Patent Publication Number: US-2023161433-A1

Title: Electrostatic Input Apparatus And Input Determination Method

Description:
CLAIM OF PRIORITY 
     This application is a Continuation of International Application No. PCT/JP2021/025999 filed on Jul. 9, 2021, which claims benefit of Japanese Patent Application No. 2020-140845 filed on Aug. 24, 2020. The entire contents of each application noted above are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an electrostatic input apparatus and an input determination method. 
     2. Description of the Related Art 
     Capacitance touch pads and touch panels detect fingers, styluses, or the like using a change in capacitance when the fingers or styluses come into contact therewith. The capacitance touch pads and touch panels can detect fingers or styluses even if an insulating plate is placed on the sensor electrode. However, a thicker plate on the sensor electrodes may decrease the resolution, sometimes causing detection of portions of the plate with which two fingers, a styluses, or the like are in contact as a single wide distribution area. Known touch panels in the relate art calculate the degree of flatness of the detected distribution area and determines whether the touch is a single touch or a multi-touch on the basis of the degree of flatness (for example, see Japanese Unexamined Patent Application Publication No. 2014-186530). 
     The detected distribution area is elliptical in both a state in which one finger extended at an angle is in contact with a touch panel or a touch pad and a state in which a plurality of fingers is in contact with the touch panel or the touch pad. The known input apparatuses determine whether a single touch or a multi-touch according to the degree of flatness of the distribution area and therefore cannot distinguish between a state in which one finger extending obliquely is in contact with the touch panel or the touch pad and a state in which a plurality of fingers is in contact with the touch panel or the touch pad. 
     SUMMARY OF THE INVENTION 
     The present invention provides an electrostatic input apparatus capable of distinguishing between a state in which one finger extending obliquely is in contact with an electrostatic coordinate input unit and a state in which a plurality of fingers is in contact with the electrostatic coordinate input unit, as well as an input determination method for the same. 
     An electrostatic input apparatus according to an aspect of the present invention includes a measuring unit that measures capacitance at a plurality of coordinates of an electrostatic coordinate input unit, a converting unit that obtains a reference value of the capacitance and subtracts the reference value from the capacitance to convert the capacitance to difference values according to a distance between the electrostatic coordinate input unit at the plurality of coordinates and a finger, a first coordinate calculating unit that calculates barycentric coordinates of a contact portion from the difference values for the plurality of coordinates, a cycle determining unit that determines whether the difference values at coordinates on a circumference of a circle with a predetermined radius centered on the barycentric coordinates exhibit periodicity of two cycles in one round along the circle, and an operation determining unit that, when the cycle determining unit determines that the difference values exhibit periodicity of two cycles, determines that an input operation using two or more fingers has been performed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram showing an electrostatic input apparatus according to a first embodiment; 
         FIGS.  2 A to  2 C  are diagrams showing the relationship between the state of one finger erected in performing a manipulated input on the electrostatic coordinate input unit and the measured values of the electrostatic coordinate input unit; 
         FIGS.  3 A to  3 C  are diagrams showing the state of one finger angled in performing a manipulated input on the electrostatic coordinate input unit and the measured values of the electrostatic coordinate input unit; 
         FIGS.  4 A to  4 C  are diagrams showing the state of two fingers in performing a manipulated input on the electrostatic coordinate input unit and the measured values of the electrostatic coordinate input unit; 
         FIGS.  5 A to  5 C  are diagrams illustrating the planar distribution of the difference values according to the difference in the positional relationship of the two fingers and the difference in the angular characteristics of the difference values; 
         FIGS.  6 A to  6 C  are diagrams illustrating the planar distribution of the difference values according to the difference in the positional relationship of the two fingers and the difference in the angular characteristics of the difference values; 
         FIG.  7    is a diagram illustrating the respective coordinates of the two fingers; 
         FIG.  8    is a flowchart for the processing of an input determination method of the first embodiment; 
         FIG.  9    is a diagram showing a correction table; 
         FIG.  10    is a diagram showing an electrostatic input apparatus according to a second embodiment; 
         FIG.  11    is a graph showing the relationship between eccentricity e and the measured value of a constant; 
         FIGS.  12 A and  12 B  are diagrams showing an example of the ellipse obtained with approximate processing performed by an approximate processing unit and the central coordinates of two fingers calculated by a coordinate calculating unit; 
         FIGS.  13 A and  13 B  are diagrams showing an example of the ellipse obtained with approximate processing performed by the approximate processing unit and the central coordinates of two fingers calculated by the coordinate calculating unit; 
         FIGS.  14 A and  14 B  are diagrams showing an example of the ellipse obtained with approximate processing performed by the approximate processing unit and the central coordinates of two fingers calculated by the coordinate calculating unit; 
         FIGS.  15 A and  15 B  are graphs showing the relationship between the distance Lm between the measured central coordinates of the two fingers and the distances Lc1 and Lc2 between the two points calculated by the coordinate calculating unit as the central coordinates of the two fingers; 
         FIGS.  16 A and  16 B  are graphs showing the relationship between the distance Lm between the measured central coordinates of the two fingers and the distances Lc1 and Lc2 between the two points calculated by the coordinate calculating unit as the central coordinates of the two fingers; 
         FIG.  17    is a flowchart for the processing of an input determination method according to the second embodiment; 
         FIG.  18    is a flowchart for the processing of an input determination method according to a third embodiment; 
         FIG.  19    is a flowchart for the processing of an input determination method according to a fourth embodiment; 
         FIG.  20    is a flowchart for the processing of an input determination method according to a fifth embodiment; 
         FIGS.  21 A and  21 B  are diagrams illustrating the planar distribution of the difference values and the difference in the angular characteristics of the difference values according to the difference in the positional relationship between the two fingers; and 
         FIG.  22    is a diagram showing corrected measured values. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of an electrostatic input apparatus and an input determination method of the present invention will be described hereinbelow. 
     First Embodiment 
       FIG.  1    is a diagram showing an electrostatic input apparatus  100  according to a first embodiment. The following is described using the X-Y-Z coordinate system. In the following, the plan view refers to an X-Y plane view. The −Z direction is a direction adjacent to the electrostatic input apparatus. The -Z direction is referred to as “lower side” or “below” for the convenience of description. The +Z direction is a direction remote from the electrostatic input apparatus. The +Z direction is referred to as “upper side” or “above” for the convenience of description. 
     The electrostatic input apparatus  100  includes an electrostatic coordinate input unit  110 , a multiplexer  120 , a drive circuit  130 , a detecting unit  140 , and a controller  150 . 
     The electrostatic coordinate input unit  110  includes multiple electrodes  111  that detect positions in the X direction and multiple electrodes  112  that detect positions in the Y direction. The multiple electrodes  111  and  112  are each made of a light-transmissive electrically conductive material, such as indium tin oxide (ITO), on the upper surface or the lower surface of a transparent substrate (not shown). The multiple electrodes  111  include electrodes X0, X1, X2, X3, . . . , Xn. The electrodes X0, X , X2, X3, . . . , Xn are arranged in the X direction at a constant pitch and extend in the Y direction. The multiple electrodes  112  include electrodes Y0, Y1, Y2, Y3, . . . , Yn. The electrodes Y0, Y, Y2, Y3, . . . , Yn are arranged in the Y direction at a constant pitch and extend in the X direction. The portions at which the multiple electrodes  111  and the multiple electrodes  112  cross each other in plan view are shown as intersections  113 . 
     The multiplexer  120  is a switching circuit that connects the multiple electrodes  111  (X0, X, X2, X3, . . . , Xn) and the multiple electrodes  112  (Y0, Y1, Y2, Y3, . . . , Yn) to the drive circuit  130  or the detecting unit  140 . 
     The drive circuit  130  outputs driving power to the groups of the multiple electrodes  111  X0, X1, X2, X3, . . . , Xn) and the multiple electrodes  112  (Y0, Y1, Y2, Y3, . . . , Yn) in order. 
     When driving power is supplied to the multiple electrodes  111  (X0, X1, X2, X3, . . . , Xn) by the drive circuit  130 , the detecting unit  140  measures electric currents flowing through the multiple electrodes  112  (Y0, Y1, Y2, Y3, . . . , Yn) and calculates the capacitance at the individual intersections  113 . When driving power is supplied to the multiple electrodes  112  (Y0, Y1, Y2, Y3, . . . , Yn) by the drive circuit  130 , the detecting unit  140  measures electric currents flowing through the multiple electrodes  112  (X0, X1, X2, X3, . . . , Xn) and calculates the capacitance at the individual intersections  113 . The capacitance at each intersection  113  measured by the detecting unit  140  is capacitance generated between the electrodes  111  and  112  at each intersection  113 . 
     The capacitance generated at each intersection  113  is influenced by a conductor (finger) near the intersection  113 . The capacitance value of each intersection  113  is input to the converting unit  151  of the controller  150 . 
     The controller  150  includes a converting unit  151 , a barycentric-coordinate calculating unit  152 , a cycle determining unit  153 , an operation determining unit  154 , and a coordinate calculating unit  155 . 
     When the capacitance measured by the detecting unit  140  is less than a threshold, the converting unit  151  finds the average value of the capacitance at the intersections  113  measured with the detecting unit  140  multiple times in time series. The converting unit  151  obtains the average value as a reference value when the electrostatic coordinate input unit  110  measures the capacitance. The converting unit  151  subtracts the reference value from the measured capacitance value measured for each intersection  113  by the detecting unit  140  and converts the value to a difference value of the capacitance (hereinafter referred to as “difference value”) according to the distance between the electrostatic coordinate input unit  110  and the finger at each intersection  113 . The reference value is obtained for each intersection  113 . 
     The barycentric-coordinate calculating unit  152  is an example of a first coordinate calculating unit. The barycentric-coordinate calculating unit  152  calculates the center of gravity on the basis of the difference values at the individual intersections  113  output from the converting unit  151 . “The center of gravity” in the embodiments of the present invention is the center of gravity when the difference value of each intersection  113  is regarded as the mass of the intersection  113 . That is, “the center of gravity” in the embodiments of the present invention is the center of the distribution of the capacitance. 
     The cycle determining unit  153  determines whether difference values at the intersections  113  of the electrodes  111  and  112  on the circumference of a circle with a predetermined radius centered on the barycentric coordinates calculated by the barycentric-coordinate calculating unit  152  exhibit periodicity of two cycles in one round along the circle. The term “periodicity of two cycles in one round” indicates that the component of the sine wave at intervals of n[rad] is large, as shown in  FIG.  4 C . The processing details of the cycle determining unit  153  will be described below with reference to  FIGS.  2 A to  2 C  to  FIGS.  4 A to  4 C . 
     If the cycle determining unit  153  determines that the difference values at the intersections  113  on the circumference of the circle with a predetermined radius centered on the barycentric coordinates calculated by the barycentric-coordinate calculating unit  152  exhibit periodicity of two cycles, the operation determining unit  154  determines that an input operation using a plurality of fingers has been performed. 
     If the operation determining unit  154  determines that an input operation using a plurality of fingers has been performed, then the coordinate calculating unit  155  calculates the central coordinates of each of the plurality of fingers. If the operation determining unit  154  determines that an input operation using one finger has been performed, then the coordinate calculating unit  155  outputs the barycentric coordinates calculated by the barycentric-coordinate calculating unit  152  as the central coordinates of the finger. 
       FIGS.  2 A to  2 C  to  FIGS.  4 A to  4 C  are diagrams showing the relationship between the state of one finger F in performing a manipulated input on the electrostatic coordinate input unit  110  and the measured values of the electrostatic coordinate input unit  110 .  FIG.  2 A  shows a state in which a manipulated input is performed with one finger F erected.  FIG.  3 A  shows a state in which a manipulated input is performed with one finger F angled.  FIG.  4 A  shows a state in which a manipulated input is performed with two fingers F and F′ erected. 
       FIGS.  2 B,  3 B, and  4 B  show the planar distribution of the difference values at the intersections  113 . The planar distribution of the difference values is expressed as contour lines (solid closed curves) corresponding to the difference values. An area FA indicating the position of the finger F detected by the detecting unit  140  (hereinafter referred to as “finger area FA”) and a measurement circle (dashed circle) with a radius r centered on the center of gravity of the finger area FA are shown together. The finger area FA is shown in monotone gradation. The black portion is a portion where the finger F is in contact with the electrostatic coordinate input unit  110 . The gray portion is a portion where the finger F is close to the electrostatic coordinate input unit  110 . The measurement circle is a circle centered on the center of gravity. The diameter of the measurement circle is the average distance between the centers of two fingers that are in contact with each other. An example of the diameter of the measurement circle is 18 mm (the radius is 9 mm). The origin of the X-Y coordinates in  FIGS.  2 B,  3 B , and  4 B is the center of gravity of the finger area FA. The radius of the measurement circle is not limited to 9 mm. Radii of 8 mm to 10 mm of the measurement circle provides sufficient accuracy. The radius of the measurement circle does not necessarily have to be fixed. For example, the radius may be the distance from the center of gravity to a position where the difference value is the maximum. 
       FIGS.  2 C,  3 C, and  4 C  show the angular characteristics of the difference values. The horizontal axis represents the angles, and the vertical axis represents the difference values on the measurement circle. The angles indicate positions on the measurement circle. The angles are set counterclockwise, with a point on the positive section of the X-axis as 0 [rad]. For this reason, the angle of a point on the positive section of the Y-axis on the measurement circle is π/2 [rad], the angle of a point on the negative section of the X-axis is π[rad], and the angle of a point on the negative section of the Y-axis is π/18 [rad]. The difference values shown in  FIGS.  2 C,  3 C, and  4 C  are difference values at sampling points at intervals of π/18 [rad] from the point of 0 [rad] on the measurement circle. If the intersection  113  is not present at the sampling point, a value obtained by performing linear approximation of the difference values at a multiple intersections  113  around the sampling point is used. 
     In a state in which a manipulated input is performed, with one finger F erected, as shown in  FIG.  2 A , the finger area FA in which the output of the converting unit  151  is higher than or equal to a predetermined threshold is circular, and the contour lines are concentric, as shown in  FIG.  2 B . In this case, the angular characteristics of the difference values are flat, as shown in  FIG.  2 C . This is because the difference values at the individual sampling points on the measurement circle are equal. 
     In a state in which a manipulated input is performed, with one finger F angled, as shown in  FIG.  3 A , the finger area FA in which the output of the converting unit  151  is higher than or equal to the predetermined threshold is elliptical, and the contour lines are elliptical, as shown in  FIG.  3 B . The interval between the contour lines is narrowest at the distal end of the finger F and widest at the base of the finger F (the side near the back of the hand). In this case, the angular characteristics of the difference values exhibit periodicity of one cycle in one round along the measurement circle, as shown in  FIG.  3 C , because a point PMAX at which the difference value is greatest in one round along the measurement circle is one. 
     In a state in which a manipulated input is performed, with two fingers F and F′ erected, as shown in  FIG.  4 A , the finger area FA in which the output of the converting unit  151  is higher than or equal to the predetermined threshold includes two circles, and the contour lines are elliptical, as shown in  FIG.  4 B . The interval between the contour lines is wider in the direction in which the two fingers F and F′ are connected (X direction) and narrower in the direction different by π/2 [rad] (Y direction). In this case, the angular characteristics of the difference values exhibit periodicity of two cycles in one round along the measurement circle, as shown in  FIG.  4 C , because there are two points PMAX at which the difference value is maximum in one round along the measurement circle. Since the measurement circle is a circle corresponding to the size of one finger, the center of gravity of the finger area FA of the two fingers F and F′ is positioned between the two fingers F and F′. For this reason, the center of the two fingers F and F′ is positioned on the measurement circle, and therefore two points PMAX are provided, and periodicity of two cycles is provided in one round along the measurement circle. 
     Thus, obtaining the angular characteristics of the difference values using the measurement circle, as shown in  FIGS.  2 A to  2 C  to  FIGS.  4 A to  4 C , allows distinguishing among a state in which a manipulated input is performed with one finger F erected, as shown in  FIG.  2 A , a state in which a manipulated input is performed with one finger F angled, as shown in  FIG.  3 A , and a state in which a manipulated input is performed with two fingers F and F′ erected, as shown in  FIG.  4 A . 
     In Fourier series expansion, the following relations of Eqs. (1) to (3) hold, where f(x) is a function of cycle T. where 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     x 
                     ) 
                   
                   = 
                   
                     
                       
                         a 
                         ⁢ 
                         0 
                       
                       2 
                     
                     + 
                     
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             1 
                           
                         
                         ∞ 
                       
                       
                         ( 
                         
                           
                             an 
                             ⁢ 
                             cos 
                             ⁢ 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 n 
                                 ⁢ 
                                 x 
                               
                               T 
                             
                           
                           + 
                           
                             bn 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 n 
                                 ⁢ 
                                 x 
                               
                               T 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               
                 
                   an 
                   = 
                   
                     
                       2 
                       T 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         T 
                       
                       
                         
                           f 
                           ⁡ 
                           ( 
                           x 
                           ) 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                           
                             2 
                             - 
                             x 
                           
                           T 
                         
                         ⁢ 
                         dx 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   bn 
                   = 
                   
                     
                       2 
                       T 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         T 
                       
                       
                         
                           f 
                           ⁡ 
                           ( 
                           x 
                           ) 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             n 
                             ⁢ 
                             x 
                           
                           T 
                         
                         ⁢ 
                         dx 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where x is replaced with θ. The difference value f(θ) of the electrostatic coordinate input unit  110  at a fixed distance r from the center of the finger area FA of the two fingers F and F′ (see  FIG.  4 B ) is found using Fourier series expansion, where f(θ) represents the measurement circle. The value f(θ) is approximated using Eq. (4), where cycle T=2π, and n in Eqs. (1) to (3)=2. 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     θ 
                     ) 
                   
                   = 
                   
                     
                       
                         a 
                         ⁢ 
                         0 
                       
                       2 
                     
                     + 
                     
                       a 
                       ⁢ 
                       2 
                       ⁢ 
                       cos 
                       ⁢ 
                       2 
                       ⁢ 
                       θ 
                     
                     + 
                     
                       b 
                       ⁢ 
                       2 
                       ⁢ 
                       sin 
                       ⁢ 
                       2 
                       ⁢ 
                       θ 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where coefficients a0, a2, and b2 are expressed as Eqs. (5) to (7), respectively. Coefficients a2 and b2 are coefficients that identify vectors representing the positions of the respective coordinates PF1 and PF2 of the two fingers F and F′, described below with reference to  FIG.  7   . 
     
       
         
           
             
               
                 
                   
                     a 
                     ⁢ 
                     0 
                   
                   = 
                   
                     
                       1 
                       π 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         
                           2 
                           ⁢ 
                           π 
                         
                       
                       
                         
                           f 
                           ⁡ 
                           ( 
                           θ 
                           ) 
                         
                         ⁢ 
                         d 
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     a 
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       1 
                       π 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         
                           2 
                           ⁢ 
                           n 
                         
                       
                       
                         
                           f 
                           ⁡ 
                           ( 
                           θ 
                           ) 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         2 
                         ⁢ 
                         θ 
                         ⁢ 
                         d 
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     b 
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       1 
                       π 
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         
                           2 
                           ⁢ 
                           π 
                         
                       
                       
                         
                           f 
                           ⁡ 
                           ( 
                           θ 
                           ) 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         2 
                         ⁢ 
                         θ 
                         ⁢ 
                         d 
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Referring to  FIGS.  4 A to  4 C  and also  FIGS.  5 A to  5 C  and  FIGS.  6 A to  6 C , the planar distribution of the difference values according to the difference in the positional relationship of the two fingers F and F′ and the difference in the angular characteristics of the difference values will be described.  FIGS.  5 A to  5 C  and  FIGS.  6 A to  6 C  are diagrams illustrating the planar distribution of the difference values according to the difference in the positional relationship of the two fingers F and F′ and the difference in the angular characteristics of the difference values. 
     In a state in which a manipulated input is performed with the two fingers F and F′ separated and erected, as shown in  FIG.  5 A , the finger area FA in which the output of the converting unit  151  is higher than or equal to a predetermined threshold is formed of two circles, as shown in  FIG.  5 B , while the contour lines form ellipses with longer major axes than the ellipses shown in  FIG.  4 B . In this case, the difference values at points PMIN with smallest difference values on the measurement circle are smaller than those in  FIG.  4 B . For this reason, the amplitude in periodicity of two cycles in one round along the measurement circle is smaller than that of  FIG.  4 C , as shown in  FIG.  5 C . 
     In a state in which a manipulated input is performed with the two fingers F and F′ attached to each other and erected at an angle with respect to the X-axis, as shown in  FIG.  6 A , the finger area FA in which the output of the converting unit  151  is higher than or equal to a predetermined threshold is formed of two circles, whereas the major axes of the elliptic contour lines form an angle of θf (θf&gt;0) with respect to the X-axis, as shown in  FIG.  6 B . In this case, the angles of the points PMAX at which the difference value is maximum on the measurement circle shift, and as a consequence, the phase of the periodicity of two cycles in one round along the measurement circle shifts, as shown in  FIG.  6 C . The angle θof is an angle of a polar coordinate system and is formed by the X-axis and a straight line connecting the positions of the respective coordinates PF1 and PF2 of the two fingers F and F′. 
     The measurement circle is represented by fθ expressed as Eq. (8). 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     θ 
                     ) 
                   
                   = 
                   
                     
                       
                         A 
                         ⁢ 
                         0 
                       
                       2 
                     
                     + 
                     
                       A 
                       ⁢ 
                       2 
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           2 
                           ⁢ 
                           
                             ( 
                             
                               θ 
                               - 
                               
                                 θ 
                                 ⁢ 
                                 f 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Modification of Eq. (8) provides Eq. (9), where A2, sin2θf, cos2θf are expressed as Eqs. (10) to (12), respectively. The value A2 in Eq. (10) represents the magnitude of a vector determined by the coefficients a2 and b2 that identify the vector. The coefficients al and a2 are of the real parts of the Fourier series expanded terms. The coefficients b1 and b2 are of the imaginary parts of the Fourier series expanded terms. Values A0, A1, and A2 are the absolute values of the complex number including the real part and the imaginary part of each Fourier series expanded term. 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     θ 
                     ) 
                   
                   = 
                   
                     
                       
                         A 
                         ⁢ 
                         0 
                       
                       2 
                     
                     + 
                     
                       b 
                       ⁢ 
                       2 
                       ⁢ 
                       sin 
                       ⁢ 
                       2 
                       ⁢ 
                       θ 
                     
                     + 
                     
                       a 
                       ⁢ 
                       2 
                       ⁢ 
                       cos 
                       ⁢ 
                       2 
                       ⁢ 
                       θ 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     A 
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       
                         a 
                         2 
                         2 
                       
                       + 
                       
                         b 
                         2 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     sin 
                     ⁢ 
                     2 
                     ⁢ 
                     θ 
                     ⁢ 
                     f 
                   
                   = 
                   
                     
                       b 
                       ⁢ 
                       2 
                     
                     
                       
                         
                           a 
                           2 
                           2 
                         
                         + 
                         
                           b 
                           2 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     cos 
                     ⁢ 
                     2 
                     ⁢ 
                     θ 
                     ⁢ 
                     f 
                   
                   = 
                   
                     
                       a 
                       ⁢ 
                       2 
                     
                     
                       
                         
                           a 
                           2 
                           2 
                         
                         + 
                         
                           b 
                           2 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The value θf can be expressed as Eq. (13) using θf in Eqs. (11) and (12). 
     
       
         
           
             
               
                 
                   
                     θ 
                     ⁢ 
                     f 
                   
                   = 
                   
                     
                       arctan 
                       ⁡ 
                       ( 
                       
                         
                           b 
                           ⁢ 
                           2 
                         
                         
                           a 
                           ⁢ 
                           2 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     The coordinates of the two fingers F and F′ can be obtained using the results of above calculation.  FIG.  7    is a diagram illustrating the respective coordinates PF1 and PF2 of the two fingers F and F′.  FIG.  7    shows the measurement circle, the center of gravity PC of the finger area FA, the points PMAX at which the difference value is maximum, and the respective coordinates PF1 and PF2 of the two fingers F and F′ (the finger area FA is omitted). In  FIG.  7   , the origin of the X-Y coordinates is the center of gravity PC of the finger area FA. The coordinates PF1 and PF2 are expressed using the distance L from the center of gravity PC to the position of each of the respective coordinates PF1 and PF2 of the two fingers F and F′ and the angle θf. The distance L can be obtained using Eq. (14). The values of coefficients K1 and K2 should be adjusted so that the double of vectors PF1 and PF2 is equal to the distance between the two fingers F and F′, where the vectors PF1 and PF2 are directed from the center of gravity PC of the finger area FA to the coordinates PF1 and PF2 of the fingers F and F′, respectively. Thus, the distance L between the two fingers F and F′ can be obtained as the distance twice the length of each of the vectors PF1 and PF2 using Eq. (14). 
         L=K 1 ×A 2 +K 2  (14)
 
     Accordingly, distinguishing the states in  FIG.  4 C  as well as  FIGS.  5 C and  6 C  from the states in  FIGS.  2 C and  3 C  allows an operation using the two fingers F and F′ to be identified, and the coordinates PF1 and PF2 of the two fingers F and F′ to be found. 
       FIG.  8    is a flowchart for the processing of an input determination method of the first embodiment. When the processing is started, the barycentric-coordinate calculating unit  152  calculates the barycentric coordinates on the basis of the output from the converting unit  151  (step S 1 ). The coordinates calculated at step S 1  are the barycentric coordinates (xMid, yMid) of the finger area FA in which the output of the converting unit  151  is higher than or equal to a predetermined threshold. 
     The cycle determining unit  153  calculates difference values at the sampling points at intervals of π/18 [rad] from the point of 0 [rad] on the measurement circle (step S 2 ). If the intersections  113  between the electrodes  111  and the electrodes  112  are present at the sampling points, the difference values at the sampling points are difference values at the intersections  113 . If the intersections  113  are not present at the sampling points, the cycle determining unit  153  uses values obtained by linearly approximating the difference values at a multiple intersections  113  around the sampling points. 
     The cycle determining unit  153  calculates the coefficients a2 and b2 in the Fourier series expanded second term from the values at the sampling points of the measurement circle using Eqs. (6) and (7) (step S 3 ). 
     The cycle determining unit  153  calculate the angle θf from Eq. (13) using the coefficients a2 and b2 calculated at step S 3  (step S 4 ). 
     The operation determining unit  154  determines whether the barycentric coordinates (xMid, yMid) calculated at step S 1  are within a predetermined range of the central portion of the electrostatic coordinate input unit  110  (step S 5 ). This is because, if the barycentric coordinates (xMid, yMid) are not within the predetermined range of the central portion of the electrostatic coordinate input unit  110 , the measurement circle is out of the measurable range of the electrostatic coordinate input unit  110 , and as a consequence, the difference values at the sampling points of the measurement circle cannot be obtained. 
     If the operation determining unit  154  determines that the barycentric coordinates (xMid, yMid) are within the predetermined range of the central portion of the electrostatic coordinate input unit  110  (S 5 : YES), then the operation determining unit  154  determines whether the number of difference values greater than or equal to a predetermined threshold (a threshold for difference values) of the difference values detected in the entire electrostatic coordinate input unit  110  is less than or equal to a predetermined number (step S 6 ). If the number of difference values greater than or equal to the predetermined threshold is greater than the predetermined number, the operation is not performed using two fingers, for example, using three or more fingers or the palm of a hand. 
     If the operation determining unit  154  determines that the number of difference values greater than or equal to the predetermined threshold (the threshold for difference values) is less than or equal to the predetermined number (S 6 : YES), then the operation determining unit  154  determines whether the magnitude of the vector A2 identified by the coefficients a2 and b2 is greater than a predetermined threshold (a threshold for the magnitude of the vector) (step S 7 ). If two fingers are used for operation, the vector A2 is greater than the predetermined threshold. Even if one finger is used for operation, the vector A2 does not come to zero because of a measurement error. If the operation determining unit  154  determines that the magnitude of the vector is greater than the predetermined threshold (the threshold for vectors) (S 7 : YES), then the operation determining unit  154  determines that the manipulated input has been performed using two fingers (step S 8 ). 
     The coordinate calculating unit  155  calculates two coordinates obtained from the barycentric coordinates (xMid, yMid), the distance L, and the angle θf as the central coordinates of the fingers F and the finger F′ (step S 9 ). If at step S 5  the operation determining unit  154  determines that the barycentric coordinates (xMid, yMid) are out of the predetermined range of the central portion of the electrostatic coordinate input unit  110  (S 5 : NO), then the operation determining unit  154  determines that the manipulated input is performed using one finger (step S 10 ). 
     If at step S 6  the operation determining unit  154  determines that the number of difference values greater than or equal to the predetermined threshold (the threshold for difference values) is not less than or equal to the predetermined number (S 6 : NO), and if at step S 7  the operation determining unit  154  determines that the magnitude of the vector is not greater than or equal to the predetermined threshold (the threshold for vectors) (S 7 : NO), then the operation determining unit  154  determines that the manipulated input has been performed using one finger (step S 10 ). 
     The coordinate calculating unit  155  calculates the barycentric coordinates (xMid, yMid) calculated at step S 1  as the central coordinates of the one finger F (step S 11 ). Thus, the series of processes ends. 
     Determining whether periodicity of two cycles can be obtained in one round along the measurement circle allows determining whether the manipulated input has been performed using two fingers. This allows providing the electrostatic input apparatus  100  capable of distinguishing between a state in which one finger extended diagonally is in contact with the electrostatic coordinate input unit and a state in which two or more fingers are in contact with the electrostatic coordinate input unit, and an input determination method for the same. 
     This is a configuration of determining that a manipulated input has been performed using two fingers when the values of the coefficients a2 and b2 are somewhat great, and the value A2 is somewhat great. Alternatively, the following configuration may be used. 
     The value A0 is determined using Eq. (15). The value AO is the direct-current component of capacitance detected by the detecting unit  140 . The value AO is expressed using a0. 
     
       
         
           
             
               
                 
                   
                     A 
                     ⁢ 
                     0 
                   
                   = 
                   
                     
                       a 
                       ⁢ 
                       0 
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     When the value A0 is obtained, and if the ratio A2/A0 between the value A2 of the magnitude of the vector and the direct-current component A0 is relatively high (higher than a first predetermined ratio), it may be determined that the manipulated input has been performed using two fingers. The determination using the ratio between the direct-current component A0 and the value A2 representing the magnitude of the vector ensures stabler determination accuracy against variations in the sensitivity of the electrostatic coordinate input unit  110 . 
     Wide variations of the electrodes  111  and  112  of the electrostatic coordinate input unit  110  cause variations in the detection sensitivity at the intersections  113  detected by the detecting unit  140 , causing variations in the difference values converted by the converting unit  151 . In such a case, a correction table as shown in  FIG.  9    may be provided, with which the difference values calculated for the intersections  113  may be corrected by the converting unit  151 .  FIG.  9    shows a correction table. In one example, a correction table in which 64 correction values for use when eight intersections  113  are arrayed in each of the X direction and the Y direction are arrayed in matrix. Since the converting unit  151  corrects the difference values, which the converting unit  151  calculates for the intersections  113  on the basis of the capacitance input from the detecting unit  140  to the controller  150 , by multiplying the difference values by correction values, finger central coordinates can be detected with higher accuracy. 
     Second Embodiment 
       FIG.  10    is a diagram illustrating an electrostatic input apparatus  200  according to a second embodiment. 
     The electrostatic input apparatus  200  includes an electrostatic coordinate input unit  110 , a multiplexer  120 , a drive circuit  130 , a detecting unit  140 , and a controller  250 . The electrostatic input apparatus  200  is configured such that the controller  150  of the electrostatic input apparatus  100  of the first embodiment is replaced with the controller  250 . Since the other configurations are the same as those of the electrostatic input apparatus  100  of the first embodiment, like components are denoted by the same reference signs, and redundant descriptions are omitted. 
     The controller  250  includes a converting unit  151 , a barycentric-coordinate calculating unit  152 , a cycle determining unit  153 , an operation determining unit  154 , an approximate processing unit  254 , and a coordinate calculating unit  255 . The converting unit  151 , the barycentric-coordinate calculating unit  152 , the cycle determining unit  153 , and the operation determining unit  154  are the same as the converting unit  151 , the barycentric-coordinate calculating unit  152 , the cycle determining unit  153 , and the operation determining unit  154  of the controller  150  of the first embodiment, respectively. 
     When the cycle determining unit  153  determines that the difference values exhibit periodicity of two cycles, the approximate processing unit  254  performs approximate processing for approximating the outline of the range in which coordinates at which difference values converted by the converting unit  151  exceed a threshold are present to an ellipse. This approximate processing will be described below with reference to  FIGS.  12 A and  12 B  to  FIGS.  14 A and  14 B . 
     The coordinate calculating unit  255  is an example of a second coordinate calculating unit, which calculates a position nearer to the center of the ellipse obtained by the approximate processing performed by the approximate processing unit  254  than the two focal points of the ellipse as the central coordinates of the two fingers. More specifically, the coordinate calculating unit  255  calculates, on a straight line connecting the two focal points of the ellipse obtained by approximate processing performed by the approximate processing unit  254  and the center of the ellipse, the coordinates of two points away from the center by a second distance obtained by multiplying a first distance between each focal point and the center by a constant less than 1 as the central coordinates of the two fingers using Eq. (16). The constant that the coordinate calculating unit  255  uses is obtained from the quadratic function of elliptical eccentricity. 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         I 
                         ) 
                       
                       ⁢ 
                           
                       If 
                       ⁢ 
                           
                       a 
                     
                     &gt; 
                     b 
                   
                   ⁢ 
                   
 
                   
                     
                       X 
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         X 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       Y 
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             sin 
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         Y 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       X 
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             
                               - 
                               cos 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         X 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       Y 
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             
                               - 
                               sin 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         Y 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       
                         ( 
                         II 
                         ) 
                       
                       ⁢ 
                           
                       If 
                       ⁢ 
                           
                       a 
                     
                     ≤ 
                     b 
                   
                   ⁢ 
                   
 
                   
                     
                       X 
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 b 
                                 2 
                               
                               - 
                               
                                 a 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             
                               - 
                               sin 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         X 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       Y 
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 b 
                                 2 
                               
                               - 
                               
                                 a 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             cos 
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         Y 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       X 
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 b 
                                 2 
                               
                               - 
                               
                                 a 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             sin 
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         X 
                         ⁢ 
                         0 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       Y 
                       ⁢ 
                       2 
                     
                     = 
                     
                       
                         C 
                         × 
                         
                           
                             ( 
                             
                               
                                 b 
                                 2 
                               
                               - 
                               
                                 a 
                                 2 
                               
                             
                             ) 
                           
                         
                         × 
                         
                           ( 
                           
                             
                               - 
                               cos 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       + 
                       
                         Y 
                         ⁢ 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where (X1, Y1) and (X2, Y2) are the coordinates of the two focal points, a is the length of the major axis, b is the length of the minor axis, (X0, Y0) is the center of the ellipse, and C is the constant. The constant C will be described later. The value θ represents the inclination of the ellipse. The calculation is made in consideration of the magnitude relation between a and b. 
     The constant C used in Eq. (16) is given by a quadratic function expressed as Eq. (17) using the eccentricity e of the ellipse obtained with approximate processing performed by the approximate processing unit  254 . 
       Constant C=−6.7833×e 2 +10.447×e−3.3596  (17)
 
     The three coefficients Eq. (17) vary according to the shape of the ellipse. For this reason, the three coefficients in Eq. (17) are values that can be changed according to the kind of the electrostatic coordinate input unit  110 . The three coefficients in Eq. (17) are obtained through an experiment in which the interval between two fingers is set from 15 mm to 20 mm. 
     If the positional accuracy of the fingers may be low, the constant may be a fixed value. The constant is greater than 0 and less than 1. The constant varies according to the size and material of the electrostatic coordinate input unit  110 , for example, 0.7. 
       FIG.  11    is a graph showing the relationship between the eccentricity e and the measured value of the constant C. A quadratic function obtained by being fitted to the relationship between the eccentricity e and the measured value of the constant C is expressed as Eq. (17). The positional relationship between the two focal points of the ellipse and the central coordinates of the two fingers will be described with reference to  FIGS.  12 A and  12 B  to  FIGS.  14 A and  14 B . 
       FIGS.  12 A and  12 B  to  FIGS.  14 A and  14 B  are diagrams showing examples of the positional relationship between the ellipse obtained with approximate processing performed by the approximate processing unit  254  and the central coordinates of two fingers calculated by the coordinate calculating unit  255 .  FIGS.  12 A and  12 B  show a result in the case where two fingers are placed parallel to the X-axis on the electrostatic coordinate input unit  110 .  FIGS.  13 A and  13 B  show a result in the case where two fingers are placed parallel to the Y-axis on the electrostatic coordinate input unit  110 .  FIGS.  14 A and  14 B  show a result in the case where two fingers are placed on the electrostatic coordinate input unit  110  at π/4 [rad] with respect to the X-axis and the Y-axis on the electrostatic coordinate input unit  110 . In any case, the interval between the centers of the two fingers is 15 mm. 
       FIGS.  12 A,  13 A, and  14 A  show the distribution of the difference values of the capacitance calculated from the output of the converting unit  151 . There are eight electrodes  111  and eight electrodes  112  and 64 intersections  113 . For the interval between the intersections  113 , values linearly interpolated from the values at the intersections  113  are calculated. The difference values of the capacitance are expressed as relative values (0 to 500, the maximum value: 500).  FIGS.  12 A,  13 A, and  14 A  show the relative values in five levels of 0-99, 100-199, 200-299, 300-399, and 400-500. 
     As shown in  FIGS.  12 A,  13 A, and  14 A , distributions in the form of an ellipse that is long in the X direction, an ellipse that is long in the Y direction, and an ellipse that is long in the direction of π/4 [rad] with respect to the X-axis and the Y-axis are obtained. 
       FIGS.  12 B,  13 B, and  14 B  show points at which the relative values of the difference values are  300  with solid black squares ( ) and, on a straight line connecting the two focal points of an ellipse fitted to a plurality of points at which the relative values of the difference values is 300 and the center of the ellipse, two points away from the center by the second distance obtained by multiplying the first distance between each focal point and the center by the constant with solid black rhombuses ( ). The relative value of 300 is measured on the outline in the range in which the ball of the finger F is in contact with the electrostatic coordinate input unit  110 . If the number of intersections  113  of the electrodes is small, the positions where the relative value is 300 when the two fingers F and F′ are erected and brought into contact with the electrostatic coordinate input unit  110  form an ellipse. 
     The ellipse fitted to the plurality of points at which the relative values of the difference values are 300 is obtained by the approximate processing unit  254  performing approximate processing for approximating the outline in the range in which coordinates at which the difference values converted by the converting unit  151  exceed a threshold (here, 300) to an ellipse. 
     The two points ( ), on the straight line connecting the two focal points and the center of the ellipse obtained with approximate processing, away from the center by the second distance obtained by multiplying the first distance between each focal point and the center by the constant are the two points calculated by the coordinate calculating unit  255  using Eq. (16) as the central coordinates of the two fingers. 
       FIGS.  12 B,  13 B, and  14 B  show the actually measured central coordinates of the two fingers, with solid black triangles ( ). Actually, the coordinates are actually the coordinates of positions where two false fingers are placed on the electrostatic coordinate input unit  110 . 
     As shown in  FIGS.  12 B,  13 B, and  14 B , the two points ( ) away from the center by the second distance obtained by multiplying the first distance by the constant, calculated as the central coordinates of the two fingers by the coordinate calculating unit  255  are very close to, substantially coincide with, the actually measured central coordinates ( ) of the two fingers. 
     The coordinate calculating unit  255  calculates the center of the two points ( ) representing the central coordinates of the two fingers as the center position of the central coordinates of the two fingers. The center position of the central coordinates of the two fingers is the position represented by the solid black dot ( M) and the center of the two points ( ) representing the central coordinates of the two fingers. 
       FIGS.  15 A and  15 B  and  FIGS.  16 A and  16 B  are graphs showing the relationship between the distance Lm between the measured central coordinates of the two fingers and the distances Lc1 and Lc2 between the two points calculated by the coordinate calculating unit  255  as the central coordinates of the two fingers.  FIGS.  16 A and  16 B  show a part corresponding to the partial section of the horizontal axis and the vertical axis of  FIGS.  15 A and  15 B  in enlarged view. 
       FIGS.  15 A and  16 A  show the distance Lc1 between two the points calculated by the coordinate calculating unit  255  using Eq. (16) and a constant (0.7).  FIGS.  15 B and  16 B  shows a distance Lc2 between the two points calculated by the coordinate calculating unit  255  using the constant C in Eqs. (16) and (17). 
     In  FIGS.  15 A and  15 B  and  FIGS.  16 A and  16 B , the horizontal axis represents measured values, and the vertical axis represents calculated values. Thus, the higher the accuracy of calculation performed by the coordinate calculating unit  255 , the closer to the solid straight line with a slope of 1. A comparison between  FIGS.  15 A and  16 A  and  FIGS.  15 B and  16 B  showed that the distance Lc2 calculated using the constant C in Eq. (17) shown in  FIGS.  15 B and  16 B  is closer to the straight line than the distance Lc1 calculated using the constant (0.7) shown in  FIGS.  15 A and  16 A . This showed that using the constant C in Eq. (17) provided higher calculation accuracy to the coordinate calculating unit  255  than using the constant (0.7). 
       FIG.  17    is a flowchart for the processing of the input determination method according to the second embodiment. The flowchart shown in  FIG.  17    includes steps S 29 A and S 29 B in place of step S 9  in the first embodiment shown in  FIG.  8   . The difference will be described hereinbelow. 
     If at step S 8  the operation determining unit  154  determines that a manipulated input has been performed using two fingers, then the approximate processing unit  254  finds an ellipse and the coordinates of the focal points of the ellipse by performing approximate processing (step S 29 A). If at step S 29 B the constant C in Eq. (17) is to be used, the approximate processing unit  254  finds the eccentricity e in addition to the ellipse and the coordinates of the focal points of the ellipse at step S 29 A. To find an ellipse is to find an equation representing the ellipse in the X-Y coordinates of the electrostatic coordinate input unit  110 . The coordinates of the focal points and the eccentricity e may be found in accordance with the equation representing the ellipse. 
     Next, the coordinate calculating unit  255  calculates using Eq. (16), on a straight line connecting the two focal points of the ellipse obtained with approximate processing performed by the approximate processing unit  254  and the center of the ellipse, the coordinates of two points away from the center by the second distance obtained by multiplying the first distance between each focal point and the center by the constant (0.7) or the constant C in Eq. (17) as the central coordinates of the two fingers (step S 29 B). Thus, the series of processes ends. 
     Thus, determination of whether periodicity of two cycles can be obtained in one round along the measurement circle allows determining whether the manipulated input has been performed using two fingers or one finger. An ellipse representing the distribution of the difference values of capacitance due to the contact of two fingers with the electrostatic coordinate input unit  110  can be obtained with approximate processing, and the central coordinates of the two fingers can be calculated using the constant in Eq. (16). The constant used in Eq. (16) is the constant in Eq. (16) or the constant (0.7). 
     Accordingly, this allows providing the electrostatic input apparatus  200  capable of distinguishing between a state in which one finger extended diagonally is in contact with the electrostatic coordinate input unit and a state in which two or more fingers are in contact with the electrostatic coordinate input unit, and an input determination method for the same. This also provides the electrostatic input apparatus  200  capable of calculating the central coordinates of two fingers with high accuracy and an input determination method for the same. 
     Third Embodiment 
       FIG.  18    is a flowchart for the processing of an input determination method according to a third embodiment. The flowchart shown in  FIG.  18    is based on the flowchart of the first embodiment shown in  FIG.  8    and can be executed by the electrostatic input apparatus  100  of the first embodiment. Here, an input determination method of a first modification of the input determination method of the first embodiment will be described as the input determination method of the third embodiment. In  FIG.  18   , the same processes as those of the steps shown in  FIG.  8    are denoted by the same reference numbers. 
     In the third embodiment, the operation determining unit  154  calculates a Fourier-analyzed real part from the difference values at the coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid) with reference to the coordinates of the maximum value or the minimum value of the difference values of capacitance at the intersection  113  according to the distance between the electrostatic coordinate input unit  110  and the finger, converted by the converting unit  151 , and if the magnitude of the Fourier-analyzed real part of two cycles in one round along the circle is greater than a threshold (a predetermined threshold), the operation determining unit  154  determines that an input operation using two or more fingers has been performed. 
     The Fourier analysis includes Fourier series expansion, complex Fourier series expansion, and Fourier transformation, any of which may be used. Fourier-analyzed real part includes a real part of complex Fourier series, a Fourier-transformed real part, and the cosine of Fourier series. When the processing is started, the barycentric-coordinate calculating unit  152  calculates coordinates at which a manipulated input is performed from the output of the converting unit  151  (step S 1 ). The coordinates calculated at step S 1  are the barycentric coordinates (xMid, yMid) of a finger area FA where the output of the converting unit  151  is higher than or equal to a predetermined threshold. 
     The operation determining unit  154  determines whether the barycentric coordinates (xMid, yMid) calculated at step S 1  is within a predetermined range of the central portion of the electrostatic coordinate input unit  110  (step S 5 ). This is because, if the barycentric coordinates (xMid, yMid) is not within the predetermined range of the central portion of the electrostatic coordinate input unit  110 , the measurement circle is out of the measurable range of the electrostatic coordinate input unit  110 , and as a result, the difference values at the sampling points of the measurement circle cannot be obtained. 
     If the operation determining unit  154  determines that the barycentric coordinates (xMid, yMid) is within the predetermined range of the central portion of the electrostatic coordinate input unit  110  (S 5 : YES), then the operation determining unit  154  determines whether the number of difference values greater than or equal to a predetermined threshold (a threshold for difference values) of the difference values detected for the entire electrostatic coordinate input unit  110  is less than or equal to a predetermined number (step S 6 ). If the number of difference values greater than or equal to the predetermined threshold is greater than the predetermined number, two fingers are not used for operation. For example, three or more fingers or the palm of a hand may be used. 
     If the operation determining unit  154  determines that the number of difference values greater than or equal to the predetermined threshold (the threshold for difference values) is less than or equal to the predetermined number (S 6 : YES), then the cycle determining unit  153  calculates difference values at sampling points at intervals of π/18 [rad] from the point of 0 [rad] on the measurement circle (step S 31 ). The sampling points are 9 mm away from the barycentric coordinates. The sampling points are at positions rotated at intervals of π/18 [rad] from 0 [rad] in the X-axis direction from the center of gravity. The coordinates of each sampling point are expressed as Eq. (18). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           x 
                           = 
                           
                             
                               9 
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                 θ 
                                 n 
                               
                             
                             + 
                             xMid 
                           
                         
                       
                     
                     
                       
                         
                           y 
                           = 
                           
                             
                               9 
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                 θ 
                                 n 
                               
                             
                             + 
                             yMid 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               θ 
               n 
             
             = 
             
               
                 { 
                 
                   
                     n 
                     ⁢ 
                     π 
                   
                   
                     1 
                     ⁢ 
                     8 
                   
                 
                 } 
               
               
                 n 
                 = 
                 0 
               
               
                 1 
                 ⁢ 
                 7 
               
             
           
         
       
     
     The process of step S 31  is the same as the process of step S 2  of the first embodiment. If the intersection  113  of the electrode  111  and the electrode  112  is present at the sampling point, the difference value at the sampling point is a difference value at the intersection  113 . If no intersection  113  is present at the sampling point, the cycle determining unit  153  uses a value linearly approximated from the difference values at multiple intersections  113  around the sampling point. 
     The operation determining unit  154  identifies the coordinates of a maximum value of the difference values at the sampling points on the circumference of the measurement circle (step S 32 ). 
     The operation determining unit  154  calculates θf from the barycentric coordinates and the coordinates (xMax, yMax) of the maximum value of the difference values at the sampling points (step S 33 ). The value θf is calculated using Eq. (19). 
     
       
         
           
             
               
                 
                   
                     θ 
                     ⁢ 
                     f 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 arctan 
                                 ⁢ 
                                 
                                   
                                     
                                       y 
                                       ⁢ 
                                       Max 
                                     
                                     - 
                                     yMid 
                                   
                                   
                                     
                                       x 
                                       ⁢ 
                                       Max 
                                     
                                     - 
                                     xMid 
                                   
                                 
                                 ⁢ 
                                     
                                 if 
                                 ⁢ 
                                     
                                 x 
                               
                               &gt; 
                               0 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   arctan 
                                   ⁢ 
                                   
                                     
                                       
                                         y 
                                         ⁢ 
                                         Max 
                                       
                                       - 
                                       yMid 
                                     
                                     
                                       
                                         x 
                                         ⁢ 
                                         Max 
                                       
                                       - 
                                       xMid 
                                     
                                   
                                 
                                 + 
                                 
                                   π 
                                   ⁢ 
                                       
                                   if 
                                   ⁢ 
                                       
                                   x 
                                 
                               
                               &lt; 
                               
                                 0 
                                 ⁢ 
                                     
                                 and 
                                 ⁢ 
                                     
                                 y 
                               
                               ≥ 
                               0 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   arctan 
                                   ⁢ 
                                   
                                     
                                       
                                         y 
                                         ⁢ 
                                         Max 
                                       
                                       - 
                                       yMid 
                                     
                                     
                                       
                                         x 
                                         ⁢ 
                                         Max 
                                       
                                       - 
                                       xMid 
                                     
                                   
                                 
                                 - 
                                 
                                   π 
                                   ⁢ 
                                       
                                   if 
                                   ⁢ 
                                       
                                   x 
                                 
                               
                               &lt; 
                               
                                 0 
                                 ⁢ 
                                     
                                 and 
                                 ⁢ 
                                     
                                 y 
                               
                               ≥ 
                               0 
                             
                             , 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     π 
                                     2 
                                   
                                   ⁢ 
                                       
                                   if 
                                   ⁢ 
                                       
                                   x 
                                   ⁢ 
                                   Max 
                                 
                                 - 
                                 xMid 
                               
                               = 
                               
                                 
                                   
                                     0 
                                     ⁢ 
                                        
                                     and 
                                     ⁢ 
                                         
                                     y 
                                     ⁢ 
                                     Max 
                                   
                                   - 
                                   yMid 
                                 
                                 &gt; 
                                 0 
                               
                             
                             , 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   π 
                                   2 
                                 
                                 ⁢ 
                                     
                                 if 
                                 ⁢ 
                                     
                                 x 
                                 ⁢ 
                                 Max 
                               
                               - 
                               xMid 
                             
                             = 
                             
                               
                                 
                                   0 
                                   ⁢ 
                                      
                                   and 
                                   ⁢ 
                                       
                                   y 
                                   ⁢ 
                                   Max 
                                 
                                 - 
                                 yMid 
                               
                               &lt; 
                               0 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     The operation determining unit  154  performs correction with θf identified at step S 33  and performs Fourier analysis to calculate the coefficient a2 of real part of the second term of Fourier series. For example, if the values on the circumference of the measurement circle are the values shown in  FIG.  6 C , the angles in the range from 0 to π/4 [rad] are corrected to angles plus 7π/4 [rad], and the angles in the range from π/4 to 2 π[rad] are corrected to values minus π/4 [rad]. As a result, the values are corrected to values shown in  FIG.  22   . The coefficient a2 of the Fourier-analyzed real part is calculated from the difference values at the sampling points at the coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid) (step S 34 ). The value 0 [rad] is the maximum value. Accordingly, if the data has periodicity of two cycles in a round (2π), the coefficient b2 of an imaginary part of the second term of Fourier series is substantially zero. Accordingly, by performing correction so that the angle of the coordinates of the maximum value of the difference values of the capacitance comes to 0 [rad] and then performing Fourier analysis, the periodicity can be determined using only the coefficient a2 of the real part. Performing correction so that the angle of the coordinates of the minimum value comes to zero also allows the coefficient a2 of the Fourier-analyzed real part to have substantially the same value. 
     The operation determining unit  154  determines whether the coefficient a2 of the Fourier-analyzed real part of two cycles in one round along the circle is greater than the threshold (the predetermined threshold) (step S 35 ). 
     If the operation determining unit  154  determines that the coefficient a2 of the real part is greater than the threshold (the predetermined threshold), the process goes to step S 36  for calculating the coordinates of the two fingers. 
     The coordinate calculating unit  155  calculates two coordinates determined from the barycentric coordinates (xMid, yMid), the coefficient a2 of the real part, and the angle θf as the central coordinates of the two fingers F and F′ (step S 36 ). The coordinates of the minimum value may be used instead of the coordinates of the maximum value. With the barycentric coordinates (xMid, yMid) and the coordinates of the minimum value of the difference values of the capacitance, the two fingers are positioned at an angle θf+π/2 and an angle θf−π/2 (an angle different from θf by π/2). For this reason, one of the maximum value and the minimum value of the difference values may be used for calculation. 
     If at step S 5  the operation determining unit  154  determines that the barycentric coordinates (xMid, yMid) are not within the predetermined range of the central portion of the electrostatic coordinate input unit  110  (S 5 : NO), it is determined that the manipulated input has been performed using one finger, and the coordinate calculating unit  155  calculates the barycentric coordinates (xMid, yMid) calculated at step S 1  as the central coordinates of the one finger F (step S 11 ). If it is determined at step S 6  that the number of difference values greater than or equal to the predetermined threshold is greater than the predetermined number (S 6 : NO), it is determined that the manipulated input has not been performed using two fingers, and the coordinate calculating unit  155  calculates the barycentric coordinates (xMid, yMid) calculated at step S 1  as the central coordinates of one finger F (step S 11 ). If it is determined at step S 35  that the magnitude of the coefficient a2 is not greater than the threshold (step S 35 : NO), it is determined that the manipulated input has been performed using one finger, and the coordinate calculating unit  155  calculates the barycentric coordinates (xMid, yMid) calculated at step S 1  as the central coordinates of one finger F (step S 11 ). Thus, the series of processes ends. 
     Thus, the Fourier analyzed-real part is calculated from the difference values at the coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid) with reference to the maximum value or the minimum value of the difference values of the capacitance, and if the magnitude of the Fourier-analyzed real part of two cycles in one cycle along the circle is greater than the threshold (the predetermined threshold), it can be determined that an input operation using two or more fingers has been performed. 
     Accordingly, this allows providing an electrostatic input apparatus capable of distinguishing between a state in which one finger extended diagonally is in contact with the electrostatic coordinate input unit and a state in which two or more fingers are in contact with the electrostatic coordinate input unit, and an input determination method for the same. This also provides an electrostatic input apparatus capable of calculating the central coordinates of two fingers with high accuracy and an input determination method for the same. 
     Fourth Embodiment 
       FIG.  19    is a flowchart for the processing of an input determination method according to a fourth embodiment. The flowchart shown in  FIG.  19    is based on the flowchart of the first embodiment shown in  FIG.  8    and can be executed by the electrostatic input apparatus  100  of the first embodiment. Here, an input determination method of a second modification of the input determination method of the first embodiment will be described as the input determination method of the fourth embodiment. In  FIG.  19   , the same processes as those of the steps shown in  FIGS.  8  and  18    are denoted by the same reference numbers. 
     In the fourth embodiment, the operation determining unit  154  calculates the ratio of the maximum value to the minimum value of the difference values at the coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid), and if the ratio is higher than a second predetermined ratio, the operation determining unit  154  determines that an input operation using two or more fingers has been performed. 
     Steps S 1 , S 5 , S 6 , S 31 , and S 11  shown in  FIG.  19    are the same as steps S 1 , S 5 , S 6 , S 31 , and S 11  shown in  FIG.  18   . 
     The operation determining unit  154  identifies the maximum value and the minimum value of the difference values at the coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid) (step S 41 ). 
     The operation determining unit  154  determines whether the ratio of the identified maximum value to the minimum value (maximum value/minimum value) of the difference values is higher than a predetermined ratio (a second predetermined ratio) (step S 42 ). 
     If the ratio of the maximum value to the minimum value (maximum value/minimum value) of the difference values is higher than the second predetermined ratio, then the operation determining unit  154  identifies the coordinates of the maximum value (or the minimum value) of the difference values at the sampling points of the measurement circle (step S 43 ). The process of step S 43  is the same as the process of step S 32  in  FIG.  18   . 
     The cycle determining unit  153  calculates the angle θf from the barycentric coordinates (xMid, yMid) and the coordinates of the maximum value of the difference values at the sampling points (step S 44 ). The process of step S 44  is the same as the process of step S 33  in  FIG.  18   . From the barycentric coordinates (xMid, yMid) and the coordinates of the maximum value of the difference values of the capacitance, the angle θf is determined. Instead of the coordinates of the maximum value, the coordinates of the minimum value may be used. From the barycentric coordinates (xMid, yMid) and the coordinates of the minimum value of the difference values of the capacitance, two fingers are positioned at the angles represented by θf+π/2 and θf−π2 (angles different from θf by π/2). For this reason, one of the maximum value and the minimum value of the difference values may be used for calculation. 
     The operation determining unit  154  calculates a finger distance D from the maximum value and the minimum value of the difference values at the sampling points (step S 45 ). The finger distance D is obtained by adding a predetermined constant to the ratio of the maximum value to the minimum value (maximum value/minimum value) of the difference values. The finger distance D increases as the ratio of the major axis to the minor axis of the ellipse increases, and the finger distance D decreases as the ratio decreases. 
     The coordinate calculating unit  155  calculates two coordinates determined from the barycentric coordinates (xMid, yMid), the finger distance D, and the angle θf as the central coordinates of the fingers F and F′ (step S 46 ). 
     A case where at step S 5  the operation determining unit  154  determines that the barycentric coordinates (xMid, yMid) are not within a predetermined range of the central portion of the electrostatic coordinate input unit  110  (S 5 : NO) indicates that the manipulated input has been performed using one finger. For this reason, the coordinate calculating unit  155  calculates the barycentric coordinates (xMid, yMid) calculated at step S 1  as the central coordinates of the one finger F (step S 11 ). Thus, the series of processes ends. 
     Thus, the ratio of the maximum value to the minimum value of the difference values at the coordinates on the circumference of a circle of a predetermined radius centered on the barycentric coordinates (xMid, yMid) is calculated, and if the ratio is higher than the second predetermined ratio, it can be determined that an input operation using two or more fingers has been performed. 
     Accordingly, this allows providing an electrostatic input apparatus capable of distinguishing between a state in which one finger extended diagonally is in contact with the electrostatic coordinate input unit and a state in which two or more fingers are in contact with the electrostatic coordinate input unit, and an input determination method for the same. This also provides an electrostatic input apparatus capable of calculating the central coordinates of two fingers with high accuracy and an input determination method for the same. 
     Fifth Embodiment 
       FIG.  20    is a flowchart for the processing of an input determination method according to a fifth embodiment.  FIGS.  21 A and  21 B  are diagrams illustrating the planar distribution of the difference values and the difference in the angular characteristics of the difference values according to the difference in the positional relationship between the two fingers F and F′. The flowchart shown in  FIG.  20    is based on the flowchart of the first embodiment shown in  FIG.  8   , and the electrostatic input apparatus  100  of the first embodiment can be executed. Here, an input determination method of a third modification of the input determination method of the first embodiment will be described as the input determination method of the fifth embodiment. In  FIG.  20   , the same processes as those of the steps shown in  FIGS.  8 ,  18 , and  19    are denoted by the same numbers. 
     In the fifth embodiment, the operation determining unit  154  calculates the ratio of the maximum value to the minimum value of the difference values at coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid), and if the ratio is higher than a third predetermined ratio, and the angle between a first line segment connecting the barycentric coordinates and the coordinates of the maximum value of the difference values and a second line segment connecting the barycentric coordinates and the coordinates of the minimum value of the difference values is larger than π/4 [rad] and smaller than 3π/4 [rad] or larger than 5π/4 [rad] and smaller than 7π/4 [rad], the operation determining unit  154  determines that an input operation using two or more fingers has been performed. 
     The steps S 1 , S 5 , S 6 , S 31 , S 41 , S 42 , S 43 , S 44 , S 45 , S 46 , and S 11  of the processing shown in  FIG.  20    are the same as those of the steps S 1 , S 5 , S 6 , S 31 , S 41 , S 42 , S 43 , S 44 , S 45 , S 46 , and S 11  shown in  FIG.  19   . 
     At step S 42 , the operation determining unit  154  determines whether the ratio of the identified maximum value to the identified minimum value (maximum value/minimum value) of the difference values is higher than a predetermined ratio (a third predetermined ratio) (step S 42 ). The predetermined ratio (the third predetermined ratio) used at step S 42  in  FIG.  20    differs in value from the predetermined ratio (the second predetermined ratio) used in step S 42  of  FIG.  19   . In the process shown in  FIG.  19   , if the ratio of the maximum value to the minimum value (maximum value/minimum value) of the difference values is higher than the predetermined ratio (the second predetermined ratio), it is determined that an input operation using two or more fingers has been performed. This requires to distinguish between one oblique finger F, as shown in  FIG.  3 A  and two fingers F and F′. For this reason, the predetermined ratio (the second predetermined ratio) is set at a relatively great value, which is greater than the predetermined ratio (the third predetermined ratio) at step S 42  in  FIG.  20   . In contrast, the processing shown in  FIG.  20    includes the process of step S 52  described below in addition to the determination process of step S 42 , and therefore, the predetermined ratio (the third predetermined ratio) may be lower than the predetermined ratio (the second predetermined ratio) at the step S 42  of  FIG.  19   . 
     After at step S 43  the operation determining unit  154  identifies the coordinates of the maximum value (or the minimum value) of the difference values at the sampling points on the measurement circle, the operation determining unit  154  calculates the angle between a line connecting the barycentric coordinates and the coordinates of the maximum value of the difference values and a line connecting the barycentric coordinates and the coordinates of the minimum value of the difference value (step S 51 ). If the sampling point showing the maximum value is in the direction of π/4 [rad] and the sampling point showing the minimum value is in the direction of 3π/4 [rad], as shown in  FIG.  21 A , the difference therebetween is π/2 [rad], as shown in  FIGS.  21 A and  21 B . For this reason, it can be determined that two fingers are present. 
     The operation determining unit  154  determines whether the angle between the first line segment connecting the barycentric coordinates and the coordinates of the maximum value of the difference values and the second line segment connecting the barycentric coordinates and the coordinates of the minimum value of the difference values is larger than π/4 [rad] and smaller than 3π/4 [rad] or larger than 5π/4 [rad] and smaller than 7π/4 [rad] (step S 52 ). 
     If at step S 52  the operation determining unit  154  determines YES, the processing goes to step S 44 . Thereafter, the processes of step S 45  and S 46  are performed as in the processing shown in  FIG.  19   . 
     Thus, the ratio of the maximum value to the minimum value of the difference values at coordinates on the circumference of a circle with a predetermined radius centered on the barycentric coordinates (xMid, yMid) is calculated, and if the ratio is higher than the third predetermined ratio, and the angle between the first line segment connecting the barycentric coordinates and the coordinates of the maximum value of the difference values and the second line segment connecting the barycentric coordinates and the coordinates of the minimum value of the difference values is larger than π/4 [rad] and smaller than 3π/4 [rad] or larger than 5π/4 [rad] and smaller than 7π/4 [rad], it can be determined that an input operation using two or more fingers has been performed. 
     Accordingly, this allows providing an electrostatic input apparatus capable of distinguishing between a state in which one finger extended diagonally is in contact with the electrostatic coordinate input unit and a state in which two or more fingers are in contact with the electrostatic coordinate input unit, and an input determination method for the same. This also provides an electrostatic input apparatus capable of calculating the central coordinates of two fingers with high accuracy and an input determination method for the same. 
     Having described electrostatic input apparatuses and input determination methods of exemplary embodiments of the present invention, it is to be understood that the present invention is not limited the specifically disclosed embodiments and various modifications and changes can be made without departing from the scope of the claims.