [0085]    The skeleton is settled in position and angle when the coordinate (X, Y, Z) of the node N 0  and the rotational angle (α, β, γ) are decided. The other arcs E 2  to E 20  are settled in angles when the relative angles at the nodes N 1  to N 18 . A group of parameters for settling the nodes and arcs is called “posture parameter”. 
       [Rotation and Composition of Postures] 
       [0086]    Next, it is described how the rotation and composition of postures are executed. Here, in order to simplify the description, the character is modeled to be a more simple model. 
         [0087]    The character CH In  FIG. 19  is rotated around the X-axis by a=270 [deg] with respect to the upright standing posture (posture parameter Pa) of  FIG. 17  and the unrotated posture with holding knees (posture parameter Pb) in  FIG. 18 . The posture parameter P of the character in  FIG. 19  is a composite posture parameter of 75 [%] of Pa and 25 [%] of Pb. The composite posture parameter P is calculated by addition of 75 [%] parameters included in Pa and 25 [%] parameters included in Pb corresponding to those of Pa. 
         [0088]    In  FIG. 20 , the character CH is of the posture parameter P as a composite posture parameter with 50 [%] of Pa ad 50 [%] Pb. The composite posture parameter P is calculated by addition of 50 [%] parameters included in Pa and 50 [%] parameters included in Pb corresponding to those of Pa. 
         [0089]    In  FIG. 21 , the character CH is rotated around the X-axis by a=360 [deg] and around the Y-axis by β=90 [deg], and its posture parameter P is a composite posture parameter with 25 [%] of Pa and 75 [%] Pb. The composite posture parameter P is calculated by addition of 25 [%] parameters included in Pa and 75 [%] parameters included in Pb corresponding to those of Pa. 
       [Rotation] 
       [0090]    In the rotational angle (ωx, ωy, ωz) allocated to each minimal unit time is applied to the rotation of the character, the rotation is abrupt and unnatural at the beginning and at the end. And the rotation is unnatural at the time when the rotational angular velocity is changed. 
         [0091]    Therefore, in this embodiment, the rotational angular velocity (ωx, ωy, ωz) is smoothed for a time distance of three minimal unit times, for example, according to formulae (1) to (3). 
         [0000]      ω x ( ti )={ω x ( ti− 1)+ω x ( ti )+ω x ( ti+ 1)}/3  formula (1) 
         [0000]      ω y ( ti )={ω y ( ti− 1)+ω y ( ti )+ω y ( ti+ 1)}/3  formula (2) 
         [0000]      ω z ( ti )={ω z ( ti− 1)+ω z ( ti )+ω z ( ti+ 1)}/3  formula (3)       ti−1: (i−1)th minimal unit time   ti: ith minimal unit time   ti+1: (i+1)th minimal unit time   ωx: ωx at ith minimal unit time   ωy: ωy at ith minimal unit time   ωz: ωz at ith minimal unit time         
         [0098]    As an exception, in the case there is not ti−1 at the time ti=0 in  FIG. 12 , ωx(ti−1), ωy(ti−1), ωz(ti−1) are omitted. In the case there is not ti+1 at the time ti=3.000, ωx(ti+1), ωy(ti+1), ωz(ti+1) are omitted. 
         [0099]    The smoothing may be executed for shorter or longer time distance. However, the smoothing in the formula (4) is a weighted addition with equal weights, the smoothing may be executed by a weighted addition with different weights for successive parameters. 
         [0100]    The smoothing execution result is shown in  FIG. 13 . The rotational angular velocity (a, β, γ) for reach minimal unit time is shown in the table of  FIG. 13 . A total rotational angle as an integration of the rotational angle in  FIG. 14  is shown in the table of  FIG. 15 . The posture parameter in  FIG. 13  and the total rotational angle in  FIG. 15  are shown in a graph of  FIG. 16 . 
         [0101]    It will be apparent from  FIG. 16 , the rotational angle (a, β, γ) clearly changes from a macro point of view but the fine angular change is soothed from micro point of view. Therefore, the angular change is extremely clear and natural as a whole. 
         [0102]    According to experiences, a very good result is obtained by the reference unit time of T=0.5 sec and D=4. The calculation condition may be improved by a combination of various reference unit time T and various number D of division. 
       [Dynamic Change of Posture] 
       [0103]    As for the posture parameter, the change of the posture parameter Pa→Pb→Pc→Pd→Pe→Pf in  FIG. 12  is realized by setting each posture parameter 100 [%] and other posture parameters 0 [%]. However, if these setting is applied to the dynamic posture change of the character CH, abrupt and unnatural posture change occurs. 
         [0104]    Therefore, in this embodiment, similarly to the posture parameter of the patent document 2, at the transition time from a posture to the other posture, both postures are composed according to formula (4) so that the posture change becomes moderate. According to the formula (4), the posture parameter composition is executed with setting the transition time to be 2×Tr times of the minimal unit time and the minimal unit time after Pa to be ith minimal unit time. 
         [0000]        P ( ti−Tr+ 1)={ Pa ×(1− R )+ Pb×R}   
         [0000]        P ( ti−Tr+ 2)={ Pa ×(1− R× 2)+ Pb ×( R× 2)} 
         [0000]      . . . 
         [0000]        P ( ti )={ Pa× 0.5+ Pb× 0.5} 
         [0000]        P ( ti+ 1)={ Pa× 0.5+ Pb× 0.5} 
         [0000]      . . . 
         [0000]        P ( ti+Tr− 1)={ Pa×R+Pb ×(1− R )}  formula (4) 
         [0105]    Here, 
         [0106]    R=1/(2×Tr) 
         [0107]    P(ti): composed posture parameter of ith minimal unit time 
         [0108]    In  FIG. 13  shows a calculation result of the composite posture parameter P in the transition time in  FIG. 12 , with D=4 and Tr=2.  FIG. 16  shows a graph of the calculation result. 
         [0109]    In  FIG. 16 , curves with reference Pa, Pb, Pc, Pd, Pe and Pf are composite posture parameters. Each posture parameter reach 100 [%] of Pa, Pb, Pc, Pd, Pe or Pf at the point Pa, Pb, Pc, Pd, Pe and Pf is attached. In the transition time, the change of Pa→Pb→Pc→Pd→Pe→Pf is moderate. 
         [0110]    In the game machine of  FIGS. 1 and 2 , the CPU  1000  and the system memory  1020  cooperatively function as a parameter setting means for setting the parameters concerning the movement of the character CH, such as, the coordinate (X, Y, Z), rotational angle (a, β, γ), rotational angular velocity (ωx, ωy, ωz), posture parameters Pa to Pf etc. The CPU  1000  and the system memory  1020  cooperatively function as a reference unit time setting means for setting a reference unit time T, as a minimal unit time setting means for setting the minimal unit time t and as a parameter allocating means for allocating the parameters to each minimal unit time. 
         [0111]    Further, the CPU  1000  and the system memory  1020  cooperatively function as a smoothing means for smoothing the rotational angular velocity (ωx, ωy, ωz) of a plurality of successive unit times, which is set by the parameter allocating means to each minimal unit time. The rotational angular velocity of each minimal unit time is substituted by the smoothed rotational angular velocity. 
         [0112]    Further, the CPU  1000 , the system memory  1020 , the video display processor  1030  and the graphic memory  1040  cooperatively function as a display means for displaying the object CH according to the smoothed rotational angular velocity of each minimal unit time set by the smoothing means. 
       [Image Display Program] 
       [0113]    An image display program for executing the above image display algorithm on the image processing apparatus of  FIG. 1  is shown in  FIG. 28 . The image display program includes following steps. 
         [0114]    Step S 2701 : First, necessary parameters for changing the object CH to be displayed is set. In this embodiment, parameters are coordinate (X, Y, Z), rotational angle (a, β, γ), rotational angular velocity (ωx, ωy, ωz), posture parameters Pa to Pf and so forth. 
         [0115]    Step S 2702 : Following to the step S 2701 , the reference unit time T is set. 
         [0116]    Step S 2703 : Following to the step S 2702 , the coordinate (X, Y, Z), rotational angle (a, β, γ), rotational angular velocity (ωx, ωy, ωz), posture parameters Pa to Pf and so forth are allocated to each reference unit time T. 
         [0117]    Step S 2704 : Following to the step S 2703 , the number of division D and the minimal unit time t are set. 
         [0118]    Step S 2705 : Following to the step S 2703 , the parameters allocated to each reference unit time T are allocated to each minimal unit time t. 
         [0119]    Step S 2706 : According to the formulae (1) to (3), the rotational angular velocity (ωx, ωy, ωz) is smoothed. 
         [0120]    Step S 2707 : According to the formula (4), the posture parameters are composed in the transition time. 
         [0121]    The image of the object is displayed for each minimal unit time. Then, the processing is terminated. 
         [0122]    According to the above image display program, the rotational angle changes clearly and naturally as a whole because the change is clear from the macro point of view and the angular change is smoothed from micro point of view. And the dynamic posture change is natural. 
         [0123]    Since the calculation of step S 2706 , that is, the calculation of formulae (1) to (3), is extremely simple, the calculation load is light and can be processed by a hardware of rather low performance. 
         [0124]    Further, the calculation of the steps S 2704  to S 2706  may be recursively executed. So, when the division of the reference unit time by D at the first processing, the calculation by division of n-th power of D is easily executed for smaller minimal unit time. 
         [0125]    Further, the calculation of the steps S 2704  to S 2706  may be always applied as a parameter output routine because they output constant parameters as far as the parameters are not changed. The software construction is simple. 
       Second Embodiment 
       [0126]    Next, the second embodiment of an image display apparatus and image display program according to the present invention. 
         [0127]    In the second embodiment, in addition to the processing of the first embodiment, the posture parameters are independently smoothed from one another. 
       [Image Display Algorithm] 
       [0128]    As shown in  FIG. 12 , generally, each posture parameter changes so that a posture is changed one after another. Each posture parameter changes from 0% to 100% and returns to 0%. Therefore, by smoothing each posture parameter independently from the others, posture change during the transition time between 0% and 100% is smoothed and abrupt change is prevented. 
         [0129]    For example, formula (5) is applied to the smoothing of the posture parameter Pa for three minimal unit time. 
         [0000]        Pa ( ti )={ Pa ( ti− 1)+ Pa ( ti )+ Pa ( ti+ 1)}/3  formula (5) 
         [0130]    Here, 
         [0131]    Pa: Pa at the ith minimal unit time 
         [0132]    As an exception, in the case there is not ti−1 at the time ti=0 in  FIG. 12 , Pa(ti−1) is omitted. In the case there is not ti+1 at the time ti=3.000, Pa(ti+1) is omitted. 
         [0133]    The smoothing may be executed for shorter or longer time distance. 
         [0134]      FIG. 29  shows a table of posture parameters Pa to Pf of  FIG. 12  independently smoothed from the others, and  FIG. 30  is a graph corresponding to the table. 
         [0135]    As is apparent from  FIG. 30 , the posture parameters successively gently change. 
         [0136]    The second embodiment, since the smoothing processing for the rotational angular velocity may be commonly applied the smoothing processing for the posture parameter, the processing routine is simple and contributes for minimizing the hardware scale. 
       [Image Display Program] 
       [0137]    An image display program is shown in  FIG. 31 , for executing the above image display algorithm on the image display apparatus in  FIG. 1 . 
         [0138]    The image display program of the second embodiment includes steps S 3001  to S 3006  and step  3008  similar to the steps S 2701  to S 2706  and step S 2708  in the first embodiment. Only step S 3007  in the second embodiment is different from the step S 2707  in the first embodiment. The step S 3707  executes the processing below. 
         [0139]    That is, 
         [0140]    Step S 3007 : Each of the posture parameters is smoothed independently from the others. 
         [0141]    Therefore, each of the posture parameters changes moderately between 0% and 100% and natural change is realized. 
         [0142]    The above embodiment is described concerning an image display processing for displaying the character diving, however, the present invention may be naturally applied to any image display of characters which rotates and changes in its posture in a virtual space, such as characters performing snowboarding, free-ski, mogul, water-skiing, trampoline, skateboard, skydiving, gymnastics etc. 
       ADVANTAGES 
       [0143]    According to the present invention, clear and natural movement is easily displayed. For example clear and natural rotational movement can be expressed even by a hardware of rather small size.