Patent Publication Number: US-8979653-B2

Title: Computer readable storage medium having information processing program stored thereon and information processing apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The disclosure of Japanese Patent Application Nos. 2009-96502, filed on Apr. 10, 2009 and 2009-83032, filed on Mar. 30, 2009 is incorporated herein by reference. 
     FIELD 
     The present invention relates to a computer readable storage medium having an information processing program stored thereon for calculating a posture of an input device based on posture/motion information obtained from predetermined detection means for detecting a posture or a motion of the input device operated by a user, and an information processing apparatus for such an information processing program; and more specifically to a computer readable storage medium having an information processing program stored thereon for making a presentation for urging a predetermined setting to be made regarding the posture of the input device, and an information processing apparatus for such an information processing program. 
     BACKGROUND AND SUMMARY 
     Conventionally, as a system for allowing a user to virtually experience sports, a virtual sports system for executing processing for a tennis game by recognizing an actual swing of a tennis racket is disclosed (for example, Japanese Laid-Open Patent Publication No. 2003-180896). The racket used for this virtual sports system includes a three-axial acceleration sensor and a three-axial angular velocity sensor. The acceleration sensor is used for recognizing the initial position of the racket, and the angular velocity sensor is used for recognizing a posture change of the racket caused by a stroke. 
     However, the above-described game has the following problems. Sensors, such as the above-described acceleration sensor and angular velocity sensor, even having a very high level of precision, generate certain errors. For example, it is assumed that angular velocities obtained by the angular velocity sensor are accumulated and integrated to calculate a posture change. In this case, as the angular velocities are accumulated for a longer time, more errors are accumulated in the angular velocity sensor. This results in a large error. Namely, the actual posture change and the calculated posture change are often significantly different from each other. In general, such a problem caused by an influence of an error is often avoided by the player making an operation of resetting the initial position (initial posture) at which the angular velocities start being accumulated, when necessary. 
     However, the above-described resetting operation is performed when the player considers or determines necessary, regardless of whether the resetting is actually necessary or not. Therefore, the resetting operation may not be made at an appropriate timing as follows, for example: the resetting operation is not made although errors are accumulated to be of a large level and the resetting operation is necessary, or resetting operation is made although errors are not accumulated to be of a large level and the resetting operation is not necessary. 
     Therefore, an object of the present invention is to provide a computer readable storage medium having stored thereon an information processing program for executing posture control processing, which is capable of appropriately presenting the player with the timing to make a resetting operation on the basic posture, and an information processing apparatus for such an information processing program. 
     The present invention has the following features to attain the objects mentioned above. The reference numerals, additional descriptions and the like in parentheses in this section of the specification indicate an example of the correspondence with the embodiments described later for easier understanding of the present invention, and do not limit the present invention in any way. 
     A first aspect of the present invention is directed to a computer readable storage medium having stored thereon an information processing program to be executed by a computer of an information processing apparatus, the information processing program being for calculating a posture of an input device based on posture/motion information obtained from predetermined detection means for detecting a posture or a motion of the input device operated by a user. The information processing program causes the computer to function as posture/motion information obtaining means (S 2 ), reference posture calculation means (S 32 ), current posture calculation means (S 141 ), posture difference calculation means (S 142 , S 143 ), re-calculation necessity degree calculation means (S 136 ) and presentation means (S 138 ). The posture/motion information obtaining means obtains posture/motion information detected by the detection means. The reference posture calculation means calculates, at a predetermined timing, a posture of the input device at the timing as reference posture data based on the posture/motion information. The current posture calculation means repeatedly calculates a posture of the input device after the reference posture is calculated, as current posture data based on the posture/motion information. The posture difference calculation means repeatedly calculates a difference between the posture represented by the reference posture data and the posture represented by the current posture data as posture difference data based on the reference posture data and the current posture data. The re-calculation necessity degree calculation means repeatedly calculates, by accumulation, a re-calculation necessity degree, which represents a necessity degree of re-calculation of the reference posture, based on the posture/motion information obtained by the posture/motion information obtaining means and the posture difference data. The presentation means makes a presentation for urging re-calculation of the reference posture when the re-calculation necessity degree exceeds a predetermined value. 
     According to the first aspect, the presentation for urging the re-calculation of the reference posture can be made at an accurate timing. 
     In a second aspect based on the first aspect, the detection means is a motion sensor included in the input device. 
     According to the second aspect, the posture of the input device can be calculated more accurately. 
     In a third aspect based on the first aspect, the posture difference calculation means calculates the difference between a posture represented by the reference posture data and a posture represented by the current posture data as the posture difference data. 
     According to the third aspect, the necessity degree can be calculated using the posture difference. Therefore, the necessity degree can be calculated more accurately. 
     In a fourth aspect based on the first aspect, the re-calculation necessity degree calculation means calculates the re-calculation necessity degree to be larger as the posture difference calculated by the posture difference calculation means is larger. 
     In a fifth aspect based on the first aspect, the re-calculation necessity degree calculation means calculates the re-calculation necessity degree also based on a time period from when the reference posture data is calculated. 
     In a sixth aspect based on the first aspect, the re-calculation necessity degree calculation means calculates the re-calculation necessity degree to be larger as the motion of the input device represented by the posture/motion information has a smaller magnitude. 
     According to the fourth through sixth aspects, the presentation for urging the re-calculation of the reference posture can be made at a more accurate timing. 
     In a seventh aspect based on the first aspect, the re-calculation necessity degree calculation means calculates the re-calculation necessity degree also based on the current posture data. 
     According to the seventh aspect, the necessity degree can be calculated also in consideration of the state of the posture of the input device. Therefore, the presentation for urging the re-calculation of the reference posture can be made at a more accurate timing. 
     In an eighth aspect based on the first aspect, the re-calculation necessity degree calculation means calculates the re-calculation necessity degree to be larger as the posture represented by the current posture data is closer to a predetermined posture. 
     According to the eighth aspect, the presentation for urging the re-calculation of the reference posture can be made at a more accurate timing. 
     In a ninth aspect based on the first aspect, the information processing program causes the computer to further function as reset means (S 34 , S 134 ) for resetting the re-calculation necessity degree at a predetermined timing. 
     According to the ninth aspect, the presentation for urging the re-calculation of the reference posture can be prevented from being made unnecessarily. 
     In a tenth aspect based on the ninth aspect, the reset means resets the re-calculation necessity degree when the reference posture calculation means calculates the reference posture. 
     According to the tenth aspect, it is made possible to have the player make the re-calculation of the reference posture at an arbitrary timing. Therefore, the presentation for urging the re-calculation of the reference posture can be prevented from being made unnecessarily. 
     In an eleventh aspect based on the ninth aspect, the reset means resets the re-calculation necessity degree when the motion of the input device represented by the posture/motion information obtained by the posture/motion information obtaining means has a magnitude equal to or greater than a predetermined value. 
     According to the eleventh aspect, the presentation for urging the re-calculation of the reference posture is not made while the input device is moved at a velocity equal to or greater than a certain level. 
     In a twelfth aspect based on the ninth aspect, the reset means resets the re-calculation necessity degree when the posture represented by the current posture data is a predetermined posture. 
     According to the twelfth aspect, it is made possible to prevent the presentation for urging the re-calculation of the reference posture when the input device has a posture far from a desirable posture for making the re-calculation of the reference posture. 
     In a thirteenth aspect based on the first aspect, the information processing apparatus further includes display means. The presentation means outputs a display for urging the re-calculation to the display means. 
     In a fourteenth aspect based on the first aspect, the information processing apparatus further includes audio signal output means. The presentation means outputs an audio signal for urging the re-calculation to the audio signal output means. 
     According to the thirteenth and fourteenth aspects, it is made possible to have the player intuitively perceive the necessity of the re-calculation of the reference posture. 
     In a fifteenth aspect based on the second aspect, the motion sensor includes at least one of an acceleration sensor and an angular velocity sensor. The posture/motion information includes at least one of acceleration information output from the acceleration sensor and angular velocity information output from the angular velocity sensor. 
     According to the fifteenth aspect, the necessity degree can be calculated more accurately. 
     In a sixteenth aspect based on the first aspect, the information processing program causes the computer to further function as game processing means for executing predetermined game processing when a posture represented by the reference posture data and a posture represented by the current posture data obtain a predetermined relationship. 
     According to the sixteenth aspect, the presentation for urging the re-calculation of the reference posture can be made at an appropriately timing in a game using the reference posture. This improves the convenience for the player and decreases the possibility of the game processing result unintended by the player being calculated. 
     A seventeenth aspect of the present invention is directed to an information processing apparatus for calculating a posture of an input device based on posture/motion information obtained from predetermined detection means for detecting a posture or a motion of the input device operated by a user. The information processing apparatus comprises posture/motion information obtaining means ( 10 ), reference posture calculation means ( 10 ), current posture calculation means ( 10 ), posture difference calculation means ( 10 ), re-calculation necessity degree calculation means ( 10 ) and presentation means. The posture/motion information obtaining means obtains posture/motion information detected by the detection means. The reference posture calculation means calculates, at a predetermined timing, a posture of the input device at the timing as reference posture data based on the posture/motion information. The current posture calculation means repeatedly calculates a posture of the input device after the reference posture is calculated, as current posture data based on the posture/motion information. The posture difference calculation means repeatedly calculates a difference between the posture represented by the reference posture data and the posture represented by the current posture data as posture difference data based on the reference posture data and the current posture data. The re-calculation necessity degree calculation means repeatedly calculates, by accumulation, a re-calculation necessity degree, which represents a necessity degree of re-calculation of the reference posture, based on the posture/motion information obtained by the posture/motion information obtaining means and the posture difference data. The presentation means makes a presentation for urging re-calculation of the reference posture when the re-calculation necessity degree exceeds a predetermined value. 
     According to the seventeenth aspect, the same effect as provided by the first aspect can be provided. 
     According to the present invention, it is made possible to inform the player that a resetting operation on a basic posture should be made at an effective timing. 
     These and other objects, features, aspects and effects of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an external view of a game system  1 ; 
         FIG. 2  is a block diagram showing a structure of a game apparatus  3 ; 
         FIG. 3  is an isometric view showing an external structure of an input device  8 ; 
         FIG. 4  is an isometric view showing an external structure of a controller  5 ; 
         FIG. 5  is an isometric view showing an internal structure of the controller  5 ; 
         FIG. 6  is an isometric view showing an internal structure of the controller  5 ; 
         FIG. 7  is a block diagram showing a structure of the input device  8 ; 
         FIG. 8  shows an example of a game screen assumed in an embodiment of the present invention; 
         FIG. 9  shows a method of operation to be made by the player; 
         FIG. 10  shows an example of a game screen assumed in an embodiment of the present invention; 
         FIG. 11  provides schematic views showing the concept of a reference plane; 
         FIG. 12  shows an example of a game screen assumed in an embodiment of the present invention; 
         FIG. 13  is provided to explain a power gauge  104 ; 
         FIG. 14  is provided to explain the power gauge  104 ; 
         FIG. 15  is provided to explain the power gauge  104 ; 
         FIG. 16  is provided to explain the power gauge  104 ; 
         FIG. 17  is provided to explain the power gauge  104 ; 
         FIG. 18  shows an example of a game screen assumed in an embodiment of the present invention; 
         FIG. 19  is provided to explain the power gauge  104 ; 
         FIG. 20  is provided to explain a twisting angle; 
         FIG. 21  is provided to explain a backspin operation; 
         FIG. 22  is provided to explain the backspin operation; 
         FIG. 23  shows an example of the relationship among the input device  8 , the reference plane and two candidate planes; 
         FIG. 24  schematically shows an example of a bend of a club head; 
         FIG. 25  is a model of the club head made using a “spring” and a “damper”; 
         FIG. 26  is a schematic view showing the concept of a reference X angle; 
         FIG. 27  is a schematic view showing the concept of a current X angle; 
         FIG. 28  is an exemplary graph usable for converting the twisting angle into a curving degree of the power gauge; 
         FIG. 29  is provided to explain how to calculate a swing-up amount H; 
         FIG. 30  is an exemplary graph usable for converting an absolute value of a swing-up angle into the swing-up amount H; 
         FIG. 31  is provided to explain how to calculate a re-holding posture accuracy St; 
         FIG. 32  shows a memory map of an external memory  12  of the game apparatus  3 ; 
         FIG. 33  shows an example of a data structure of operation data  127  shown in  FIG. 32 ; 
         FIG. 34  shows an example of a data structure of game processing data  128  shown in  FIG. 32 ; 
         FIG. 35  is a flowchart showing game processing according to an embodiment of the present invention; 
         FIG. 36  is a flowchart showing the game processing according to the embodiment of the present invention; 
         FIG. 37  is a flowchart showing the game processing according to the embodiment of the present invention; 
         FIG. 38  is a flowchart showing the details of re-hold processing shown in step S 8  in  FIG. 36 ; 
         FIG. 39  is a flowchart showing the details of reference plane setting processing shown in step S 32  in  FIG. 38 ; 
         FIG. 40  is provided to explain an overview of processing in step S 47  in  FIG. 39 ; 
         FIG. 41  is a flowchart showing the details of swing-related processing shown in step S 16  in  FIG. 37 ; 
         FIG. 42  is a flowchart showing the details of power gauge updating processing shown in step S 52  in  FIG. 41 ; 
         FIG. 43  is a flowchart showing the details of twisting angle calculation processing shown in step S 61  in  FIG. 42 ; 
         FIG. 44  is a flowchart showing the details of swing-up angle calculation processing shown in step S 62  in  FIG. 42 ; 
         FIG. 45  is a flowchart showing the details of struck ball power calculation processing shown in step S 53  in  FIG. 41 ; 
         FIG. 46  is a flowchart showing the details of bending angle calculation processing shown in step S 54  in  FIG. 41 ; 
         FIG. 47  is a flowchart showing the details of impact-related processing shown in step S 17  in  FIG. 37 ; 
         FIG. 48  is a flowchart showing the details of shot-related processing shown in step S 115  in  FIG. 47 ; 
         FIG. 49  is a flowchart showing the details of re-hold guide processing shown in step S 18  in  FIG. 37 ; 
         FIG. 50  is a flowchart showing the details of Kr calculation processing shown in step S 134  in  FIG. 49 ; 
         FIG. 51  is a flowchart showing the details of Ks calculation processing shown in step S 135  in  FIG. 49 ; 
         FIG. 52  is a flowchart showing the details of ball moving processing shown in step S 4  in  FIG. 35 ; 
         FIG. 53  is a flowchart showing the details of backspin setting processing shown in step S 162  in  FIG. 52 ; 
         FIG. 54  shows an example of a change of the shape of the power gauge  104 ; 
         FIG. 55  provides exemplary graphs usable for converting the swing-up angle into the swing-up amount H; 
         FIG. 56  shows an exemplary graph usable for converting the twisting angle into the curving degree of the power gauge  104 ; and 
         FIG. 57  shows an exemplary graph usable for converting the twisting angle into the curving degree of the power gauge  104 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     (Overall Structure of the Game System) 
     With reference to  FIG. 1 , a game system  1  including a game apparatus, which is an example of a posture calculation device according to one embodiment of the present invention, will be described.  FIG. 1  is an external view of the game system  1 . Hereinafter, a game apparatus and a game program according to this embodiment will be described. In the following example, the game apparatus is of an installation type. As shown in  FIG. 1 , the game system  1  includes a television receiver  2  (hereinafter, referred to simply as the “TV”)  2 , a game apparatus  3 , an optical disc  4 , an input device  8 , and a marker section  6 . In the game system  1 , game processing is executed by the game apparatus  3  based on a game operation performed using the input device  8 . 
     In the game apparatus  3 , the optical disc  4 , which is an example of an information storage medium exchangeably usable for the game apparatus  3 , is detachably inserted. The optical disc  4  has stored thereon a game program to be executed by the game apparatus  3 . The game apparatus  3  has an insertion opening for inserting the optical disc  4  on a front surface thereof. The game apparatus  3  reads and executes the game program stored on the optical disc  4  inserted into the insertion opening, and thus performs the game processing. 
     The game apparatus  3  is connected to the TV  2 , which is an example of a display device, via a connection cord. The TV  2  displays a game image obtained as a result of the game processing executed by the game apparatus  3 . A marker section  6  is provided in the vicinity of a display screen of the TV  2  (above the display screen in  FIG. 1 ). The marker section  6  includes two markers  6 R and  6 L respectively at two ends thereof. Specifically, the marker  6 R (also the marker  6 L) includes one or more infrared LEDs, and outputs infrared light forward from the TV  2 . The marker section  6  is connected to the game apparatus  3 , and the game apparatus  3  can control each of the infrared LEDs of the marker section  6  to be lit up or out. 
     The input device  8  provides the game apparatus  3  with operation data representing the particulars of the operation made thereon. In this embodiment, the input device  8  includes a controller  5  and a gyrosensor unit  7 . As described later in detail, in the input device  8 , the gyrosensor unit  7  is detachably connected to the controller  5 . The controller  5  and the game apparatus  3  are connected with each other via wireless communication. In this embodiment, the controller  5  and the game apparatus  3  are wirelessly communicable to each other by, for example, the Bluetooth (registered trademark) technology. In other embodiments, the controller  5  and the game apparatus  3  may be connected with each other in a wired manner. 
     (Internal Structure of the Game Apparatus  3 ) 
     Next, with reference to  FIG. 2 , an internal structure of the game apparatus  3  will be described.  FIG. 2  is a block diagram showing a structure of the game apparatus  3 . The game apparatus  3  includes a CPU  10 , a system LSI  11 , an external main memory  12 , a ROM/RTC  13 , a disc drive  14 , an AV-IC  15 , and the like. 
     The CPU  10  performs the game processing by executing a game program stored on the optical disc  4 , and acts as a game processor. The CPU  10  is connected to the system LSI  11 . The system LSI  11  is connected to the CPU  10  and also to the external main memory  12 , the ROM/RTC  13 , the disc drive  14  and the AV-IC  15 . The system LSI  11  performs the processing of, for example, controlling data transfer between the elements connected thereto, generating images to be displayed, and obtaining data from external devices. An internal structure of the system LSI  11  will be described later. The external main memory  12 , which is of a volatile type, has stored thereon a program such as a game program read from the optical disc  4 , a game program read from a flash memory  17  or the like, or various other data. The external main memory  12  is used as a work area or a buffer area of the CPU  10 . The ROM/RTC  13  includes a ROM having a program for starting the game apparatus  3  incorporated thereon (so-called boot ROM) and a clock circuit for counting time (RTC: Real Time Clock). The disc drive  14  reads program data, texture data or the like from the optical disc  4  and writes the read data onto an internal main memory lie described later or the external main memory  12 . 
     The system LSI  11  includes an input/output processor (I/O processor)  11   a , a GPU (Graphics Processor Unit)  11   b , a DSP (Digital Signal Processor)  11   c , a VRAM  11   d , and the internal main memory  11   e . Although not shown, these elements  11   a  through  11   e  are connected with each other via an internal bus. 
     The GPU  11   b  is a part of drawing means and generates an image in accordance with a graphics command (a command to draw an image) from the CPU  10 . The VRAM  11   d  has stored thereon data necessary for the GPU  11   b  to execute the graphics command (polygon data, texture data or other data). The GPU  11   b  uses the data stored on the VRAM  11   d  to generate an image. 
     The DSP  11   c  acts as au audio processor and generates audio data using sound data or sound wave (sound tone) data stored on the internal main memory  11   e  or the external main memory  12 . 
     The image data and the audio data generated as described above are read by the AV-IC  15 . The AV-IC  15  outputs the read image data to the TV  2  via an AV connector  16 , and outputs the read audio data to a speaker  2   a  built in the TV  2 . Thus, the image is displayed on the TV  2  and also the sound is output from the speaker  2   a.    
     The input/output processor  11   a  transmits or receives data to or from the elements connected thereto, or downloads data from external devices. The input/output processor  11   a  is connected to the flash memory  17 , a wireless communication module  18 , a wireless controller module  19 , an expansion connector  20 , and a memory card connector  21 . The wireless communication module  18  is connected to an antenna  22 , and the wireless controller module  19  is connected to an antenna  23 . 
     The input/output processor  11   a  is connected to a network via the wireless communication module  18  and the antenna  22 , and thus can communicate with other game apparatuses or various servers also connected to the network. The input/output processor  11   a  periodically accesses the flash memory  17 , and detects whether or not there is data which needs to be transmitted to the network. When there is such data, the input/output processor  11   a  transmits such data to the network via the wireless communication module  18  and the antenna  22 . The input/output processor  11   a  also receives data transmitted from other game apparatuses or data downloaded from a download server via the network, the antenna  22  and the wireless communication module  18 , and stores the received data on the flash memory  17 . The CPU  10  executes the game program and thus reads the data stored on the flash memory  17  to be used for the game program. The flash memory  17  may have stored thereon data saved as a result of playing the game using the game apparatus  3  (data representing a result or a state in the middle of the game) as well as the data to be transmitted to, or data received from, the other game apparatuses or various servers. 
     The input/output processor  11   a  receives operation data which is transmitted from the controller  5  via the antenna  23  and the wireless controller module  19  and stores (temporarily stores) the operation data in a buffer area of the internal main memory  11   e  or the external main memory  12 . 
     The input/output processor  11   a  is connected to the expansion connector  20  and the memory card connector  21 . The expansion connector  20  is a connector for an interface such as USB, SCSI or the like. The expansion connector  20  may be connected to a medium such as an external storage medium or the like, may be connected to a peripheral device such as another controller or the like, or may be connected to a wired communication connector, to communicate with the network instead of the wireless communication module  18 . The memory card connector  21  is a connector for an external storage medium such as a memory card or the like. For example, the input/output processor  11   a  can access an external storage medium via the expansion connector  20  or the memory card connector  21  to store data on the external storage medium or read data from the external storage medium. 
     The game apparatus  3  has a power button  24 , a reset button  25 , and an eject button  26 . The power button  24  and the reset button  25  are connected to the system LSI  11 . When the power button  24  is turned on, the elements of the game apparatus  3  are provided with power via an AC adaptor (not shown). When the reset button  25  is pressed, the system LSI  11  restarts a starting program of the game apparatus  3 . The eject button  26  is connected to the disc drive  14 . When the eject button  26  is pressed, the optical disc  4  is dismounted from the disc drive  14 . 
     (Structure of the Input Device  8 ) 
     With reference to  FIG. 3  through  FIG. 6 , the input device  8  will be described.  FIG. 3  is an isometric view showing an external structure of the input device  8 .  FIG. 4  is an isometric view showing an external structure of the controller  5 .  FIG. 3  is an isometric view of the input device  8  seen from the top rear side thereof.  FIG. 4  is an isometric view of the controller  5  seen from the bottom front side thereof. 
     As shown in  FIG. 3  and  FIG. 4 , the controller  5  includes a housing  31  formed by, for example, plastic molding. The housing  31  has a generally parallelepiped shape extending in a longitudinal or front-rear direction (Z-axis direction shown in  FIG. 3 ). The overall size of the housing  31  is small enough to be held by one hand of an adult or even a child. A player can perform a game operation by, for example, pressing buttons provided in the controller  5  or moving the controller  5  itself to change the position or posture thereof. 
     The housing  31  has a plurality of operation buttons. As shown in  FIG. 3 , provided on a top surface of the housing  31  are a cross button  32   a , a first button  32   b , a second button  32   c , an A button  32   d , a minus button  32   e , a home button  32   f , a plus button  32   g , and a power button  32   h . In this specification, the top surface on which these buttons  32   a  through  32   h  are provided will be occasionally referred to as the “button surface”. As shown in  FIG. 4 , a recessed portion is formed on a bottom surface of the housing  31 , and a B button  32   i  is provided on a slope surface of the recessed portion. The operation buttons  32   a  through  32   i  are assigned various functions in accordance with the game program executed by the game apparatus  3 . The power button  32   h  is for remote-controlling the power of the main body of the game apparatus  3  to be on or off. The home button  32   f  and the power button  32   h  have a top surface thereof buried in the top surface of the housing  31 , so as not to be inadvertently pressed by the player. 
     On a rear surface of the housing  31 , a connector  33  is provided. The connector  33  is used for connecting the controller  5  with another device (for example, the gyrosensor unit  7  or another controller). On both sides of the connector  33  on the rear surface of the housing  31 , engagement holes  33   a  are provided for preventing such another device from easily coming off. 
     In a rear part of the top surface of the housing  31 , a plurality of LEDs (in  FIG. 3 , four LEDs)  34   a  through  34   d  are provided. The controller  5  is assigned a controller type (number) so as to be distinguishable from other main controllers. The LEDs  34   a  through  34   d  are used for, for example, informing the player of the controller type which is currently set to the controller  5  that he/she is using, or for informing the player of the remaining battery amount. Specifically, when the controller  5  is used for the game operation, one of the plurality of LEDs  34   a  through  34   d  corresponding to the controller type is lit up. 
     The controller  5  includes an imaging information calculation section  35  ( FIG. 6 ). As shown in  FIG. 4 , a light incident face  35   a  of the imaging information calculation section  35  is provided on a front surface of the housing  31 . The light incident face  35   a  is formed of a material which allows infrared light from the markers  6 R and  6 L to be at least transmitted therethrough. 
     On the top surface of the housing  31 , sound holes  31   a  are formed between the first button  32   b  and the home button  32   f  for releasing the sound outside from a speaker  49  ( FIG. 5 ) built in the controller  5 . 
     Now, with reference to  FIG. 5  and  FIG. 6 , an internal structure of the controller  5  will be described.  FIG. 5  and  FIG. 6  illustrate an internal structure of the controller  5 .  FIG. 5  is an isometric view illustrating a state where an upper casing (a part of the housing  31 ) of the controller  5  is removed.  FIG. 6  is an isometric view illustrating a state where a lower casing (a part of the housing  31 ) of the controller  5  is removed.  FIG. 6  shows a reverse side of a substrate  30  shown in  FIG. 5 . 
     As shown in  FIG. 5 , the substrate  30  is fixed inside the housing  31 . On a top main surface of the substrate  30 , the operation buttons  32   a  through  32   h , the LEDs  34   a  through  34   d , an acceleration sensor  37 , an antenna  45 , the speaker  49  and the like are provided. These elements are connected to a microcomputer  42  (see  FIG. 6 ) via lines (not shown) formed on the substrate  30  and the like. In this embodiment, the acceleration sensor  37  is provided off the center line of the controller  5  along an X-axis direction. This makes it easier to calculate the motion of the controller  5  when the controller  5  is rotated around the Z axis. The acceleration sensor  37  is also located forward with respect to the center of the controller  5  along the longitudinal direction thereof (Z-axis direction). The provision of a wireless module  44  ( FIG. 7 ) and the antenna  45  allows the controller  5  to function as a wireless controller. 
     As shown in  FIG. 6 , at a front edge of a bottom main surface of the substrate  30 , the imaging information calculation section  35  is provided. The imaging information calculation section  35  includes an infrared filter  38 , a lens  39 , an imaging element  40  and an image processing circuit  41  located in this order from the front surface of the controller  5 . These elements  38  through  41  are attached to the bottom main surface of the substrate  30 . 
     On the bottom main surface of the substrate  30 , the microcomputer  42  and a vibrator  48  are provided. The vibrator  48  may be, for example, a vibration motor or a solenoid, and is connected to the microcomputer  42  via lines provided on the substrate  30  and the like. The controller  5  is vibrated by an actuation of the vibrator  48  based on an instruction from the microcomputer  42 , and the vibration is conveyed to the hand of the player holding the controller  5 . Thus, a so-called vibration-responsive game is realized. In this embodiment, the vibrator  48  is located slightly forward with respect to the center of the housing  31 . Since the vibrator  48  is provided closer to a front end than the center of the controller  5 , the vibration of the vibrator  48  can vibrate the entire controller  5  more significantly. The connector  33  is attached at a rear edge of the main bottom surface of the substrate  30 . In addition to the elements shown in  FIG. 5  and  FIG. 6 , the controller  5  includes a quartz oscillator for generating a reference clock of the microcomputer  42 , an amplifier for outputting an audio signal to the speaker  49 , and the like. 
     The gyrosensor unit  7  includes gyrosensors (gyrosensors  55  and  56  shown in  FIG. 7 ) for sensing an angular velocity around three axes. The gyrosensor unit  7  is detachably attached on the connector  33  of the controller  5 . At a front end of the gyrosensor unit  7  (an end thereof in a positive Z-axis direction shown in  FIG. 3 ), a plug (a plug  53  shown in  FIG. 7 ) connectable to the connector  33  is provided. On both sides of the plug  53 , hooks (not shown) are provided. In the state where the gyrosensor unit  7  is attached to the controller  5 , the plug  53  is connected to the connector  33  and the hooks are engaged with the engagement holes  33   a  of the controller  5 . Thus, the controller  5  and the gyrosensor unit  7  are firmly secured to each other. The gyrosensor unit  7  also includes buttons  51  on side surfaces thereof (side surfaces perpendicular to the X-axis direction shown in  FIG. 3 ). The buttons  51  are structured so as to release the hooks from the engagement holes  33   a  when being pressed. By pulling the plug  53  from the connector  33  while pressing the buttons  51 , the gyrosensor unit  7  can be detached from the controller  5 . 
     At a rear end of the gyrosensor unit  7 , a connector having the same shape as that of the connector  33  is provided. Therefore, other devices attachable to the controller  5  (the connector  33  of the controller  5 ) can be attached to the connector of the gyrosensor unit  7 . In  FIG. 3 , a cover  52  is detachably attached to the connector of the gyrosensor unit  7 . 
     The shape of the controller  5  and the gyrosensor unit  7 , the shape, number and position of the operation buttons, the acceleration sensor and the vibrator, and the like shown in  FIG. 3  through  FIG. 6  are merely exemplary, and may be altered without departing from the scope of the present invention. In this embodiment, the imaging direction of the imaging means is the positive Z-axis direction, but the imaging direction may be any direction. Specifically, the position of the imaging information calculation section  35  (the light incident face  35   a  of the imaging information calculation section  35 ) in the controller  5  does not need to be on the front surface of the housing  31 , and may be on another surface as long as light can enter from the outside of the housing  31 . 
       FIG. 7  is a block diagram showing a structure of the input device  8  (the controller  5  and the gyrosensor unit  7 ). The controller  5  includes the operation section  32  (operation buttons  32   a  through  32   i ), the connector  33 , the imaging information calculation section  35 , a communication section  36 , and the acceleration sensor  37 . The controller  5  transmits operation data representing the particulars of the operation made thereon to the game apparatus  3  as operation data. 
     The operation section  32  includes the above-described operation buttons  32   a  through  32   i , and outputs operation button data representing an input state of each of the operation buttons  32   a  through  32   i  (whether or not each of the operation buttons  32   a  through  32   i  has been pressed) to the microcomputer  42  of the communication section  36 . 
     The imaging information calculation section  35  is a system for analyzing image data taken by the imaging means, distinguishing an area having a high brightness in the image data, and calculating the center of gravity, the size and the like of the area. The imaging information calculation section  35  has, for example, a maximum sampling cycle of about 200 frames/sec., and therefore can trace and analyze even a relatively fast motion of the controller  5 . 
     The imaging information calculation section  35  includes the infrared filter  38 , the lens  39 , the imaging element  40  and the image processing circuit  41 . The infrared filter  38  allows only infrared light to pass therethrough, among light incident on the front surface of the controller  5 . The lens  39  collects the infrared light which has been transmitted through the infrared filter  38  and causes the infrared light to be incident on the imaging element  40 . The imaging element  40  is a solid-state imaging device such as, for example, a CMOS sensor or a COD sensor. The imaging element  40  receives the infrared light collected by the lens  39  and outputs an image signal. The markers  6 R and  6 L of the marker section  6  located in the vicinity of the screen of the TV  2  each include an infrared LED for outputting infrared light forward from the TV  2 . The provision of the infrared filter  38  allows the imaging element  40  to receive only the infrared light transmitted through the infrared filter  38  to generate image data. Therefore, the image of each of the markers  6 R and  6 L can be taken more accurately. Hereinafter, an image taken by the imaging element  40  will be referred to as a “taken image”. The image data generated by the imaging element  40  is processed by the image processing circuit  41 . The image processing circuit  41  calculates the positions of imaging targets (the markers  6 R and  6 L) in the taken image. The image processing circuit  41  outputs a coordinate representing the calculated position to the microcomputer  42  of the communication section  36 . The data on the coordinate is transmitted by the microcomputer  42  to the game apparatus  3  as operation data. Hereinafter, this coordinate will be referred to as a “marker coordinate”. The marker coordinate changes in accordance with the direction (inclining angle) or the position of the controller  5  itself, and therefore the game apparatus  3  can calculate the direction or the position of the controller  5  using the marker coordinate. 
     In other embodiments, the controller  5  does not need to include the image processing circuit  41 , and a taken image itself may be transmitted from the controller  5  to the game apparatus  3 . In this case, the game apparatus  3  may include a circuit or program having substantially the same function as that of the image processing circuit  41  and calculate the marker coordinate. 
     The acceleration sensor  37  detects an acceleration (including a gravitational acceleration) of the controller  5 . Namely, the acceleration sensor  37  detects a force (including the force of gravity) applied to the controller  5 . The acceleration sensor  37  detects a value of the acceleration in a linear direction along a sensing axis (linear acceleration) among accelerations acting on a detection section of the acceleration sensor  37 . For example, in the case of a multi-axial (at least two-axial) acceleration sensor, an acceleration component along each axis is detected as an acceleration acting on the detection section of the acceleration sensor. For example, a three-axial or two-axial acceleration sensor may be of a type available from Analog Devices, Inc. or STMicroelectronics N.V. The acceleration sensor  37  is, for example, of an electrostatic capacitance type, but may be of any other system. 
     In this embodiment, the acceleration sensor  37  detects a linear acceleration in each of an up-down direction with respect to the controller  5  (Y-axis direction shown in  FIG. 3 ), a left-right direction with respect to the controller  5  (X-axis direction shown in  FIG. 3 ), and a front-rear direction with respect to the controller  5  (Z-axis direction shown in  FIG. 3 ). Since the acceleration sensor  37  detects an acceleration in the linear direction along each axis, the output from the acceleration sensor  37  represents a value of the linear acceleration along each of the three axes. Namely, the detected acceleration is represented as a three-dimensional vector (ax, ay, az) in an XYZ coordinate system (controller coordinate system) which is set with respect to the input device (controller  5 ). Hereinafter, a vector having, as components, acceleration values along the three axes detected by the acceleration sensor  37  will be referred to as the “acceleration vector”. 
     Data representing the acceleration detected by the acceleration sensor  37  (acceleration data) is output to the communication section  36 . Since the acceleration detected by the acceleration sensor  37  changes in accordance with the direction (inclining angle) or the motion of the controller  5  itself, the game apparatus  3  can calculate the direction or the motion of the controller  5  using the acceleration data. In this embodiment, the game apparatus  3  calculates the posture of the controller  5  based on the acceleration data. 
     Data (acceleration data) representing the acceleration detected by the acceleration sensor  37  (acceleration vector) is output to the communication section  36 . In this embodiment, the acceleration sensor  37  is used as a sensor for outputting data for determining the inclining angle of the controller  5 . 
     A computer such as a processor of the game apparatus  3  (for example, the CPU  10 ) or a processor of the controller  7  (for example, the microcomputer  42 ) executes processing based on an acceleration signal which is output from the acceleration sensor  37 , and as a result, can estimate or calculate (determine) further information on the controller  5 . A person of ordinary skill in the art would easily understand this from the description of this specification. For example, when the computer executes processing with a premise that the controller  5  including the acceleration sensor  37  is in a static state (i.e., when the computer executes processing with a premise that the acceleration detected by the acceleration sensor  37  includes only a gravitational acceleration), if the controller  5  is actually in a static state, it can be found based on the detected acceleration whether or not the posture of the controller  5  is inclined with respect to the direction of gravity, or how much the posture of the controller  5  is inclined with respect to the direction of gravity. Specifically, where the state in which a detection axis of the acceleration sensor  37  is directed vertically downward is a reference state, it can be found whether or not the controller  5  is inclined with respect to the reference state based on whether or not 1 G (gravitational acceleration) is applied to the controller  5 . Based on the magnitude of the gravitational acceleration, it can also be found how much the controller  5  is inclined with respect to the reference state. In the case of a multi-axial acceleration sensor  37 , it can be found more precisely how much the controller  5  is inclined with respect to the direction of gravity by processing a signal representing an acceleration along each axis. In this case, the processor may calculate the inclining angle of the controller  5  based on an output from the acceleration sensor  37 , or may calculate the inclining direction of the controller  5  without calculating the inclining angle. By using the acceleration sensor  37  in combination with a processor in this manner, the inclining angle or posture of the controller  5  can be determined. 
     By contrast, with a premise that the controller  5  is in a dynamic state (in the state where the controller  5  is being moved), the acceleration sensor  37  detects an acceleration in accordance with the motion of the controller  5  in addition to the gravitational acceleration. Therefore, the moving direction of the controller  5  can be found by removing a component of the gravitational acceleration from the detected acceleration using predetermined processing. Even with the premise that the controller  5  is in a dynamic state, the inclination of the controller  5  with respect to the direction of gravity can be found by removing a component of the acceleration in accordance with the motion of the acceleration sensor from the detected acceleration using predetermined processing. In other embodiments, the acceleration sensor  37  may include an incorporated processing device or any other type of dedicated device for executing predetermined processing on an acceleration signal detected by built-in acceleration detection means before the detected acceleration signal is output to the microcomputer  42 . In the case where the acceleration sensor  37  is used for, for example, detecting a static acceleration (for example, a gravitational acceleration), the incorporated or dedicated processing device may be of a type for converting the acceleration signal into an inclining angle (or any other preferable parameter). 
     The communication section  36  includes the microcomputer  42 , a memory  43 , the wireless module  44  and the antenna  45 . The microcomputer  42  controls the wireless module  44  for wirelessly transmitting the data obtained by the microcomputer  42  to the game apparatus  3  while using the memory  43  as a storage area during processing. The microcomputer  42  is connected to the connector  33 . Data transmitted from the gyrosensor unit  7  is input to the microcomputer  42  via the connector  33 . Hereinafter, the gyrosensor unit  7  will be described. 
     The gyrosensor unit  7  includes the plug  53 , a microcomputer  54 , the two-axial gyrosensor  55  and the mono-axial gyrosensor  56 . As described above, the gyrosensor unit  7  detects an angular velocity around three axes (in this embodiment, the X, Y and Z axes) and transmits data representing each detected angular velocity (angular velocity data) to the controller  5 . 
     The two-axial gyrosensor  55  detects an angular velocity (per unit time) around the X axis and an angular velocity around the Y axis (per unit time). The mono-axial gyrosensor  56  detects an angular velocity around the Z axis (per unit time). In this specification, with respect to the imaging direction of the controller  5  (the positive Z-axis direction), the rotation directions around the X, Y and Z axes will be referred to as the “roll direction”, the “pitch direction” and “yaw direction”, respectively. Namely, the two-axial gyrosensor  55  detects the angular velocity in the roll direction (rotation direction around the X axis) and the pitch direction (rotation direction around the Y axis), and the mono-axial gyrosensor  56  detects the angular velocity in the yaw direction (rotation direction around the Z axis). 
     In this embodiment, the two-axial gyrosensor  55  and the mono-axial gyrosensor  56  are used in order to detect the angular velocity around the three axes. In other embodiments, the number and combination of the gyrosensors to be used are not specifically limited as long as the angular velocity around the three axes can be detected. 
     In this embodiment, for the purpose of facilitating calculations in posture calculation processing described later, the three axes around which the gyrosensors  55  and  56  detect the angular velocity are set to match the three axes along which the acceleration sensor  37  detects the acceleration (X, Y and Z axes). In other embodiments, the three axes around which the gyrosensors  55  and  56  detect the angular velocity do not need to match the three axes along which the acceleration sensor  37  detects the acceleration. 
     Data representing the angular velocity detected by each of the gyrosensors  55  and  56  is output to the microcomputer  54 . Accordingly, data representing the angular velocity around the three axes, i.e., the X, Y and Z axes is input to the microcomputer  54 . The microcomputer  54  transmits the data representing the angular velocity around the three axes as the angular velocity data to the controller  5  via the plug  53 . The transmission from the microcomputer  54  to the controller  5  is performed at a predetermined cycle. Since game processing is generally performed at a cycle of 1/60 sec. (at a cycle of frame time), the transmission is preferably performed at a cycle of a time period equal to or shorter than 1/60 sec. 
     Now, the description of the controller  5  will be resumed. Data which is output from the operation section  32 , the imaging information calculation section  35 , and the acceleration sensor  37  to the microcomputer  42 , and data transmitted from the gyrosensor unit  7  to the microcomputer  42 , are temporarily stored on the memory  43 . Such data is transmitted to the game apparatus  3  as the operation data. Namely, at the transmission timing to the wireless controller module  19  of the game apparatus  3 , the microcomputer  42  outputs the operation data stored on the memory  43  to the wireless module  44 . The wireless module  44  modulates a carrier wave of a predetermined frequency with the operation data and radiates the resultant very weak radio signal from the antenna  45 , using, for example, the Bluetooth (registered trademark) technology. Namely, the operation data is modulated into a very weak radio signal by the wireless module  44  and transmitted from the controller  5 . The very weak radio signal is received by the wireless controller module  19  on the side of the game apparatus  3 . The received very weak radio signal is demodulated or decoded, and thus the game apparatus  3  can obtain the operation data. The CPU  10  of the game apparatus  3  executes the game processing based on the obtained operation data and the game program. The wireless communication from the communication section  36  to the wireless controller module  19  is performed at a predetermined cycle. Since game processing is generally performed at a cycle of 1/60 sec. (at a cycle of frame time), the wireless transmission is preferably performed at a cycle of a time period equal to or shorter than 1/60 sec. The communication section  36  of the controller  5  outputs each piece of the operation data to the wireless controller module  19  of the game apparatus  3  at a rate of, for example, once in 1/200 seconds. 
     By using the controller  5 , the player can perform an operation of inclining the controller  5  at an arbitrary inclining angle, in addition to a conventional general game operation of pressing the operation buttons. With the controller  5  described above, the player can also perform an operation of indicating an arbitrary position on the screen by the controller  5  and also an operation of moving the controller  5  itself. 
     Now, an overview of a game assumed in this embodiment will be described.  FIG. 8  shows an example of a game screen assumed in this embodiment. The game assumed in this embodiment is a golf game. As shown in  FIG. 8 , a golf course constructed in a three-dimensional virtual space is displayed as the game screen. The game screen displays a player object  101  holding a golf club  102 , a golf ball object  103  (hereinafter, referred to simply as the “ball”), a power gauge  104  and the like. In the power gauge  104 , a swing bar  106  is displayed. 
     Now, a method of operation to be made by the player in this game will be described. This game is played with the input device  8  being regarded as a golf club. For example, as shown in  FIG. 9 , the player holds the input device  8  with both hands, with the front surface of the input device  8  (the surface having the light incident face  35   a ) being directed downward. Then, the player makes a motion mimicking a golf swing. In association with this swing motion, the player object  101  in the virtual space also makes a swing motion. In accordance with this, the golf club  102  moves. Namely, the motion of the player swinging his/her arms is reflected as the swing motion of the player object  101 . 
     The above-described operation will be described more specifically. First, in an initial state before hitting the ball (before starting the swing), the player object is located slightly away from the ball  103  as shown in  FIG. 8 . By making a swing as described above in this state, the player can make a “practice swing”. For hitting the ball, the player presses the A button  32   d . Then, as shown in  FIG. 10 , the player object  101  moves forward to approach the ball  103 . By making the above-described swing motion while pressing the A button  32   d , the player can hit the ball  103  with the golf club  102  to cause the ball  103  to fly, namely, can make a shot. In this game, as described above, when the player holds the input device  8  and makes a swing motion without pressing the A button  32   d , he/she can make a practice swing. When the player makes a swing motion while pressing the A button  32   d , he/she can hit the ball  103  to cause the ball  103  to fly. Thus, the player can enjoy the golf game close to actual golfing. 
     In addition, in this game, the player can make a “re-hold” operation by pressing the B button  32   i  in the state of not pressing the A button  32   d . The “re-hold” operation is made to define the forward direction of the player in the actual world (the “re-hold” operation has a concept close to taking the posture of “address” in golf). Since the gyrosensor only senses a “change” in the posture, the forward direction is defined by having the player press the B button  32   i . Based on the forward direction defined by this operation, various types of processing for this golf game are executed. 
     More specifically, the following processing is executed. Based on the posture of the input device  8  which is taken when the B button  32   i  is pressed, a virtual plane which extends toward the forward direction of the player in the actual space is calculated, and this plane is set as the “reference plane”.  FIG. 11  provides schematic views showing the concept of the reference plane. As shown in  FIG. 11(   a ), the reference plane is a (virtual) plane which extends toward the forward direction of the player in the actual space. The reference plane also corresponds to a plane, as shown in  FIG. 11(   b ), which extends toward the forward direction of a position in the virtual space corresponding to the position of the player, namely, toward the forward direction of the player object  101 . By comparing the reference plane against the posture of the input device  8  during a swing, a parameter such as a swing angle (how much the player swings up the input device  8 ) or the like is calculated, and whether or not an impact has been generated (whether or not the golf club  102  has hit the ball  103 ) is determined, for example. More specifically, the swing angle (swing-up angle described later) is calculated with a premise that the position of the reference plane is 0°, the side to which the ball is to fly has a positive value angle, and the side to which the club is to be swung has a negative value angle. (In this embodiment, the swing angle is in the range of +180° to −180°.) For example, when the swing angle is changed from a negative value angle to a positive value angle, it is determined that the input device  8  has contacted, or has passed, the reference plane (an impact has been generated). 
     However, even if the forward direction (reference plane) is once determined, the relationship between the forward direction defined above and the posture of the input device  8  may become gradually inaccurate while the player swings the input device  8 . This occurs as a result of accumulation of measuring errors of the gyrosensor or calculation errors. In addition, the player himself/herself may change the direction in which he/she faces and in this case, the forward direction defined above is not the forward direction from the viewpoint of the player anymore. As a result, while swinging the input device  8 , the player in the actual world may lose the sense of the direction in which he/she is facing in the virtual game space (may lose the sense of whether or not he/she is facing forward in the virtual game space). When this problem occurs, although the player considers himself/herself as making a swing while facing forward, the game processing is executed as if he/she was making a swing while not facing forward. For this reason, it is necessary for the player to press the B button  32   i  periodically to reset the forward direction (reference plane). In addition, for example, in the case where the player swings up the input device  8  and keeps that state for a certain period of time without swinging down the input device  8 , the influence of the accumulation of calculation errors may possibly occur. Therefore, where the difference between the posture of the input device  8  obtained when the B button  32   i  is pressed (posture at the time of address) and the current posture of the input device  8  is large and further, no motion of the input device  8  is made for a certain period of time, it is preferable to reset the forward direction (reference plane). 
     In this embodiment, in order to avoid the calculation for finding the forward direction from becoming unstable due to the difference in the manner in which the input device  8  is held when the B button  32   i  is pressed, the forward direction (reference plane) is defined based on multiple points of view by executing the processing described later. 
     Also in this embodiment, the processing of estimating that it is necessary to reset the reference plane and displaying a message  105  as shown in  FIG. 12  to urge the player to make a “re-hold” operation at an appropriate timing (hereinafter, the message  105  will be referred to as the “re-hold guide”) is also executed. 
     Now, the power gauge  104  displayed on the game screen will be described. The power gauge  104  is displayed as having a shape of a bar, and provides two types of information, i.e., a swing-up amount of the golf club  12  (information which allows the player to roughly estimate the power of the struck ball) and a twisting degree of the wrists (rotation angle around the Z axis). The swing-up amount is indicated by the position of the swing bar  106  in the gauge  104 . The swing bar  106  goes up and down in accordance with the swing-up amount. For example, as shown in  FIG. 13 , when the player object  101  is in the state of a reference posture (address posture), the swing bar  106  is located at the bottom of the power gauge  104 . After this, until the golf club  102  impacts the ball  103 , the swing bar  106  goes up and down in real time in accordance with the swing-up amount. 
     Specifically, when the golf club  102  (in the real world, the input device  8 ) is swung up, as shown in  FIG. 14 , the swing bar  106  moves up. As the swing-up amount is larger, the swing bar  106  moves to a higher position. Then, when the golf club  102  is swung clown, the swing bar  106  moves down. At the time of impact, as shown in  FIG. 15 , the swing bar  106  is located at the bottom of the gauge  104 . At the time of impact, the power of the struck ball is determined. When the power of the struck all is determined (namely, when the impact is generated), the display of the swing bar  106  disappears. Instead, as shown in  FIG. 16 , a power bar  107  extends from the bottom of the gauge  104  by such a length that indicates the power of the struck ball. When the power bar  107  reaches the position corresponding to the power of the struck ball, the power bar  107  stops and does not extend any further. 
     As shown in  FIG. 18 , the twisting degree of the wrists (rotation angle around the Z axis) is represented by curving the power gauge  104 . For example, when the player twists his/her wrists rightward (clockwise), as shown in  FIG. 19(   a ), the power gauge  104  is curved rightward. When the player twists his/her wrists leftward (counterclockwise), as shown in  FIG. 19(   b ), the power gauge  104  is curved leftward. As the twisting degree is larger, the curving degree is larger. By contrast, as the twisting degree is smaller, the curving degree is smaller as shown in  FIG. 19(   c ). In this embodiment, as shown in  FIG. 20 , the maximum value of the twisting degree (rotation angle around the Z axis) is 35° rightward and leftward (−35° to +35°) with respect to the Y axis of the input device  8  (even when the twisting degree exceeds this range, such a degree is also treated as 35°). In this embodiment, the twisting degree is calculated with a premise that the angle at which the re-hold operation is made is 0°, the rightward twist has a positive value angle and the leftward twist has a negative value angle. 
     As described above, in this embodiment, two different elements of the swing-up amount and the twisting degree of the wrists are displayed by one power gauge  104 . 
     Now, among various types of processing in this embodiment, distinctive processing will be described. The distinctive processing in this embodiment is roughly classified into the following three.
     (1) Shot-related processing   (2) Power gauge-related processing   (3) Re-hold guide processing   

     The (1) shot-related processing is roughly classified into the following three.
     (1-1) Reference plane setting processing   (1-2) Swing-down motion reflection processing   (1-3) Backspin processing   

     First, the (1-1) reference plane setting processing calculates and sets the reference plane when the B button  32   i  is pressed as described above. The reference plane is calculated based on multiple points of view in order to avoid the calculation for finding the forward direction from becoming unstable due to the difference in the manner in which the controller  5  is held, as described above. 
     The (1-2) swing-down motion reflection processing calculates a shot power based on the height of the swing bar  106  when the club is swung up. Specifically, when the club is once swung up and then is swung down slowly, the shot power is calculated to be weak in accordance with the fall of the swing bar  106 . By contrast, when the club is once swung up and then is swung down with some vigor, a shot power corresponding to a position close to the height of the swing bar  106  when the club is swung up is calculated. When the club is once swung up and then is swung down more vigorously, the shot power is calculated to be stronger. Namely, the swing-down motion reflection processing causes the motion of swinging down the club during a swing to be reflected on the shot, in other words, reflects the manner of movement of the club when the club is swung down on the shot power. Specifically, when the club is once swung up and then is swung down slowly, the swing bar  106  goes down in accordance with the movement of the club. By contrast, when the club is once swung up and then is swung down vigorously, a shot can be made at substantially the same power as that when the club is swung up. 
     The (1-3) backspin processing will be described. In this embodiment, when the club is swung to impact the ball, a backspin can be applied to the ball  103  by stopping the golf club  102  at a position of the ball  103  as shown in  FIG. 22  (by applying a sudden brake at the position of the impact to stop the club  102 ), instead of swinging the club  102  all the way through as shown in  FIG. 21 . The (1-3) backspin processing detects that a sudden brake has been applied to the swing in the middle (a swing with a braking power) and causes the movement of the club at this point to be reflected on the struck ball as a backspin. 
     The (2) power gauge-related processing calculates the swing-up amount (swing angle) and the twisting degree of the wrists (rotation angle around the Z axis) described above and causes each of the swing-up amount and the twisting degree of the wrists to be reflected on the display of the power gauge  104 . 
     The (3) re-hold guide processing will be described. In this embodiment, it is necessary to perform a “re-hold” operation (to reset the reference plane) by pressing the B button  32   i  periodically as described above. The (3) re-hold guide processing estimates that it is necessary to reset the reference plane and displays the re-hold guide message  105  at an appropriate timing. 
     Now, an overview of each of the processing will be described. 
     (Overview of the Reference Plane Setting Processing) 
     First, an overview of the (1-1) reference plane setting processing of the (1) shot-related processing will be described. As described above, this processing defines the reference plane (forward direction) when the B button  32   i  is pressed. In this embodiment, in order to avoid the calculation result from becoming unstable due to the difference in the manner in which the player holds the input device  8  when pressing the B button  32   i , the following processing is executed. 
     First, a plane including the Z-axis direction and a gravity direction (in a local coordinate system of the input device  8 ) is calculated based on the current posture of the input device  8 . Hereinafter, this plane will be referred to as the “first candidate plane”. 
     Next, a rotation which directs the positive Z-axis direction toward the gravity direction is applied to the Y axis to calculate a Y′ axis. This means virtually redirecting the input device  8  vertically downward and finding the Y-axis direction in this state. Then, a plane including the Y′-axis direction and the gravity direction is calculated. Hereinafter, this plane will be referred to as the “second candidate plane”. 
     The reason why the Y axis is not used but the Y′ axis is calculated is as follows. In general, it is considered that when the player takes a posture of holding a golf club to be ready to swing, the input device  8  is more often at an inclining posture (posture of raising up the Z axis) than a posture of being directed vertically downward. Often, the Y-axis direction is deviated from the forward direction of the player as a result of the input device  8  being pulled by a rotation made to take this posture of raising up the Z axis. Therefore, it is considered that a better calculation result is provided for executing the golf game processing by using the Y′ axis obtained by assuming that the input device  8  is once directed vertically downward than using the Y axis. Hence, the Y axis may be used instead of the Y′ axis depending on the particulars of the game processing. 
     Based on the above-described two candidate planes and the reference plane already calculated at each point in time (i.e., the reference plane calculated immediately previously), a new reference plane is calculated. The new reference plane can be calculated by, for example, as follows. According to one method, the new reference plane is found by blending the two candidate planes. In this case, the two planes are blended after being weighted such that the candidate plane located closer to the current reference plane is relied on more heavily. 
     For example, it is assumed that the input device  8 , the reference plane and the two candidate planes have the relationship shown in  FIG. 23 .  FIG. 23  is a schematic view of the input device  8  as seen from the negative Z-axis direction. Where the angle made by the first candidate plane and the current reference plane is θA and the angle made by the second candidate plane and the current reference plane is θB, the new reference plane is calculated by, for example, the following expression.
 
Weight  a= 1−cos(θ B/ 2)
 
Weight  b= 1−cos(θ A/ 2)
 
Ratio  a =weight  a /(weight  a +weight  b )
 
Ratio  b =weight  b /(weight  a +weight  b )
 
New reference plane=ratio  a ×first candidate plane ratio  b ×second candidate  expression 1
 
     In the above expression, weight a is larger as the second candidate plane is more deviated from the current reference plane. Weight b is larger as the first candidate plane is more deviated from the current reference plane. 
     Ratio a and ratio b may be calculated by the following expression.
 
Weight  a= 1−cos(θ B/ 2)
 
Weight  b= 1−cos(θ A/ 2)
 
Ratio  a =(weight  a ) 2 /((weight  a ) 2 +(weight  b ) 2 )
 
Ratio  b =(weight  b ) 2 /((weight  a ) 2 +(weight  b ) 2 )
 
New reference plane=ratio  a ×first candidate plane+ratio  b ×second candidate plane  expression 1′
 
     Expressions 1 and 1′ shown above pay attention to the “closeness” between the current reference plane and each of the candidate planes. Alternatively, the new reference plane may be calculated by a technique paying attention to the angle made by each of the candidate planes and the gravity direction, as follows. The angle made by the Z-axis direction and the gravity direction, and the angle made by the Y-axis direction (or the Y′-axis direction) and the gravity direction, are calculated. As the calculated angles are larger, the ratios of the weighted averages (ratio a and ratio b) are made larger. 
     Still alternatively, the new reference plane may be calculated by selecting only the candidate plane which is closer to the current reference plane and blending the selected candidate plane and the current reference plane. Assuming that the candidate plane and the reference plane have the relationship shown in  FIG. 23 , the new reference plane is calculated by, for example, the following expression.
 
New reference plane=0.9×current reference plane+0.1×selected candidate plane  expression 2
 
     In expression 2, the ratios of the weighted averages are fixed (0.9 and 0.1). In this expression, the current reference plane is weighted more heavily, namely, is relied on more heavily. 
     The ratios of the weighted averages, although being fixed in expression 2, do not need to be fixed. For example, the ratios of the weighted averages in expression 2 may be made higher as the angle made by the axis used for calculating the “candidate plane closer to the current reference plane” (Z axis or the Y′ axis) and the gravity direction is larger. 
     Instead of using the “candidate plane closer to the current reference plane”, the angle made by the Z axis and the gravity direction and the angle made by the Y′ axis and the gravity direction may be calculated, and the plane corresponding to a larger angle may be selected. In other words, the new reference plane may be calculated by relying more heavily on the candidate plane calculated using the Y′ axis when the input device  8  is directed downward like a golf club which is held to be ready to swing; or by relying more heavily on the candidate plane calculated using the Z axis when the input device  8  is directed upward like a baseball bat which is held to be ready to swing. 
     The above-described blending methods are merely exemplary, and any other processing method is usable as long as each of the two candidate planes and the current reference plane can be appropriately blended together. 
     As a result of using any of the above-described calculation methods, the reference plane can be corrected as follows. Where the candidate planes calculated by a plurality of methods contradict each other, the reference plane can be corrected mildly in consideration of the reliability; whereas where the candidate planes match each other, the reference plane can be corrected boldly and significantly. By paying attention to the relationship of the candidate planes with the “gravity direction” and the “current reference plane”, the calculation result is avoided from becoming unstable due to the difference in the manner in which the player holds the input device  8 . Namely, the forward direction (reference plane) is avoided from being set to be a direction unintended by the player due to a slight unintentional movement of the input device  8  made while the input device  8  is held by the player. As a result, the processing is executed such that the position of the reference plane is corrected in accordance with the manner in which the player holds the input device  8 . 
     (Overview of the Swing-Down Motion Reflection Processing) 
     Now, an overview of the (1-2) swing-down motion reflection processing will be described. This processing causes the movement of the club when being swung down to be reflected on the power of the struck ball. For example, when the player swings up the club widely and swings down the club strongly, the power of the struck ball is calculated to be strong; whereas when the player swings the club weakly or slowly, the power of the struck ball is calculated to be weak accordingly. Specifically, it is assumed that the player swings up the controller  5  and as a result, the swing bar  106  goes up to the top of the power gauge  104  (a state where the power of the struck ball is expected to be 100%). When the player swings down the club quickly from this state, the power (the expected value of the power of the struck ball represented by the position of the swing bar  106 ) which is reflected on the power of the struck ball is almost 100%. By contrast, it is assumed that, where the swing bar  106  is at the top of the power gauge  104 , the player changes his/her mind (for example, considers that this is too strong) and lowers the input device  8  (golf club  102 ) slowly to a position corresponding to about 75% of the power gauge  104  (position which is about ¾ of the power gauge  104  from the bottom thereof) (in association with this movement, the swing bar  106  is lowered) to make a swing at this position. In this case, the power reflected on the power of the struck ball is not 100% as above but is about 75% in correspondence with the position of the club after the player changes his/her mind and lowers the club. In this manner, the swing-down motion reflection processing causes the particulars of the swing-down motion to be reflected on the power of the struck ball. 
     In this embodiment, the above-described processing is specifically executed as follows. First, a swing-up amount H corresponding to the swing bar  106  is calculated. How to calculate the swing-up amount H will be described later in the explanation of the “power gauge-related processing” and the like. Briefly, the amount by which the player swing up the input device  8  (swing angle) is calculated as the swing-up amount (namely, the position of the swing bar  106  in the power gauge  104 ). In addition, in this embodiment, a follow-up amount T (T is 0.0 to 1.0) which follows the swing-up amount (swing bar  106 ) is calculated. The follow-up amount T is found by the following expression. 
     When H&lt;T,
 
 T=T +follow-up coefficient  Kt ×( H−T )  expression 3
 
     When H≧T,
 
 T=H  
 
     The above expressions will be explained. “H&lt;T” refers to when a swing-down motion is made. “H≧T” mainly refers to when a swing-up motion is made. While the swing-up motion is being made, the follow-up amount T is the same as the swing-up amount H. The follow-up amount T follows the swing-up amount only while the swing-down motion is being made. The follow-up coefficient Kt is provided for decreasing the followability when the swing is strong (when the acceleration is large) and for increasing the followability when the swing is weak (when the acceleration is small). The follow-up coefficient Kt is obtained by converting the strength of the swing which is calculated in terms of the acceleration. Specifically, the follow-up coefficient Kt is found as follows. First, from the acceleration obtained by the acceleration sensor  37 , a gravity component (1.0 G) is removed. An absolute value of the result is set as the “magnitude of the acceleration”. In this embodiment, this absolute value is in the range of 0.0 G to 1.2 G. The magnitude of the acceleration in the range of 0.0 G to 1.2 G is converted (assigned) into a value in the range of 0.2 to 0.01, and the obtained value is set as the follow-up coefficient Kt (i.e., Kt=0.2 to 0.01). 
     This calculation provides the following results. As the player, after swinging up the input device  8 , swings down the input device  8  more rapidly or more strongly, the follow-up amount T can be maintained at a value closer to the maximum value of the past swing-up amounts (hereinafter, referred to as the “maximum swing-up amount”). As the player swings down the input device  8  more slowly or more weakly, the follow-up amount T is decreased in accordance with the swing-up amount H. 
     Expression 3 uses “(H−T)”. Therefore, as the difference between the swing-up amount H and the follow-up amount T is larger, the value of T decreases (follows) by a larger amount. 
     When H≧T, the swing-up amount H is the lower limit of the value of the follow-up amount T. This means that even while the swing-down motion is being made, the value of the follow-up amount T does not decrease to be lower than the value of the swing-up amount H. 
     For determining the power of the struck ball, to conventional golf games, the maximum swing-up amount is set as the swing power. In this embodiment, when the golf club  102  and the ball  103  make an impact, the final power of the struck ball (hereinafter, referred to as the “struck ball power P”) is determined. As the struck ball power P, the value of the follow-up amount T is used instead of the maximum swing-up amount or the swing-up amount H. Namely, the fallow-up amount T corresponding to a value obtained by correcting the swing-up amount H is used as the struck ball power P. Owing to this, the struck ball power can be made different between when the input device  8  is swung down strongly and when the input device  8  is swung down slowly. In this embodiment, the following processing is further executed to determine the final struck ball power P. 
     In this embodiment, in addition to the follow-up amount T, an element of “excessive swing strength S” is calculated (S is 0.0 to 1.0). This is performed in order to evaluate the “strength” of a down swing as, for example, a “strong down swing with a force” or a “light down swing with little force”, and cause the evaluation result to be reflected on the struck ball power P. Owing to the above-described calculation method of the follow-up amount T, especially the calculation of decreasing the follow-up coefficient Kt as the acceleration during the swing is larger, the struck ball power P is increased as the input device  8  is swung more strongly (as the acceleration is larger). However, the upper limit of the struck ball power P is equal to the maximum value of the swing-up amount H. Therefore, however strongly the input device  8  may be swung, the struck bail power P does not exceed the maximum value of the swing-up amount H. In order to solve this, it is considered to evaluate an acceleration during an excessively strong swing which does not influence the struck ball power P (the follow-up amount T) as the “excessive swing strength S” and superpose the “excessive swing strength S” on the struck ball power P. In this embodiment, the “excessive swing strength S” is evaluated by a series of swing motions as follows. The acceleration during a swing is virtually decreased, and it is observed how the struck ball power P calculated with such a decreased acceleration changes. For example, the follow-up amount T is re-calculated with an assumption that where the “swing-down strength” from the state of the swing-up amount H is 100%, the acceleration is only 20% (i.e., the acceleration is decreased by 80%). When the re-calculation is performed with the acceleration being estimated smaller in this manner, it is expected that the “swing-down strength” is finally calculated to be 60% to 80% with an influence of the element of the follow-up amount T and the like. In the case where, even though the swing-down strength is calculated with the acceleration being decreased by 80%, the resultant swing-down strength is merely different from the original swing-down strength by a small amount (the re-calculation result has a value of about 80%), namely, the resultant swing-down strength is not much different from the original swing-down strength, it can be evaluated that the value of the original acceleration is too large. By contrast, in the case where the resultant swing-down strength is much different from the original swing-down strength the re-calculation result has a value of about 60%), it can be evaluated that there is no waste in the acceleration. In other words, when the struck ball power P is decreased in accordance with the decrease in the acceleration, it is considered that the swing has no waste in the acceleration. When the struck ball power P is not much decreased even though the acceleration is decreased, it is considered that the original acceleration is too large, namely, the swing is excessive in terms of the acceleration. Hence, a difference between the original “swing-down strength” and the “swing-down strength” obtained by the re-calculation performed with the decreased acceleration is evaluated as the “excessive swing strength S”. 
     Specifically, the processing is executed as follows. First, assuming that the acceleration during the swing is merely 20% of the actual acceleration (the acceleration is decreased by 80%), the same calculation as that performed to find the follow-up amount T is made. The result is set as a decreased follow-up amount T′ (in this embodiment, T is 0.0 to 1.0). The follow-up amount T and the decreased follow-up amount T are compared with each other to find the difference. When the difference is small, it is considered that a swing with a relatively strong force (swing excessive in terms of the acceleration) is performed. When the difference is large, it is considered that the actually performed swing has an appropriate strength (in the game processing) (i.e., the actually performed swing is a swing with no waste in the acceleration). 
     A more specific calculation method will be described. In this embodiment, T′/T is first calculated. Among the calculation results, a value in the range of 0.6 to 0.8 is assigned to a value of the excessive swing strength S (0.0 to 1.0). Using the excessive swing strength S and the follow-up amount T, the final struck ball power P is calculated by the following expression.
 
 P=T +coefficient  Kz×S   expression 4
 
     The coefficient Kz represents the weight applied on S, which is 0.25 in this embodiment. Namely, the struck ball power P is determined by superposing 25% of the excessive swing strength S on the follow-up amount T (the value of the coefficient Kz is appropriately determined in consideration of the game balance or the like). 
     As described above, in this embodiment, by executing the processing of calculating the struck ball power P in consideration of the elements of the follow-up amount T and the excessive swing strength S, the particulars of the motion of swinging down the input device  8  can be reflected on the struck ball power P. For example, according to this processing, when the input device  8  is swung until the level of the swing bar  106  reaches 100% (the state where the swing bar  106  is at the top of the power gauge  104 ) and then swung down quickly, a struck ball power corresponding to almost 100% level of the swing bar  106  is obtained. When the input device  8  is swung down slowly, a struck ball power which is lower accordingly is obtained. 
     (Overview of the Backspin Processing) 
     Now, an overview of the (1-3) backspin processing will be described. As described above, a backspin can be applied to the struck ball by making a swing which stops the golf club in the middle instead of swinging the club all the way through. In this embodiment, in order to realize such a movement, a “bend” of the head of the golf club is used. More specifically, a model of the “bend” in which “the head is bent rearward by a swing, bent back when the swing is stopped, and in a certain case, bent forward by inertia” is used. 
     The bend of the club head during a swing in such a model will be discussed. When a swing is made normally, the golf club is swung up and starts being swung down. Until the club head hits the ball, the club head is bent rearward. When the swing is suddenly stopped as described above, namely, a braking power is applied, the club head is considered to be bent forward by inertia. In this embodiment, processing of finding the maximum value of the forward bend and causing the maximum value to be reflected on the backspin ratio is executed. Namely, after the swing (club) is stopped, how forward (in the direction in which the ball is to fly) the club head is bent by inertia is measured, and the backspin ratio (backspin strength) is set in accordance with the bending degree. 
       FIG. 24  schematically shows an example of the bend of the head. In  FIG. 24 , angle θ represents the swing-up angle described above. Angle θh (hereinafter, referred to as the “follow-up angle”) represents the angle of the bent head of the club. Thus, a bending angle φ can be calculated by the following expression (in  FIG. 24 , φ&lt;0).
 
φ=θ h−θ   expression 5
 
     A change of the bending angle φ into a forward bend (φ&gt;0) is monitored. The maximum value of the change to the forward bend is found and caused to be reflected on the backspin ratio. 
       FIG. 25  shows a model of the above-described bend provided using a “spring” and a “damper”. In the model shown in  FIG. 25 , the club head is connected to the main body of the club by the “spring” Kp and the “damper” Kd. In this embodiment, the bend of the club head is simulated using such a model. Specifically, an acceleration A of the head is calculated using the following expression.
 
 A=−Kp (θ h −θ)− Kd (θ hd−θd )  expression 6
 
     In expression 6, variable θhd represents a difference between θh in the immediately previous frame and θh in the current frame. Variable θd represents a difference between θ in the immediately previous frame and θ in the current frame. In “−Kp(θh−θ)” in expression 6, θh is the follow-up angle in the immediately previous frame, and θ is the current swing-up angle. 
     In this embodiment, variables Kp (spring) and Kd (damper) are updated in accordance with the absolute value of the swing-up angle θ. Namely, the bending characteristic is varied in accordance with the swing-up angle θ. This is performed in order to make the head likely to be bent in the vicinity of the impact and unlikely to be bent far from the impact. As a result, a backspin is likely to be applied when the club is stopped in the vicinity of the impact, and is unlikely to be applied when the club is swung all the way through. 
     Using the acceleration A, the velocity of the club head is calculated. Based on the velocity, the follow-up angle, i.e., the angle (position) θh of the head is calculated. Once the follow-up angle θh is calculated, the bending angle θ can be calculated using expression 5. 
     Then, processing of updating the backspin ratio K using the maximum value of the forward bending angle φ is executed. In this embodiment, processing of varying the degree, at which the bending angle φ is reflected on the backspin ratio, in accordance with the type of the club or the struck ball power is also executed. 
     Owing to such processing, when the club is stopped in the vicinity of the impact during a swing, a backspin can be applied. In addition, when the swing is vigorous before the club is stopped, a stronger backspin can be applied (because the club head is bent forward by inertia). 
     (Overview of the Power Gauge-Related Processing) 
     Now, an overview of the (2) power gauge-related processing will be described. In this embodiment, as described above, the twisting degree of the wrists (rotation around the Z axis) and the swing-up amount H are calculated. The swing-up amount H is displayed as the swing bar  106 , and the twisting degree is displayed by curving the power gauge  104  itself. Thus, two different elements are displayed with one power gauge. 
     In this embodiment, the twisting degree is specifically calculated as follows. As described above, at the time of the re-hold operation, the reference plane is calculated. At this point, an angle of the X axis of the input device  8  with respect to the reference plane is calculated and stored (hereinafter, this angle will be referred to as the “reference X angle”).  FIG. 26  is a schematic view showing the concept of the reference X angle.  FIG. 26  shows the input device  8  directed vertically downward, which is seen from the negative Z-axis direction. In  FIG. 26 , the angle of the X-axis direction of the input device  8  with respect to the reference plane is 90°. 
     Next, during the swing (processing in each frame after the reference plane is set), a reference plane is virtually calculated using the same technique as that used for calculating the reference plane, based on the posture of the input device  8  at each point in time (hereinafter, this plane will be referred to as the “virtual reference plane”). An angle of the X-axis direction of the input device  8  with respect to the virtual reference plane is calculated. For example, it is assumed that the input device  8  is slightly inclined rightward with the Z axis being directed vertically downward, and that the virtual reference plane including the Z axis and the gravity direction and the angle of the X-axis direction with respect to the virtual reference plane at this point are as shown in  FIG. 27  (hereinafter, this angle will be referred to as the “current X angle”). It is assumed that the current X angle is, for example, 100°. A difference between reference X angle and the current X angle is calculated, and this difference is set as the twisting angle. In the above example, the twisting angle is 100°−90°−10°. Based on the twisting angle thus calculated, the power gauge  104  is displayed as being curved in real time during the swing motion (until the shot is made). For example, the curving degree of the power gauge  104  is defined at a value in the range of −1.0 to 1.0 (a negative value indicates that the power gauge  104  is curved leftward and a positive value indicates that the power gauge  104  is curved rightward). Then, as shown in  FIG. 28 , the value of the twisting degree is assigned to a value in this range in accordance with the line graph. Thus, the curving degree of the power gauge  104  is calculated. Based on the curving degree, the power gauge  104  is curved. 
     It is conceivable that the twisting degree is calculated using only the angular velocity of the Z axis. However, the actual swing motion is not performed by only the rotation around the Z axis, but is performed by a combination of the rotation around the Z axis, the rotation around the X axis and the rotation around the Y axis. Therefore, even if the “accumulated value of the angular velocity of the Z axis” is zero, it may not be determined that there is no twisting of the wrists. For this reason, in this embodiment, the twisting degree is calculated using the plane based on the posture of the input device  8 . 
     The swing-up amount H is obtained by calculating the angle, at which the golf club  102  (input device  8 ) is swung up, with respect to the reference posture, namely, how much the Z axis of the input device  8  is raised from the ground. This swing-up angle is converted into the swing-up amount H and is caused to be reflected on the position of the swing bar  106 . In the case of a golf swing, the input device  8  is considered to be at the reference posture when the positive Z-axis direction is directed vertically downward. By finding the inclination of the Z axis with respect to this state, the swing-up angle can be found. 
     More specifically, in this embodiment, the swing-up amount H is calculated as follows. First, based on the reference plane, a coordinate system {L} shown in  FIG. 29  is set, in which an upper gravity direction is the Y direction and a vertical direction with respect to the reference plane is the X direction. Hereinafter, this coordinate system will be referred to as the “{L} coordinate system”. 
     Next, a vector D is calculated by converting the positive Z-axis direction in the local coordinate system of the input device  8  during the swing into a direction in the {L} coordinate system. 
     Based on three axial components of the vector D (Dx, Dy, Dz), the swing-up angle θ is calculated using the following expression.
 
θ− A  tan( Dx, −Dy+K×Dz )  expression 7
 
     In the above expression, variable K&gt;0. The element of Dz is added in consideration of the case where the input device  8  is swung horizontally (like in baseball). Namely, the calculation result of the angle is avoided from becoming unstable when Dx and Dy both approach zero (a state where the input device  8  is held horizontally). In the case where Dz is on the positive side, the same effect as that obtained when the input device  8  is directed more downward than actual is provided. In the case where Dz is on the negative side, the same effect as that obtained when the input device  8  is directed more upward than actual is provided. In other words, even when the input device  8  is swung horizontally (even when the input device  8  is swung like in baseball), an effect as that obtained when the input device  8  is swung vertically (golf swing) is provided to a certain degree. 
     As a result of using the above expression, when the input device  8  takes the posture of the re-hold operation (the posture at which the B button  32   i  is pressed), θ=0. When the input device  8  is swung forward (in the direction in which the ball is to fly), θ is calculated to have a positive value. When the input device  8  is swung up, θ is calculated to have a negative value. The swing-up angle θ thus obtained is converted into the swing-up amount H. For example, the swing-up angle θ is set to be in a range of −180° to +180°, and the swing-up amount H is set to be in a range of 0.0 to 1.0. In accordance with the line graph shown in  FIG. 30 , the absolute value of the swing-up angle θ is converted into the swing-up amount H. By moving the swing bar  106  up and down in accordance with the swing-up amount H, the swing-up amount is displayed. In this embodiment, when the swing-up amount H is 0.0, the swing bar  106  is at the bottom of the power gauge  104 ; whereas when the swing-up amount H is 1.0, the swing bar  106  is at the top of the power gauge  104 . 
     As described above, in this embodiment, the twisting degree is represented by the curving of the power gauge  104 , and the swing bar  106  is moved up and down in the power gauge  104 . Thus, for example, the power gauge  104  is displayed as shown in  FIG. 18 . Two elements of the swing-up amount (providing an estimate on the struck ball power) and the twisting degree of the wrists (opening degree of the face) are displayed together. This makes it possible to allow the player to intuitively perceive the influence on the golf ball at the time of shot. 
     (Overview of the Re-Hold Guide Processing) 
     Now, an overview of the (3) re-hold guide processing will be described. As described above, in this embodiment, the re-hold guide  105  shown in  FIG. 12  is displayed at an appropriate timing for urging the player to make a “re-hold” operation by pressing the B button  32   i . The re-hold guide  105  is displayed as follows. Basically, at the timing when the B button  32   i  is pressed, an internal counter starts counting up (hereinafter, referred to as the “guide display counter”). The guide display counter counts up frame by frame, and when the value of the guide display counter reaches a predetermined value or greater, the re-hold guide  105  is displayed. In this embodiment, in order to determine the “appropriate timing”, the “necessity degree of re-hold” (hereinafter, referred to as the “necessity degree Kr”) and the “possibility that the holding posture is taken” (hereinafter, referred to as the “holding posture possibility Ks”) are calculated and caused to be reflected on the count-up described above. Moreover, the guide display counter is reset at a predetermined timing in order to make the “appropriate timing” more accurate. Specifically, the guide display counter is reset at the following timings. 
     (1) When the B button  32   i  is pressed. 
     (2) When the posture of the input device  8  is significantly different from the posture expected at the time of “re-hold” (address posture). For example, when the positive Z-axis direction of the input device  8  is directed above the horizontal direction while the positive Y-axis direction is directed below the horizontal direction (like the posture of a baseball batter). 
     (3) During a swing. Whether or not a swing is being made is determined based on whether or not the absolute value of the angular velocity or the acceleration is greater than a predetermined value; specifically, whether or not the absolute value of the angular velocity is larger than 30 deg/sec., and whether or not the absolute value of the acceleration is larger than 0.2 G. 
     Now, methods for calculating the necessity degree Kr and the holding posture possibility Ks will be described. The necessity degree Kr is the degree at which the re-hold operation is considered to be necessary. The holding posture possibility Ks is the possibility at which the player is in a state of holding. Herein, the “state of holding” is a state where the front surface of the input device  8  is directed downward to a certain degree (state closer to the address state). Namely, a state where the golf club is swung up is excluded. 
     In this embodiment, the necessity degree Kr is calculated as follows. First, assuming that “the B button is pressed at this instance”, a temporary reference plane is created. An absolute value of the angle between the temporary reference plane and the current reference plane is calculated. (The angle made by these two planes means the angle made by surface normals of the two planes.) When this angle is 0°, it is determined that the re-hold operation is not necessary; whereas when this angle is 11° or greater, it is determined that the re-hold operation is necessary. 
     The necessity degree Kr is set to be in the range of 0.0 to 1.0. A value of 0.0 means that the re-hold operation is not necessary, whereas a value of 1.0 means that the re-hold operation is highly necessary. Namely, when the angle is 0°, Kr=0.0; whereas when the angle is 11°, Kr=1.0. A value of Kr between 0° to 11° is calculated by linear interpolation. 
     Now, the holding posture possibility Ks is calculated using the elements of an angular velocity stable state Sw, an acceleration stable state Sa (i.e., a state where no active motion is generated), and a re-holding posture accuracy St. The angular velocity stable state Sw is calculated as follows. When it is considered that a swing is not being made based on the angular velocity, namely, when the absolute value of the angular velocity is 30 deg/sec. or less, the absolute value of such an angular velocity is converted into a value in the range of 0.0 to 1.0. The obtained value is set to be Sw. The acceleration stable state Sa is calculated in substantially the same manner. When it is considered that a swing is not being made based on the acceleration, the absolute value of such an acceleration in the range of 0 G to 0.2 G is assigned to a value in the range of 0.0 to 1.0. The obtained value is set to be Sa. 
     The element of the re-holding posture accuracy St represents the degree at which the input device  8  is lowered. This is represented by the closeness of the X axis of the input device  8  to a horizontal state.  FIG. 31  shows the concept of the re-holding posture accuracy St. As shown in  FIG. 31(   a ), in a state where the front surface of the input device  8  is directed downward, the X axis in the local coordinate system of the input device is in the horizontal state (see  FIG. 31(   d )). This state is set as an ideal re-holding posture. By checking whether or not the X axis of the input device  8  of the posture calculated at each point in time is horizontal (see  FIGS. 31(   b ) and ( c )), the re-holding posture accuracy St can be calculated. More specifically, an absolute value of the gravity direction component of the X axis is calculated and indicated by a value in the range of 0.0 to 1.0. The obtained value is the re-holding posture accuracy St. 
     Using the above-described elements, the holding posture possibility Ks is calculated by the following expression.
 
 Ks=Sw×Sa×St   expression 8
 
     Once the necessity degree Kr and the holding posture possibility Ks are calculated as described above, count-up is performed by the guide display counter C based on Kr and Ks using the following expression.
 
 C=C+Kr×Ks   expression 9
 
     When the value of the guide display counter C exceeds  30 , the above-described processing of displaying the re-hold guide  105  shown in  FIG. 12  is executed. Owing to this, the re-hold guide  105  is displayed after measuring the timing at which the “re-hold” is necessary and effective. Thus, the re-hold operation by the player is expected to be performed at a more appropriate timing. 
     Now, game processing executed by the main body of the game apparatus  3  will be described in detail. First, data to be stored on the external main memory  12  for executing the game processing will be described.  FIG. 32  shows a memory map of the external main memory  12  of the game apparatus  3 . As shown in  FIG. 32 , the external main memory  12  includes a program storage area  121  and a data storage area  126 . Data stored in the optical disc  4  is transferred to, and stored in, the program storage area  121  and the data storage area  126  of the external main memory  12  for executing the game program. 
     The program storage area  121  stores the game program to be executed by the CPU  10 . The game program includes a main processing program  122 , a swing-related processing program  123 , an impact-related processing program  124 , a ball moving processing program  125 , and the like. The main processing program  122  corresponds to the processing in a flowchart in  FIG. 35  through  FIG. 37  described later. The swing-related processing program  123  causes the CPU  10  to execute various types of processing relating to the swing motion made by the player. The impact-related processing program  124  causes the CPU  10  to execute, for example, processing for determining whether or not an impact has been generated. The ball moving processing program  125  causes the CPU  10  to execute processing for moving the struck ball. 
     The data storage area  126  stores data such as operation data  127 , game processing data  128  and the like, as well as various flags and variables temporarily used during the game processing. 
     The operation data  127  is sent from the controller  5  to the game apparatus  3 . As described above, the operation data is sent from the controller  5  to the game apparatus  3  at a rate of once in 1/200 seconds. Therefore, the operation data  127  stored on the external main memory  12  is updated at this rate. In this embodiment, the external main memory  12  only needs to store the latest operation data (data obtained at the most recent time). 
     As shown in  FIG. 33 , the operation data  127  includes angular velocity data  131 , acceleration data  132 , marker coordinate data  133 , and operation button data  134 . The angular velocity data  131  represents an angular velocity detected by the gyrosensors  55  and  56  of the gyrosensor unit  7 . Herein, the angular velocity data  131  represents an angular velocity around each of the three axes of X, Y and Z shown in  FIG. 3 . The acceleration data  132  represents an acceleration (acceleration vector) detected by the acceleration sensor  37 . Herein, the acceleration data  132  represents a three-dimensional acceleration vector having, as a component, an acceleration in each of the three axes of X, Y and Z shown in  FIG. 3 . In this embodiment, the magnitude of the acceleration vector which is detected by the acceleration sensor  37  in the state where the controller  5  is still is “1”. Namely, the magnitude of the gravitational acceleration which is detected by the acceleration sensor  37  is “1”. 
     The marker coordinate data  133  represents a coordinate calculated by the image processing circuit  41  of the imaging information calculation section  35 , namely, the above-described marker coordinate. The marker coordinate is represented by a two-dimensional coordinate system which indicates a position on a plane corresponding to the taken image. In the case where the imaging element  40  takes an image of two markers  6 R and  6 L, two marker coordinates are calculated. By contrast, in the case where only one of the markers  6 R and  6 L is present in the range which can be imaged by the imaging element  40 , an image of only one marker is taken by the imaging element  40  and thus only one marker coordinate is calculated. In the case where neither the marker  6 R nor  6 L is present in the range which can be imaged by the imaging element  40 , no image of the marker is taken by the imaging element  40  and thus no marker coordinate is calculated. Therefore, the marker coordinate data  133  may represent two marker coordinates, one marker coordinate or absence of marker coordinate. 
     The operation button data  134  represents an input state of each of the operation buttons  32   a  through  32   i.    
     As shown in  FIG. 34 , the game processing data  128  includes input device posture data  141 , reference plane data  142 , reference X angle data  143 , virtual reference plane data  144 , current X angle data  145 , twisting angle data  146 , swing-up amount data  147 , {L} coordinate system data  148 , vector D data  149 , first candidate plane data  150 , second candidate plane data  151 , immediately previous swing-up angle data  152 , immediately previous follow-up angle data  153 , immediately previous bending angle data  154 , a guide display counter  155 , struck ball power data  156 , backspin ratio data  157 , struck ball parameters  158 , current state data  159 , image data  160 , a shot flag  161 , an in-flight flag  162 , a backspin flag  163 , a termination flag  164  and the like. 
     The input device posture data  141  represents a posture of the input device  8 . In this embodiment, the posture of the input device  8  is represented by a set of three vectors perpendicular to one another (i.e., X axis, Y axis, and Z axis). In this embodiment, when the power is turned on or the game processing is started, the posture of the input device  8  in a world coordinate system (i.e., posture as seen in the local coordinate system of the input device  8 ) is set as X axis=(1,0,0), Y axis=(0,1,0) and Z axis=(0,0,1) as an initial value. After the game processing is started, the posture represented by the input device posture data  141  is calculated as a posture with respect to the world coordinate system based on the value obtained from the gyrosensor unit  7 . 
     The reference plane data  142  and the reference X angle data  143  respectively represent the reference plane and the reference X angle described above. In this embodiment, data representing various planes is stored as angle data of a rotation around the gravity direction as the axis. Since the various planes include (are parallel to) the gravity direction, the angle data is stored in order to define the respective planes. In addition, although being redundant, one axis of horizontal vector (vertical to the gravity direction) included in the plane may be stored as the data. Such data is easy to use in the processing described later. Alternatively, three-axis vector data, including the one axis of horizontal vector as well as one axis of vector in the upward gravity direction and one axis of vector in the direction of normal to the plane, may be stored. 
     The virtual reference plane data  144  and the current X angle data  145  respectively represent the virtual reference plane and the current X angle used for, for example, calculating the twisting angle described above. The twisting angle data  146  represents the calculated twisting angle. 
     The swing-up amount data  141  corresponds to the swing-up amount H described above. The coordinate system data  148  represents the {L} coordinate system (see  FIG. 29 ) described above. The vector D data  149  represents the vector D shown in  FIG. 29 . 
     The first candidate plane data  150  and the second candidate plane data  151  respectively represent the first candidate plane and the second candidate plane used for calculating the reference plane described above. 
     The immediately previous swing-up angle data  152 , the immediately previous follow-up angle data  153 , and the immediately previous bending angle data  154  are used for, for example, determining whether or not an impact has been generated. Such data represents a value of the swing-up angle or the respective element calculated in the immediately previous loop. 
     The guide display counter  155  is provided for measuring a timing for displaying the re-hold guide  105  shown in  FIG. 12 . 
     The struck ball power data  156  represents the power of the struck ball (data corresponding to the struck bail power P described above). The backspin ratio data  157  represents the backspin ratio described above. The struck ball parameters  158  are various parameters used for moving the struck ball, which include an orbit (trajectory) on which the struck ball moves, the moving velocity and the like. 
     The current state data  159  includes data regarding the environments around the player object in the virtual game space, such as the type of the golf club currently selected, the current location (e.g., fairway or rough), the direction and strength of the wind, and the like. 
     The image data  160  includes data on various types of images to be displayed as game images. The image of the re-hold guide  105  is included in the image data  160 . 
     The shot flag  161  is used to determine whether or not the A button  32   d  is pressed at the time of the swing, namely, whether or not the swing made by the player is a practice swing. When the A button  32   d  is pressed, the shot flag  161  is set to be on. 
     The in-flight flag  162  is used to determine whether the current state is before or after an impact is generated (before or after the ball is hit). The in-flight flag  162  is set to be off before the impact is generated, and is set to be on after the impact is generated. 
     The backspin flag  163  indicates whether or not it is necessary to execute the processing of calculating the backspin ratio. The backspin flag  163  is set to be on at the time when an impact is generated, and is set to be off when the calculation of the backspin ratio is finished (because, in this embodiment, the processing of calculating the backspin ratio is executed after an impact is generated and before the struck ball makes a landing). 
     The termination flag  164  indicates whether or not the processing corresponding to one shot has been terminated. 
     Now, with reference to  FIG. 35  through  FIG. 53 , the game processing executed by the game apparatus  3  will be described. When the power of the game apparatus  3  is turned on, the CPU  10  of the game apparatus  3  executes a starting program stored on the ROM/RTC  13  to initialize various units including the external main memory  12 . The game program stored on the optical disc  4  is read onto the external main memory  12 , and the CPU  10  starts the execution of the game program. The flowchart in  FIG. 35  through  FIG. 37  shows the game processing corresponding to one shot in the golf game. For the motion of each shot made by the player, the processing shown in the flowchart in  FIG. 35  through  FIG. 37  is executed. The processing loop of steps S 1  through S 21  shown in  FIG. 35  through  FIG. 37  is performed repeatedly for each frame. 
     As shown in  FIG. 35 , the CPU  10  first executes initialization processing (step S 1 ). This processing initializes various flags and variables. 
     Next, the CPU  10  obtains the operation data  127  (step S 2 ). Then, the CPU  10  determines whether the in-flight flag  162  is on or not (step S 3 ). The in-flight flag  162  indicates whether the current state is before or after the impact. When it is determined that the in-flight flag  162  is on, namely, when the current state is after the impact (YES in step S 3 ), the CPU  10  advances to step S 4 . The processing after this will be described later. 
     By contrast, when the in-flight flag  162  is off (NO in step S 3 ), the current state is before the club impacts the ball  103 . Therefore, the CPU  10  executes environment setting processing (step S 5  in  FIG. 36 ). This processing sets shot-related environments. For example, it is determined whether the current position of the player object  101  is in the fairway/rough or in the bunker; and the upper limit of the struck ball power is set, or the outgoing direction of the ball is changed in accordance with the topography or the like. Data representing the particulars set by this processing is stored on the external main memory  12  as the current state data  159 . This processing is not directly related to the essence of the present invention and will not be described in detail. 
     Next, the CPU  10  determines whether or not the operation particular represented by the operation data  127  obtained in step S 2  is regarding an operation other than the swing operation (step S 6 ). An operation other than the swing operation is an operation not related to the essence of the present invention, for example, an operation of selecting the golf club or an operation of changing the direction of the shot (changing the direction of the virtual camera). When the operation of selecting the golf club is performed, data representing the type of the selected golf club (driver, iron, etc.) is stored on the external main memory  12  as a part of the current state data  159 . 
     When it is determined that an operation other than the swing operation has been performed (YES in step S 6 ), the CPU  10  advances to step S 19  described later. By contrast, when the operation is not other than the swing operation (NO in step S 6 ), the CPU determines whether or not the operation particular represented by the operation data  127  is that the B button  32   i  is pressed (step S 7 ). When it is determined that the B button  32   i  has been pressed (YES in step S 7 ), the CPU  10  executes re-hold processing (step S 8 ). The re-hold processing, for example, calculates the reference plane described above. 
       FIG. 38  is a flowchart showing the details of the re-hold processing shown in step S 8 . As shown in  FIG. 38 , the CPU  10  first executes processing of calculating the posture of the input device  8  based on the acceleration data  132  and the angular velocity data  131  included in the operation data  127  (step S 31 ). This processing, which may be executed in any method, is executed as follows in this embodiment. As described above, first, the posture of the input device  8  is calculated based on the angular velocity detected by the gyrosensor unit  7 . The posture can be calculated from the angular velocity by, for example, successively adding the angular velocity (per unit time) to the initial posture. Namely, starting from the initial state, the posture calculated immediately previously is successively changed and thus updated based on the angular velocity successively output from the gyrosensor unit  7 . In this manner, the current posture can be calculated. Next, the posture calculated from the angular velocity is corrected based on the acceleration data detected by the acceleration sensor  37 . According to the correction in this embodiment, the posture calculated from the angular velocity is made closer to the posture determined by the acceleration data. The next time the posture is updated based on the angular velocity, the angular velocity is added to the corrected posture. The posture determined by the acceleration data is, specifically, the posture of the input device  8  with an assumption that the direction of the acceleration represented by the acceleration data is vertically downward; namely, the posture calculated with an assumption that the acceleration represented by the acceleration data is a gravitational acceleration. The posture determined by the acceleration, by nature, is correct when the sensor is in a still state but has an error when the sensor is moving. By contrast, the posture calculated by a gyrosensor, by nature, has error accumulated along with time where the sensor output has errors. Accordingly, by updating the posture with constant corrections, a posture with little error is calculated. The posture thus corrected is stored on the external main memory  12  as the input device posture data  141  (hereinafter, this posture will be referred to as the “current posture”). In the case where the acceleration data is not to be reflected on the posture of the input device  8 , an accumulation result of the angular velocities may be added to the initial posture. 
     Next, the CPU  10  executes the reference plane setting processing (step S 32 ).  FIG. 39  is a flowchart showing the details of the reference plane setting processing. As shown in  FIG. 39 , the CPU  10  first calculates a plane, including the current Z-axis direction of the input device  8  in the local coordinate system (hereinafter, the Z axis in the local coordinate system will be referred to as tree “local Z axis”) and the gravity direction, as the first candidate plane, and stores the first candidate plane on the external main memory  12  as the first candidate plane data  150  (step S 41 ). 
     Next, the CPU  10  calculates a rotation matrix which directs the local Z axis at the current posture toward the gravity direction. The CPU  10  applies the calculated rotation matrix to the current Y axis of the input device B in the local coordinate system (hereinafter, the Y axis in the local coordinate system will be referred to as the “local Y axis”) to calculate the Y′ axis (step S 42 ). 
     Next, the CPU  10  calculates a plane including the Y′ axis and the gravity direction as the second candidate plane, and stores the second candidate plane on the external main memory  12  as the second candidate plane data  151  (step S 43 ). 
     Next, the CPU  10  calculates an angle made by the current reference plane (the reference plane most recently calculated) and the first candidate plane and an angle made by the current reference plane and the second candidate plane (θA and θB in  FIG. 23 ) (step S 44 ). Based on the angles, the CPU  10  calculates a new reference plane using expression 1 (or expression 1′ or 2) and stores the obtained new reference plane on the external main memory  12  as the reference plane data  142  (step S 45 ). 
     When this processing is first executed after the game processing is started, the reference plane has not been calculated. Therefore, only when this processing is first executed, the reference plane is calculated as follows. The CPU  10  calculates a plane which equally divides the angle made by the first candidate plane and the second candidate plane (θA+θB) into two (i.e., averages the two angles), and sets this plane as a new reference plane. 
     When this processing is first executed, the reference plane may be calculated by the following method, alternatively. An angle between the Z-axis direction and the gravity direction is set as a weight to be applied on the first candidate plane, and an angle between the Y′-axis direction and the gravity direction is set as a weight to be applied on the second candidate plane. A new reference plane may be calculated by obtaining a weighted average of the first candidate plane and the second candidate plane. 
     Next, based on the (new) reference plane, the CPU  10  sets the {L} coordinate system (see  FIG. 29 ) described above (step S 46 ). 
     Next, the CPU  10  applies a virtual rotation which makes the local Z axis parallel to the reference plane to the current X axis of the input device  8  (hereinafter, referred to as the “local X axis”) to calculate the X′ axis (step S 47 ).  FIG. 40  shows an overview of this processing.  FIG. 40(   a ) shows the actual posture of the input device  8 , and  FIG. 40(   b ) shows a virtual posture of the input device  8  obtained by applying the above-described rotation. 
     Next, the CPU  10  calculates an angle of the X′ axis with respect to the reference plane, and stores the obtained angle on the external main memory  12  as the reference X angle data  143  (step S 48 ). Thus, the reference plane setting processing is finished. 
     Returning to  FIG. 38 , after the reference plane setting processing, the CPU  10  executes, for example, posture control on the player object  101  (step S 33 ). Namely, based on the current posture calculated above, the CPU  10  moves the position of the golf club  102  or the like or causes the player object  101  to make a re-hold operation (e.g., causes the player object  101  to behave like re-gripping the golf club). 
     Next, the CPU  10  resets the guide display counter  155  used for displaying the re-hold guide  105  (see  FIG. 12 ) (step S 34 ). 
     Next, the CPU  10  initializes the display particulars of the power gauge  104  (step S 35 ). Specifically, the CPU  10  makes the power gauge  104  straight as shown in  FIG. 8  or  FIG. 12  and sets the position of the swing bar  106  at the bottom of the power gauge  104 . Thus, the re-hold processing is finished. 
     Returning to  FIG. 36 , after the re-hold processing, the CPU  10  executes drawing processing (step S 20  in  FIG. 37 ). Namely, the CPU  10  displays an image of the virtual game space taken by the virtual camera on the TV  2  as a game image. After step S 20 , the CPU  10  determines whether or not the game is to be terminated based on whether the termination flag  164  is on or not (step S 21 ). When YES, the CPU  10  terminates the game; whereas when NO, the CPU  10  returns to step S 2  to repeat the game processing. 
     Next, processing executed when it is determined in step S 7  that the B button  32   i  has not been pressed (NO in step S 7 ) will be described. In this case, the CPU  10  determines whether or not the operation particular of the operation data is that the A button is pressed, namely, whether or not the A button  32   d  has been pressed (step S 9 ). 
     When it is determined that the A button  32   d  has been pressed (YES in step S 9 ), the CPU  10  executes setting processing for treating the swing made by the player as a “shot” motion of hitting the ball, not as a “practice swing”, as follows. The CPU  10  first determines whether the shot flag  161  is on or not (step S 13 ). When it is determined that the shot flag  161  is not on (NO in step S 13 ), it is considered that the current state is immediately after the A button  32   d  is pressed. Therefore, the CPU  10  sets the shot flag  161  to be on (step S 14 ). Then, the CPU  10  controls the player object  101  to advance toward the position of the ball  103  (to approach the ball  103 ) (controls the state in  FIG. 8  into the state in  FIG. 10 ) (step S 15 ). Then, the CPU  10  advances to step S 16  ( FIG. 37 ) described later. 
     By contrast, when it is determined in step S 3  that the shot flag  16  is set to be on (YES in step S 13 ), it is considered that the A button  32   d  has been continuously pressed. Therefore, the CPU  10  advances to step S 16 . 
     When it is determined in step S 9  that the A button has not been pressed (NO in step S 9 ), the CPU  10  executes setting processing for treating the swing made by the player as a “practice swing”, as follows. The CPU  10  first determines whether the shot flag  161  is on or not (step S 10 ). When it is determined that the shot flag  161  is on (YES in step S 10 ), it is considered that the current state is immediately after the A button  32   d  is released after being pressed continuously. Therefore, the CPU  10  sets the shot flag  161  to be off (step S 11 ). Then, the CPU  10  controls the player object  101  to retract from the position of the ball  103  (controls the state in  FIG. 10  back to the state in  FIG. 8 ) (step S 12 ). Then, the CPU  10  advances to step S 16 . 
     By contrast, when it is determined in step S 10  that the shot flag  161  is off (NO in step S 10 ), the CPU  10  advances to step S 16  without executing the processing in step S 11  and S 12 . 
     Next, the CPU  10  executes swing-related processing (step S 16  in  FIG. 37 ).  FIG. 41  is a flowchart showing the details of the swing-related processing. As shown in  FIG. 41 , the CPU  10  first calculates the current posture of the input device  8  based on the operation data  127  (step S 51 ). 
     Next, the CPU  10  executes power gauge updating processing (step S 52 ). This processing determines (updates) the display particulars of the power gauge  104  described above (corresponding to the (2) power gauge-related processing, an overview of which is described above). 
       FIG. 42  is a flowchart showing the details of the power gauge updating processing. As shown in  FIG. 42 , the CPU  10  first executes twisting angle calculation processing (step S 61 ). This processing obtains the twisting angle described above.  FIG. 43  is flowchart showing the details of the twisting angle calculation processing. As shown in  FIG. 43 , the CPU  10  first generates a virtual reference plane based on the current posture of the input device  8  (step S 71 ). Namely, the CPU  10  virtually generates the reference plane as described above with an assumption that the B button  32   i  has been just pressed. Hereinafter, such a reference plane will be referred to as the “virtual reference plane”. The virtual reference plane is generated by the same processing as that in steps S 41  through S 45  described above with reference to  FIG. 39 . The generated plane is stored on the external main memory  12  as the virtual reference plane data  144 . 
     Next, the CPU  10  applies a rotation which makes the local Z axis of the input device  8  parallel to the virtual reference plane to the local X axis to calculate a virtual X′ axis (step S 72 ). Then, the CPU  10  calculates an angle of the virtual X′ axis with respect to the virtual reference plane, and stores the obtained angle on the external main memory  12  as the current X angle data  145  (step S 73 ). The processing in steps S 72  and S 73  is substantially the same as the processing in steps S 47  and S 48  described above with reference to  FIG. 39  except for being executed with respect to the virtual reference plane, and will not be described in detail. 
     Next, the CPU  10  calculates the twisting angle by the following expression and stores the obtained twisting angle on the external main memory  12  as the twisting angle data  146  (step S 74 ).
 
Twisting angle=current  X  angle−reference  X  angle  expression 10
 
     Thus, the twisting angle calculation processing is finished. 
     Returning to  FIG. 42 , after the twisting angle calculation processing, the CPU  10  executes swing-up angle calculation processing (step S 62 ).  FIG. 44  is a flowchart showing the details of the swing-up angle calculation processing. As shown in  FIG. 44 , the CPU  10  first converts the local Z axis of the current posture of the input device  8  into the {L} coordinate system ( FIG. 29  regarding the swing angle calculation) to calculate the vector D (step S 81 ). 
     Next, the CPU  10  calculates the swing-up angle θ using expression 7 (θ=A tan (Dx, −Dy+K×Dz)) (step S 82 ). As described above, the swing-up angle θ is 0° at the posture of the re-hold operation, has a positive value when the club is swung forward, and has a negative value when the club is swung up. Thus, the swing-up angle calculation processing is finished. 
     Returning to  FIG. 42 , after the swing-up angle θ is calculated, the CPU  10  executes processing of determining the degree at which the twisting angle is to be reflected on the curving of the power gauge  104  based on the absolute value of the swing-up angle θ (reflection degree) (step S 63 ). According to this processing, as the swing-up angle is larger (as the club is swung more widely) the influence of the twisting angle is made smaller; whereas as the swing-up angle is smaller (as the head of the golf club  102  is closer to the ball  103 ), the influence of the twisting angle is made larger. Namely, where the twisting angle of the wrists is the same, when the club is swung widely, the power gauge  104  is not curved much; whereas when the head of the club is closer to the ball  103 , the twisting angle is reflected on the curving of the power gauge  104  at a larger degree and the power gauge  104  is displayed as curving more. For example, where the reflection degree is in the range of 0.0 (low reflection degree) to 1.0 (high reflection degree), when the swing-up angle is 0°, the reflection degree is 1.0; whereas when the absolute value of the swing-up angle is 180°, the reflection degree is 0.0. Values between these angles are assigned so as to make a line graph (the values may be assigned so as to be nonlinear, needless to say). 
     Next, the CPU  10  curves the power gauge  104  based on the twisting angle and the reflection degree (step S 64 ). For example, the CPU  10  executes the processing of converting a twisting angle in the range of −35° to +35° into a curving degree in the range of −1.0 to 1.0 using the function corresponding to the graph shown in  FIG. 28 . For the conversion, the reflection degree is used as the coefficient. For example, where the twisting angle is 10°, when the reflection degree is 1.0 (close to the address state), 10° is reflected as it is; whereas when the reflection degree is 0.5 (a state where the club is swung about half), a value obtained by multiplying 10° by 0.5 is calculated as the curving degree. 
     Next, the CPU  10  converts the swing-up angle θ into the swing-up amount H (step S 65 ). Specifically, the CPU  10  converts the absolute value of the swing-up angle θ (−180° to +180°) into the swing-up amount H (0.0 to 1.0) using the function corresponding to the graph shown in  FIG. 30 . 
     Next, the CPU  10  moves the swing bar  106  based on the swing-up amount H (step S 66 ). Thus, the power gauge updating processing is finished. 
     Returning to  FIG. 41 , after the power gauge updating processing, the CPU  10  executes struck ball power calculation processing (step S 53 ).  FIG. 45  is a flowchart showing the details of the struck ball power calculation processing. As shown in  FIG. 45 , the CPU  15  first sets the follow-up coefficient Kt and calculates the follow-up amount T using the follow-up coefficient Kt as described above in the section of the “swing-down motion reflection processing” (step S 91 ). 
     Next, the CPU  10  calculates the excessive swing strength S described above (step S 92 ). Namely, assuming that the acceleration is decreased by 80%, the CPU  10  executes substantially the same calculation as that for finding the follow-up amount T to calculate the excessive swing strength S. 
     Next, the CPU  10  calculates the struck bail power P using expression 4 and stores the obtained struck ball power P on the external main memory  12  as the struck ball power data  156  (step S 93 ). Thus, the struck ball power calculation processing is finished. 
     Returning to  FIG. 41 , after the struck ball power calculation processing, the CPU  10  executes bending angle calculation processing (step S 54 ). This processing calculates the bending angle of the head of the golf club  102 , which is used for calculating the backspin ratio described above.  FIG. 46  is a flowchart showing the details of the bending angle calculation processing. As shown in  FIG. 46 , the CPU  10  first sets a bending characteristic (step S 101 ). Namely, the CPU  10  sets the variables Kp (spring) and Kd (damper) in accordance with the absolute value of the swing-up angle θ. Kp and Kd are set as follows. The absolute value |θ| of the swing-up angle is in the range of 0° to 180°. Kp is set by assigning values of 0.01 to 0.015 to values in the range of 0° to 90° in the above range (to the values exceeding 90°, Kp is uniformly 0.015). Kd is set by assigning values of 0.001 to 0.3 also to the values in the range of 0° to 90° (to the values exceeding 90°, Kd is uniformly 0.3). Owing to this, the club head can be provided with the bending characteristic of being likely to bend in the vicinity of the impact and being unlikely to bend far from the impact. 
     Next, the CPU  10  calculates acceleration A of the club head using expression 6, and also calculates the follow-up angle θh (see  FIG. 25 ) (step S 102 ). 
     Next, the CPU  10  calculates the bending angle φ using expression 5 (φ−θh−θ) (step S 103 ). Thus, the bending angle calculation processing is finished. 
     Returning to  FIG. 41 , after the bending angle calculation processing, the CPU  10  updates the posture of the player object  101 , the golf club  102  and the like based on the current posture of the input device  8  (step S 55 ). Thus, the swing-related processing is finished. 
     Returning to  FIG. 37 , after the swing-related processing, the CPU  10  executes impact-related processing (S 17 ). This processing determines whether or not an impact has been generated, and determines the parameters of the struck ball when the impact is generated. 
       FIG. 47  is a flowchart showing the details of the impact-related processing. As shown in  FIG. 47 , the CPU  10  determines whether or not the golf club  102  has passed the reference plane (step S 111 ). More specifically, the CPU  10  refers to the immediately previous swing-up angle data  152  to obtain the value of the swing-up angle θ calculated in the immediately previous frame (immediately previous processing loop). The CPU  10  compares the obtained value against the swing-up angle θ calculated by the processing in the current frame, and determines whether or not the value of the swing-up angle θ has changed from a negative value to a positive value to determine whether or not the golf club  102  has passed the reference plane. This determination is mainly made with an assumption that a normal swing has been made with no backspin motion. 
     When it is determined that the golf club  102  has passed the reference plane (YES in step S 111 ), the CPU  10  advances to step S 113  described later. By contrast, when it is determined that the golf club  102  has not passed the reference plane (NO in step S 111 ), the CPU  10  determines whether or not the golf club  102  has passed the reference plane, in consideration of the bend of the head of the golf club  102  when the backspin motion is performed (step S 112 ). When the backspin motion is performed, there may be a case where, although the player thinks he/she has impacted the ball, the determination made using the swing-up angle θ indicates that the golf club  102  almost hit, but did not hit, the bail  103  (did not pass the reference plane) and was stopped immediately before the ball  103  in the virtual game space. Assuming such a case, the CPU  10  determines whether or not the club head bent forward has passed the reference plane, namely, has impacted the ball  103 , in consideration of the forward bend of the golf club  102 , which is considered to be generated when the backspin motion is made. In order to make this determination, the CPU  10  determines whether or not the value of the follow-up angle θh has changed from a negative value to a positive value. When it is determined that the club head has passed the reference plane (YES in step S 112 ), the CPU  10  advances to step S 113 . When it is determined that the club head has not passed the reference plane (NO in step S 112 ), the CPU  10  advances to step S 116 . 
     Next, the CPU  10  determines whether the shot flag  161  is on or not (step S 113 ). Namely, the CPU  10  determines whether or not the swing currently made is a “practice swing”. When it is determined that the shot flag  161  is off (NO in step S 113 ), the swing is the “practice swing”. Therefore, the CPU  10  reads the struck ball power data  156 , converts the struck ball power P into the power bar  107  (see  FIG. 16 , etc.) and displays the power bar  107  (step S 114 ). In the case where the power gauge  104  is curved, the power bar  107  is also curved along with the shape of the power gauge  104 . 
     By contrast, it is determined in step S 113  that the shot flag  161  is on (YES in step S 113 ), the CPU  10  executes shot processing for causing the struck ball to fly (step S 115 ).  FIG. 48  is a flowchart showing the details of the shot processing. As shown in  FIG. 48 , the CPU  10  first sets the backspin flag  163  to be on (step S 121 ). The CPU  10  also sets the in-flight flag  162  to be on (step S 122 ). 
     Next, the CPU  10  reads the struck ball power data  156 , converts the struck ball power P into the power bar  107  and displays the power bar  107  (step S 123 ). Then, the CPU  10  calculates the parameters of the struck ball such as the trajectory, the moving velocity and the like based on the struck ball power P, the twisting angle, and data obtained by referring to the current state data  159 , for example, the type of the golf club currently selected, the location of the shot (fairway, rough, etc.), and the direction of the wind (step S 124 ). The calculated parameters are stored on the external main memory  12  as the struck ball parameters  158 . Thus, the shot processing is finished. 
     Returning to  FIG. 47 , after the shot processing, the CPU  10  stores the swing-up angle θ on the external main memory  12  as the immediately previous swing-up angle data  152  (step S 116 ). Also, the CPU  10  stores the follow-up angle θh on the external main memory  12  as the immediately previous follow-up angle data  153  (step S 117 ). The CPU  10  stores the bending angle calculated in the swing-related processing on the external main memory  12  as the bending angle data  154  (step S 118 ). Thus, the impact-related processing is finished. 
     Returning to  FIG. 37 , after the impact-related processing, the CPU  10  executes the re-hold guide processing (step S 18 ) This processing measures the display timing of the re-hold guide  105  shown in  FIG. 12  and displays the guide message (corresponding to the (3) guide message display-related processing, an overview of which is described above). 
       FIG. 49  is a flowchart showing the details of the re-hold guide processing. As shown in  FIG. 49 , the CPU  10  first determines whether or not conditions for resetting the guide display counter  155  are fulfilled (step S 131 ). Such conditions are that the posture of the input device  8  is significantly different from the posture expected for the “re-hold” (the posture is close to the address posture), and that the state is during a swing (whether or not the B button  32   i  has been pressed is determined by the processing in step S 34  in  FIG. 38 ). 
     More specifically, the CPU  10  determines whether or not the following three conditions are fulfilled. 
     (1) The local Z axis of the input device  8  is above the horizontal direction and the local Y axis of the input device  8  is below the horizontal direction (for example, like the posture of holding a baseball bat). 
     (2) The absolute value of the angular velocity is greater than 30 deg/sec. 
     (3) The absolute value of the acceleration is greater than 0.2 G. 
     Next, the CPU  10  determines whether or not at least one of the three conditions is fulfilled (step S 132 ). When it is determined that at least one of the three conditions is fulfilled (YES in step S 132 ), the CPU  10  considers that the reset condition is fulfilled and resets the guide display counter  155  (step S 133 ). Thus, the re-hold guide processing is finished. 
     By contrast, when it is determined that none of the three conditions is fulfilled (NO in step S 132 ), the CPU  10  executes processing for counting up the guide display counter  155 . Specifically, the CPU  10  executes necessity degree Kr calculation processing for the re-hold operation (step S 134 ).  FIG. 50  is a flowchart showing the details of the necessity degree Kr calculation processing. As shown in  FIG. 50 , the CPU  10  first calculates the above-described virtual reference plane and stores the obtained virtual reference plane on the external main memory  12  (step S 141 ). This processing is substantially the same as that executed in step S 71  in  FIG. 43 . 
     Next, the CPU  10  calculates an absolute value of the angle made by the current reference plane and the virtual reference plane (angle made by the surface normals thereof) (step S 142 ). 
     Next, the CPU  10  converts the angle calculated in step S 142  into the necessity degree Kr (step S 143 ). Specifically, it is defined that when the angle is 11° or greater, the re-hold operation is necessary; whereas when the angle is 0°, the re-hold operation is not necessary. An angle in the range of 0° to 11° is converted into a value in the range of 0.0 to 1.0 and set as the necessity degree Kr. Thus, the necessity degree Kr calculation processing is finished. 
     Returning to  FIG. 49 , the CPU  10  executes holding posture possibility Ks calculation processing (step S 135 ).  FIG. 51  is a flowchart showing the details of the holding posture possibility Ks calculation processing. As shown in  FIG. 51 , the CPU  10  converts the current angular velocity into variable Sw which represents a stable state of the angular velocity based on an angular velocity data included in the operation data  127  (step S 151 ). Specifically, the CPU  10  converts the absolute value of the angular velocity of 0 deg/sec. to 30 deg/sec. into a value in the range of 0.0 to 1.0 using linear interpolation. The obtained value is set as variable Sw. 
     Next, the CPU  10  converts the current acceleration into variable Sa which represents a stable state of the acceleration based on the acceleration data included in the operation data  127  (step S 152 ). Specifically, the CPU  10  converts the absolute value of an acceleration of 0 G to 0.2 G into a value in the range of 0.0 to 1.0 using linear interpolation. The obtained value is set as variable Sa. 
     Next, the CPU  10  converts the gravity direction component of the local X axis into variable St which represents the re-holding posture accuracy (step S 153 ). Namely, the CPU  10  converts the horizontal degree of the X axis described above with reference to  FIG. 31  into a value in the range of 0.0 (where the X axis is vertical) to 1.0 (where the X axis is horizontal). The obtained value is set as variable St. 
     Then, the CPU  10  calculates the holding posture possibility Ks using expression 8 (Ks=Sw×Sa×St) (step S 154 ). Thus, the holding posture possibility Ks calculation processing is finished. 
     Returning to  FIG. 49 , the CPU  10  causes the guide display counter C to count up using expression 9 (C=C+Kr×Ks) based on the necessity degree Kr and the holding posture possibility K (step S 136 ). 
     Next, the CPU  10  determines whether or not the value of the guide display counter C has exceeded  30  (step S 137 ). When it is determined that the value of the hold display counter C has exceeded  30  (YES in step S 137 ), the CPU  10  executes the processing of displaying the re-hold guide  105  shown in  FIG. 10  (step S 138 ). By contrast, when it is determined that the value of the guide display counter C has not exceeded  30  (NO in step S 137 ), the CPU  10  terminates the re-hold guide processing. 
     Returning to  FIG. 37 , after the re-hold guide processing, the CPU  10  executes the other game processing (step S 19 ). Namely, the CPU  10  executes the processing on the golf game which is not related to the essence of the present invention. Then, the processing in steps S 20  and thereafter is executed. 
     Now, processing executed when it is determined in step S 3  in  FIG. 35  that the in-flight flag  162  is on (YES in step S 3 ) will be described. In this case, the current state is after the impact, namely, after a shot is made. Therefore, the CPU  10  executes the ball moving processing (step  4 ). By this processing, processing of moving the struck ball and processing regarding the backspin are executed. 
       FIG. 52  is a flowchart showing the details of the ball moving processing. As shown in  FIG. 52 , the CPU  10  first determines whether the backspin flag is on or not (step S 161 ). When it is determined that the backspin flag is on (YES in S 161 ), the CPU  10  executes backspin ratio setting processing (step S 162 ) and advances to step S 163 . When it is determined that the backspin flag is off (NO in S 161 ), the CPU  10  advances to step S 163  without executing the processing in step S 162 . 
       FIG. 53  is a flowchart showing the details of the backspin ratio setting processing. This processing detects the maximum value of the forward bending angle of the club head and causes the obtained maximum value to be reflected on the backspin ratio. As shown in  FIG. 53 , the CPU  10  first executes bending angle calculation processing for calculating the bending angle φ (S 171 ). This processing is the same as that executed in step S 54  in  FIG. 41  and will not be described again. 
     Next, the CPU  10  determines whether or not the calculated bending angle φ has a positive value (step S 172 ). When it is determined that the bending angle φ does not have a positive value (NO in step S 172 ), the CPU  10  updates the immediately previous bending angle data  154  with the calculated bending angle (step S 177 ) and terminates the backspin ratio setting processing. 
     By contrast, when it is determined that the calculated bending angle φ has a positive value (YES in step S 172 ), the CPU  10  determines whether or not a return of the bend has been generated (step S 173 ). The “return of the bend” means that after the head of the golf club is bent forward by a swing provided with a backspin, the head returns rearward by repulsion. For example, when the bending angle represented by the immediately previous bending angle data  154  is larger than the bending angle φ calculated in step S 171 , the CPU  10  determines that the return of the bend has been generated. When it is determined that the return of the bend has not been generated (NO in step S 173 ), it is considered that the forward bend is still continued. Therefore, the CPU  10  executes the processing in step S 177  and terminates the backspin ratio setting processing. 
     By contrast, when it is determined that the return of the bend has been generated (YES in step S 173 ), the CPU  10  executes processing of determining the reflection ratio of the bending angle on the backspin, based on the type of the golf club currently selected or the like (step S 174 ). For example, when the type of the club is driver, the CPU  10  sets a low value as the reflection ratio such that the backspin is unlikely to be applied. 
     Next, the CPU  10  determines the backspin ratio based on the reflection ratio determined above and the bending angle represented by the immediately previous bending angle data  154  (i.e., the maximum value of the forward bend) (step S 175 ). The determined backspin ratio is stored on the external main memory  12  as the backspin ratio data  157 . 
     Next, the CPU  10  sets the backspin flag  163  to be off (step S 176 ). Thus, the backspin ratio setting processing is finished. 
     Returning to  FIG. 52 , after the backspin ratio setting processing, the CPU  10  moves the struck ball (the ball  103 ) based on the struck ball parameters  158 . After the backspin ratio is determined, the CPU  10  moves the struck ball also based on the backspin ratio (step S 163 ). Namely, immediately after the shot, the backspin ratio is not yet determined. Therefore, the stuck ball is moved only based on the struck ball parameters  158  (with no backspin). Then, once the backspin ratio is determined (after the backspin flag  163  is set to be off), the struck ball is moved based on the backspin ratio data  157  as well as the struck ball parameters  158 . In general, a struck ball with a backspin has a trajectory of flying high. Therefore, where the struck ball is moved with the backspin ratio being applied in the middle of the way, the struck ball can have a trajectory of rapidly rising midway. At this point, for example, a virtual camera may be set as necessary so as to provide camerawork following the struck ball. 
     The backspin ratio may be caused to be reflected on the behavior of the struck ball, for example, as follows, instead of using the above-described method. Even after the backspin ratio is determined, the struck ball is moved only based on the struck ball parameters  158  until the struck ball makes a landing, and after that, the backspin ratio is caused to be reflected on the behavior of the struck ball. For example, at the timing when the struck ball makes a landing, an orbit of the struck ball from the time of impact in the state where the backspin ratio is applied is re-calculated. This provides the final position of the struck ball in consideration of the backspin. Therefore, the behavior of the struck ball after the bail makes a landing can be controlled such that the ball is located at this position. 
     Next, the CPU  10  determines whether or not the movement of the struck ball has been finished (step S 164 ). When it is determined that the movement of the struck ball has not been finished (NO in step S 164 ), the CPU  10  terminates the ball moving processing. When it is determined that the movement of the struck ball has been finished (YES in step S 164 ), the CPU  10  sets the in-flight flag  162  to be off (step S 165 ) and executes the other game processing to be executed after the shot is made (step S 166 ). Such game processing is, for example, score calculation or the like. Then, the CPU  10  sets the termination flag  164  to be on (step S 167 ). Thus, the ball moving processing is finished. 
     Returning to  FIG. 35 , after the ball moving processing, processing after the drawing processing in step S 20  is executed. It is determined whether the termination flag  164  is set to be on or not (step S 21 ). When the termination flag  164  is set to be on in the ball moving processing, the processing in this embodiment, namely, the processing for each shot is terminated as a result of the determination in step S 21 . Thus, the detailed description of the processing in this embodiment is finished. 
     As described above, in this embodiment, one power gauge  104  presents the player with information on two different elements of the twisting angle and the swing-up amount (providing an estimate on the struck ball power). This allows the player to intuitively perceive the opening angle of the face, the strength of the shot he/she can make, and the like. 
     In this embodiment, the calculation for finding the reference plane for “re-hold” is avoided from becoming unstable due to the difference in the manner in which the player holds the input device  8  when pressing the B button  32   i . This allows the reference plane to be calculated more appropriately. As a result, a more appropriate determination on the impact can be made. 
     Regarding the timing at which the “re-hold” operation is to be made, a more appropriate timing is obtained by use of the necessity degree Kr of re-hold and the holding posture possibility Ks. This avoids having the player make a re-hold operation unnecessarily, and allows the player make a re-hold operation when necessary. 
     Regarding the swing operation, the particulars of the motion of swinging down (swing-down strength) is caused to be reflected on the struck ball power P. Therefore, the player can feel that his/her motion of moving the input device  8  is strongly associated with the movement of the golf club, which makes the game more entertaining. Since the struck ball power P is determined using the acceleration, the following effects are provided. In addition to a simply rapid down swing made after the player swings up the input device  8 , a down swing by which the angle is changed slowly along with time but a large acceleration (i.e., centrifugal force) is generated is also regarded as, and is reflected on the struck ball power as, a strong swing. Such a swing is made when, for example, a player having a long arm reach makes a big swing. 
     A backspin can be applied on the struck ball by the manner of swing instead of the button operation. Therefore, a golf game operable with a higher degree of reality can be provided to the player. 
     In the above embodiment, the “re-hold” operation is performed when the B button  32   i  is pressed. Alternatively, in the case where the input device  8  is kept still for a predetermined time period at a posture expected for “re-hold”, it may be considered that the B button  32   i  is pressed and the processing for “re-hold” may be executed even though the button input is not actually made. 
     In the above embodiment, the re-hold guide  105  is displayed in order to urge the player to make a re-hold operation. The re-hold operation may be urged by, for example, outputting a predetermined audio guide instead of displaying the re-hold guide  105 . 
     The power gauge  104  is curved in accordance with the twisting angle. The power gauge  104  may be curved in additional consideration of an element of the location at which the ball is hit (topography). Namely, information on a change in the outgoing direction or the orbit (trajectory) caused depending on the location at which the ball is hit may be presented by the change in the shape of the power gauge  104 .  FIG. 54  shows examples of shapes of the power gauge  104  different by the location at which the ball is hit.  FIG. 54(   a ) shows the case where the ball is hit in the fairway, and  FIG. 54(   b ) shows the case where the ball is hit in, for example, the bunker. The power gauge  104  in  FIG. 54(   a ) indicates that the outgoing direction of the ball is straight forward (namely, the ball is output straight and then is sliced rightward). By contrast, the power gauge  104  in  FIG. 54(   b ) is slightly inclined rightward from the base thereof, which indicates that the outgoing direction is right forward (the ball flies right forward from the beginning and then is sliced further rightward).  FIG. 54  also indicates that the power gauge is not inclined from the base thereof in the fairway, and is inclined from the base thereof in the bunker. Namely, the power gauge may be inclined from the base thereof when the ball is hit at a location of particular topography. 
     In the above embodiment, the power gauge  104  is curved. Alternatively, the power gauge  104  may be displayed with different colors. For example, the power gauge  104  may be usually displayed with a white frame, and with a red frame when the curving degree is equal to or greater than a predetermined value. Similarly, the swing bar  106  and the power bar  107  may be displayed with different colors in accordance with the swing-up amount H, the twisting angle, the struck ball power P or the like. 
     In the above embodiment, the struck ball power P and the twisting angle results in being determined at the same time, i.e., at the time of impact. The struck ball power P and the twisting angle do not need to be determined at the same time. One of the two may be determined first and the other may be determined later. For example, in the case where the twisting angle is determined before the struck ball power P, the swing bar  106  and the power gauge  104  may be controlled as follows: until the twisting angle is determined, the swing bar  106  is moved and the power gauge  104  is curved at the same time; and after the twisting angle is determined, the curving state of the power gauge  104  is fixed and only the swing bar  106  is moved. Alternatively, at the time when either the struck ball power P or the twisting angle is determined, the curving state of the power gauge  104  and the position of the swing bar  106  (i.e., only the display states) may be fixed. For example, this may be done as follows. At the moment when a shot is made, the curving state of the power gauge  104  and the position of the swing bar  106  are fixed (the display states are fixed at the same time) and also the manner of curving the struck ball relating to the curving state is determined (one of the parameters is determined), but the struck ball power is determined after the player swings the input device  8  all the way through (the other parameter is determined at a later timing). 
     In the reference plane setting processing in the above embodiment, the reference plane is updated by replacing the current reference plane with a newly calculated reference plane. Alternatively, for example, the posture of the golf club  102  may be adjusted while the position of the reference plane is fixed. The reference plane includes the gravity direction (is parallel to the gravity direction). Therefore, the correction of the reference plane corresponds to an operation of rotating the current reference plane around the gravity direction. Accordingly, even where the golf club (the posture of the input device  8 ) is rotated oppositely around the gravity direction while the current reference plane is fixed, substantially the same effect is provided. For example, an angle between the first candidate plane and the reference plane at a certain time is calculated. Assuming that, for example, the angle is 30°, the posture of the golf club may be rotated by 30°. 
     In the above embodiment, the conversion of the swing-up angle θ into the swing-up amount H is performed so as to provide a line graph (see  FIG. 30 ). Alternatively, the swing-up angle θ may be converted into the swing-up amount H so as to provide a nonlinear graph as shown in  FIG. 55 . In  FIG. 55 , the rightward direction of the horizontal axis represents the positive direction of θ, and the upward direction of the vertical axis represents the positive direction of H. In  FIG. 55(   a ), the graph is of a curve expanding upward. In this case, as the player swings up the club more widely (as H is closer to 1.0), detailed adjustment can be made more easily. In  FIG. 55(   b ), the graph is of a curve expanding downward. In this case, as the player swings up the club less widely (as H is closer to 0.0), detailed adjustment can be made more easily. 
     The twisting angle and the curving degree of the power gauge  104  may also be caused to correspond to each other so as to provide a nonlinear graph. Linear or nonlinear graphs may be used in accordance with the difficulty degree of the game. For setting the difficulty level, a setting screen which allows the player to select the difficulty level of the game may be prepared. For example, three difficulty levels of “easy”, “medium” and “difficult” are prepared. When “easy” is selected, the curving degree is converted so as to provide a downward curve as shown in  FIG. 56 . When “medium” is selected, the curving degree is converted so as to provide a line graph as shown in  FIG. 28 . When “difficult” is selected, the curving degree is converted so as to provide an upward curve as shown in  FIG. 57 . Regarding the conversion into the swing-up amount H also, different graphs may be used in accordance with the difficulty level in this manner. 
     Regarding the calculation of the struck ball power P, the following technique may be used in addition to the method described in the above embodiment. A time period from when the player swings up the input device  8  until he/she swings down the input device  8  (until an impact is generated) is measured, and the struck ball power P is corrected in accordance with the time period. The struck ball power P may be set to be stronger when the input device  8  is swung down quickly (when the time period from when the input device  8  is swung up until the input device  8  is swung down and impacts the bail is relatively short) than when the input device  8  is swung down slowly. For example, the following processing may be executed. In the struck ball power calculation processing (step S 53 ), the struck ball power P is once determined based only on the swing-up amount H without using the follow-up amount T; then, in the shot processing (step S 115 ), the struck ball power P is corrected to be increased or decreased in accordance with the time period required for the swing-down (e.g., the struck ball power P is increased when the time period required for the swing-down is relatively short, whereas the struck ball power P is decreased when the time period required for the swing-down is relatively long). 
     For determining the struck ball power P, a “shot with too much force (excessively forceful shot)” may be reflected. For example, a predetermined value is preset as the “upper limit” of the struck ball power. When the calculated struck ball power P exceeds the “upper limit”, the shot is considered to be “with too much force” and, for example, the direction in which the ball is to fly may be varied randomly. For example, when the struck ball power is equal to or less than the “upper limit”, the struck ball flies straight forward; whereas when the shot is “with too much force”, the trajectory of the struck ball is slightly sliced rightward, or output left forward or the like. In this case, it may be visually shown to the player that the shot is “with too much force” by changing the color of the power bar  107  and providing a visual effect of swinging the power bar  107  right and left. 
     For determining the struck ball power P, the maximum value of the swing-up amount (the maximum swing-up amount) may be simply used as the struck ball power P without using the follow-up amount T or the excessive swing strength S. This is done as follows specifically. The maximum swing-up amount is stored on the external main memory  12 . When an impact is generated, the struck ball power P is determined based on the maximum swing-up amount, and is displayed as the power bar  107 . This is advantageous in alleviating the processing load although the motion of swinging down the input device  8  is not reflected on the struck ball power. In this case, it is still possible to present the player with information on the opening angle of the face and the struck ball power by the position of the swing bar  106  and the curving of the power gauge  104  so that the player can intuitively perceive these elements. 
     Regarding the backspin ratio calculation processing, in the above information, the “bend” is simulated based on a model using a spring and a damper. Alternatively, the following processing may be executed without using such a model. For example, a change in the angular velocity in each frame is monitored. When the angular velocity is rapidly decreased, it is determined that a sudden brake (braking force) has been applied to the swing, namely, a swing with a backspin as shown in  FIG. 22  has been made, and thus the backspin ratio is determined. 
     For calculating the backspin ratio, it may be determined that a braking power has been generated using the acceleration instead of the above-described change in the angular velocity. For example, when an operation of suddenly stopping the swing is made as described above, an acceleration is generated in the opposite direction as a reaction to the sudden stop. Using this, a change in the acceleration in the opposite direction (corresponding to the forward bend) may be monitored and processing of determining the backspin ratio may be executed based on such a change. 
     Regarding the impact-related processing described above with reference to  FIG. 47 , it is determined in this embodiment that an impact has been generated using the swing-up angle θ. As an example, it is determined whether or not an impact has been generated by determining whether or not the sign of the swing-up angle θ has been inverted (step S 111 ). Also using the swing-up angle θ, it may be determined whether or not an impact has been generated by determining whether or not the posture of the input device  8  in the Z-axis direction and the reference plane have become horizontal. When both are horizontal (i.e., the swing-up angle θ is 0°), it may be determined that an impact has been generated. 
     In the above embodiment, the posture of the input device  8  is detected using the gyrosensor unit  7  or the acceleration sensor  37 . Alternatively, an image of the input device  8  may be taken by a predetermined camera and the posture of the input device  8  may be calculated based on the obtained data. This may be performed as follows, for example. An image of the input device  8  is taken by a predetermined camera and data on the taken image is supplied to the game apparatus  3 . The CPU  10  identifies the input device  8  in the image and distinguishes the posture thereof to execute processing such as, for example, detecting the motion of the input device  8 . 
     While the invention has been described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is understood that numerous other modifications and variations can be devised without departing from the scope of the invention.