Patent Publication Number: US-11662860-B2

Title: Reference position setting method and operation detection device for displaying an operation surface as a virtual image

Description:
TECHNICAL FIELD 
     The present disclosure relates to a reference position setting method and an operation detection device of setting a reference position for detecting an operation. 
     BACKGROUND ART 
     Patent Literature 1 discloses a spatial coordinate input device that inputs coordinates in an actual space in which a virtual object is displayed. In the spatial coordinate input device, a screen to which an image for three-dimensionally displaying the virtual object is projected is provided in front of an operator, a magnetic field generating device that generates a magnetic field is provided behind the operator, and a position input device including a tip end portion configured to detect the magnetic field is held by the operator. The position input device is a device that inputs spatial coordinates at which the magnetic field is detected at the tip end portion to a control device. An optical measurement device including three TV cameras is provided around the operator. 
     In the above-described spatial coordinate input device, a corresponding relationship between the spatial coordinates input to the control device by the position input device and actual coordinates in the actual space is corrected by performing optical measurement using the optical measurement device. Specifically a grid plate in which a transparent plate is provided with scales with regular intervals is provided in the actual space. In addition, a pointer including a mark for image detection indicates a plurality of points on the grid plate, and the tip end portion of the position input device is disposed at the mark of the pointer. Then, the three TV cameras of the optical measurement device image the pointer to obtain a spatial coordinate value (that is, an optical coordinate value) indicating a position of the mark of the pointer. In addition, the tip end portion of the position input device detects a magnetic field to input a spatial coordinate value (that is, a magnetic coordinate value) indicating a position of the mark of the pointer to the control device. Then, the spatial coordinate input device obtains a 4×4 matrix for transforming the magnetic coordinate value to an optical coordinate value, and the magnetic coordinate value is transformed to the optical coordinate value by using the obtained matrix. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: Japanese Unexamined Patent Publication No. 2000-330709 
     SUMMARY OF INVENTION 
     Technical Problem 
     In the above-described spatial coordinate input device, calibration using the optical measurement device is performed as an operation for correcting a corresponding relationship between the spatial coordinates input to the control device by the position input device and the actual coordinates in the actual space. However, in order to perform calibration, it is necessary for the spatial coordinate input device to be provided with a large-scaled instrument including the grid plate provided in the actual space, and the optical measurement device including three TV cameras configured to detect the mark of the pointer that points a site on the grid plate. 
     The present disclosure is to provide a reference position setting method and an operation detection device which are not necessary to be provided with a large-scaled instrument for performing calibration and are capable of simplifying a device configuration. 
     Solution to Problem 
     A reference position setting method according to an aspect of the present disclosure is a reference position setting method of setting a reference position for detecting an operation on an operation surface displayed as a virtual image. The reference position setting method includes: a process of displaying at least three markers on the operation surface in such a manner that the at least three markers form vertices of a triangle; a process of acquiring coordinate values of the markers in a sensor coordinate system including a first Z-axis extending from a sensor toward the operation surface, and a first X-axis and a first Y-axis intersecting the first Z-axis, by the sensor detecting a target approaching the marker; a process of transforming the coordinate values acquired in the acquisition process into coordinate values in a temporary coordinate system including a second X-axis and a second Y-axis intersecting each other on a plane parallel to the operation surface; and a process of transforming the coordinate values transformed in the transformation process into coordinate values in a screen coordinate system including a third X-axis and a third Y-axis extending in directions parallel to the second X-axis and the second Y-axis on the operation surface, respectively. In the transformation process into the coordinate values in the temporary coordinate system, at least one of parallel movement and rotation is performed with respect to the sensor coordinate system to transform the sensor coordinate system into the temporary coordinate system. In the transformation process into the coordinate value in the screen coordinate system, movement of the temporary coordinate system in a direction parallel to a plane including the second X-axis and the second Y-axis, and enlargement or reduction of the temporary coordinate system are performed to transform the temporary coordinate system into the screen coordinate system. 
     An operation detection device according to the present disclosure is an operation detection device configured to set a reference position for detecting an operation on an operation surface displayed as a virtual image. The operation detection device includes: a display unit configured to display at least three markers on the operation surface in such a manner that the at least three markers form vertices of a triangle; a sensor configured to acquire coordinate values of the markers in a sensor coordinate system including a first Z-axis extending toward the operation surface, and a first X-axis and a first Y-axis intersecting the first Z-axis, by detecting a target approaching the markers; a first coordinate transformation unit configured to transform coordinate values of the markers in the sensor coordinate system into coordinate values in a temporary coordinate system including a second X-axis and a second Y-axis intersecting each other on a plane parallel to the operation surface; and a second coordinate transformation unit configured to transform the coordinate values of the markers in the temporary coordinate system into coordinate values in a screen coordinate system including a third X-axis and a third Y-axis extending in directions parallel to the second X-axis and the second Y-axis on the operation surface, respectively. The first coordinate transformation unit performs at least one of parallel movement and rotation with respect to the sensor coordinate system to transform the sensor coordinate system into the temporary coordinate system. The second coordinate transformation unit performs movement of the temporary coordinate system in a direction parallel to a plane including the second X-axis and the second Y-axis, and enlargement or reduction of the temporary coordinate system to transform the temporary coordinate system into the screen coordinate system. 
     In the reference position setting method and the operation detection device as described above, at least three markers for setting the reference position are displayed on the operation surface as a virtual image. The sensor acquires coordinate values of the markers in the sensor coordinate system by detecting a target approaching the markers displayed on the operation surface. The coordinate values in the sensor coordinate system are transformed into coordinate values in the temporary coordinate system, and then transformed into coordinate values in the screen coordinate system including the third X-axis and the third Y-axis located on the operation surface. Here, even when directly transforming the coordinate values of the markers in the sensor coordinate system displayed on the operation surface into the coordinate values in the screen coordinate system, conditions for obtaining a transformation coefficient matrix required for coordinate system transformation are insufficient, and thus it is difficult to directly transform the sensor coordinate system into the screen coordinate system. In the reference position setting method and the operation detection device as described above, at least one of parallel movement and rotation is performed with respect to the sensor coordinate system to transform the sensor coordinate system into the temporary coordinate system. In addition, movement of the temporary coordinate system in a direction parallel to a plane including the second X-axis and the second Y-axis, and enlargement or reduction of the temporary coordinate system are performed to transform the temporary coordinate system into the screen coordinate system. In this manner, the process of transforming the sensor coordinate system into the temporary coordinate system, and the process of transforming the temporary coordinate system into the screen coordinate system include processing of performing rotation of the coordinate system, and processing of performing enlargement or reduction of the coordinate system, respectively. According to this, conditions for obtaining the transformation coefficient matrix required for the coordinate system transformation can be satisfied, and transformation from the sensor coordinate system into the temporary coordinate system, and transformation from the temporary coordinate system into the screen coordinate system can be performed, respectively. As a result, the coordinate values of the markers in the screen coordinate system are obtained from the coordinate values of the markers in the sensor coordinate system, and thus another measurement instrument for actually measuring the coordinate values of the markers in the screen coordinate system is not necessary when performing calibration for setting the reference position. According to this, a configuration of the apparatus can be simplified. If actually measuring the coordinate values in the screen coordinate system by using another measurement instrument, a positional relationship of the markers may be distorted before and after the coordinate system transformation due to a measurement error of the measurement instrument or the like. According to the reference position setting method and the operation detection device as described above, since the coordinate values of the marker in the screen coordinate system are obtained from the coordinate values of the markers in the sensor coordinate system, the positional relationship of the markers before and after the coordinate system transformation is not distorted. That is, the transformation coefficient matrix required for the coordinate system transformation can be obtained with accuracy. Accordingly, the coordinate values of the markers in the sensor coordinate system can be transformed into the coordinate values in the screen coordinate system with accuracy, and calibration can be performed with accuracy. 
     In the transformation process into the coordinate value in the temporary coordinate system, a coordinate value of one marker among the at least three markers in the sensor coordinate system may be set as the origin of the temporary coordinate system. In this case, components of the coordinate value of the one marker in the temporary coordinate system become zero. According to this, a processing load in accordance with transformation from the sensor coordinate system into the temporary coordinate system, and a processing load in accordance with transformation from the temporary coordinate system into the screen coordinate system can be reduced, respectively. 
     In the transformation process into the coordinate values in the temporary coordinate system, a coordinate value of one marker among the at least three markers in the sensor coordinate system may be set as a coordinate value on the second X-axis of the temporary coordinate system, and a coordinate value of another one marker among the at least three markers in the sensor coordinate system may be set as a coordinate value on the second Y-axis of the temporary coordinate system. In this case, a component of the second Y-axis of the coordinate value of the one marker in the temporary coordinate system becomes zero, in addition, a component of the second X-axis of the coordinate value of the other one marker in the temporary coordinate system becomes zero. According to this, a processing load in accordance with transformation from the sensor coordinate system into the temporary coordinate system, and a processing load in accordance with transformation from the temporary coordinate system into the screen coordinate system can be reduced, respectively. 
     Advantageous Effects of Invention 
     According to the present disclosure, a large-scaled instrument for executing calibration is not necessary, and a device configuration can be simplified. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a perspective view illustrating a display apparatus including an operation detection device according to an embodiment. 
         FIG.  2    is a schematic configuration diagram illustrating the operation detection device in  FIG.  1   . 
         FIG.  3    is a view for describing a process of setting a reference position by the operation detection device in  FIG.  1   . 
         FIG.  4    is a block diagram illustrating a functional configuration of a control unit of the operation detection device in  FIG.  1   . 
         FIG.  5    is a view for describing a process of transforming a sensor coordinate system into a temporary coordinate system. 
         FIG.  6    is a view for describing a process of transforming the temporary coordinate system into a screen coordinate system. 
         FIG.  7    is a flowchart illustrating an example of a reference position setting method according to another embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of a reference position setting method and an operation detection device according to the present disclosure will be described with reference to the accompanying drawings. In description of the drawings, the same reference numeral will be given to the same or equivalent element, and redundant description will be appropriately omitted. The drawings are partially simplified or exaggerated for easy understanding, and dimension ratios and the like are not limited to description in the drawings. 
     In this embodiment, “target” is a target detected by a sensor, and operates an operation surface to cause a device to operate. For example, the “target” is a rod-shaped object such as a users finger. “Operation surface” represents a surface capable of causing a device to operate. For example, the “operation surface” is a plane on which a button such as a switch is displayed as a virtual image. “Sensor” is a sensor that detects operation on an operation unit by the target. “Reference position” is a position that becomes a reference for recognizing whether or not the operation surface is operated. For example, the “reference position” is a predetermined position with respect to the operation surface displayed as a virtual image. The predetermined position may be a position immediately above the operation surface displayed as a virtual image, or may be a position spaced apart from the operation surface by a predetermined distance. 
       FIG.  1    is a perspective view illustrating a display apparatus  1  including an operation detection device  2  according to this embodiment. The display apparatus  1  constructs a human machine interface (HMI) between a vehicle and a passenger of the vehicle. For example, the display apparatus  1  is installed at the central portion in a right and left direction of the vehicle. As illustrated in  FIG.  1   , the display apparatus  1  includes the operation detection device  2  that is provided on a rear side of the display apparatus  1  in a front and rear direction of the vehicle, and an image display device  3  that is provided on a front side of the display apparatus  1  in the front and rear direction of the vehicle. For example, the operation detection device  2  is provided at a flat portion  1   a  of the display apparatus  1 , and the image display device  3  is provided at an inclined portion  1   b  of the display apparatus  1 . The flat portion  1   a  is a portion that extends in both the front and rear direction and a right and left direction of the vehicle in the display apparatus  1 . The inclined portion  1   b  is a portion that extends diagonally upward from a front side of the flat portion  1   a.    
     For example, the operation detection device  2  displays an operation surface  5  for causing respective devices (for example, an in-vehicle back camera or an air conditioner) mounted in the vehicle to operate as a virtual image K. The operation detection device  2  includes a sensor  20  that detects a target F (refer to  FIG.  2   ) that approaches the operation surface  5 . For example, the operation surface  5  is a rectangular operation plane including a plurality of buttons  5   a  capable of operating the in-vehicle back camera. The “operation plane” represents a planar user interface capable of operating devices. When the sensor  20  detects the target F, the operation detection device  2  detects an operation by the target F on the operation surface  5  on the basis of a position of the target F detected by the sensor  20 . The operation detection device  2  causes respective devices to operate on the basis of the detected operation. According to the operation detection device  2 , operations of the devices become possible due to approaching of the target F toward the operation surface  5  displayed as the virtual image K, and thus physical buttons and the like are not necessary. 
     In this embodiment, meaning of “approaching” includes both a case where an arbitrary object comes into contact with another object, and a case where an arbitrary object is close another object up to a predetermined distance. Examples of the operation include a pressing operation, a tapping operation, and a sliding operation against the operation surface  5  by the target F, but the kind of the operation is not particularly limited. In this embodiment, as an operation on the operation surface  5 , the pressing operation on the buttons  5   a  is exemplified. The pressing operation includes both an operation of pressing down the buttons  5   a  on the operation surface  5 , and an operation of pushing up the buttons  5   a  on the operation surface  5 . 
     For example, the image display device  3  includes a display  3   a  that displays at least any one of vehicle information, road information, and degree-of-danger information. The information displayed by the operation detection device  2  and the image display device  3  may be read aloud by voice output from a voice output unit (not illustrated) provided in the display apparatus  1 . When the voice output from the voice output unit is associated with display by the operation detection device  2  and the image display device  3 , it is possible to provide more reliable information in a visible and audible manner. 
       FIG.  2    is a schematic configuration diagram illustrating the operation detection device  2 . As illustrated in  FIG.  2   , the operation detection device  2  includes a display unit  10 , the sensor  20 , and a control unit  30 . The display unit  10  displays the operation surface  5  in the air as the virtual image K. The display unit  10  includes an aerial imaging (AI) plate (registered trademark)  11  that is an aerial imaging element, and a liquid crystal panel  12 . For example, the AI plate  11  is manufactured by using a technology described in Japanese Patent No. 4865088. 
     For example, the liquid crystal panel  12  is a display of a personal computer (PC), a tablet terminal, and a portable terminal such as a portable telephone. The liquid crystal panel  12  displays an image on the basis of a signal output from the control unit  30 . The AI plate  11  is diagonally inclined with respect to the liquid crystal panel  12 . The image displayed by the liquid crystal panel  12  is displayed as the virtual image K at a position on a user (target F) side with respect to the AI plate  11  and the liquid crystal panel  12  by the AI plate  11 . An inclination angle of the AI plate  11  with respect to the liquid crystal panel  12  may be variable. 
     For example, the sensor  20  is a depth sensor, and is provided on a side opposite to the target F with the operation surface  5  interposed therebetween. For example, the sensor  20  is provided on a virtual straight line connecting the operation surface  5  and the target F, that is, at a position in front of the operation surface  5  that is the virtual image K. The sensor  20  acquires position data including information of a position (that is, a two-dimensional position) of the target F on a plane orthogonal to the virtual straight line, and information of a distance D from the target F to the sensor  20 . The sensor  20  outputs the acquired position data to the control unit  30  at a predetermined period (for example, 1/30 seconds). 
     For example, the sensor  20  measures a distance between the sensor  20  and respective points on an object existing in an imaging region including the target F by a time of flight (TOF) method. In the TOF method, the sensor  20  calculates flight time (that is, delay time) of light beams until reaching the sensor  20  after the light beams are reflected from the respective points on the object. In addition, the sensor  20  measures a distance between the sensor  20  and the respective points on the object from the calculated flight time and the speed of light. 
     The control unit  30  can communicate with the liquid crystal panel  12  and the sensor  20 . For example, the control unit  30  includes a storage unit such as a central processing unit (CPU) that executes a program, a read only memory (ROM), and a random access memory (RAM), an input/output unit, and a driver. Each function of the control unit  30  is realized when the input/output unit operates under the control by the CPU, and data reading-out and data writing in the storage unit are performed. An aspect and a disposition location of the control unit  30  are not particularly limited. 
     For example, the control unit  30  includes a determination unit  30   a  that determines whether or not the operation surface  5  is operated. The determination unit  30   a  performs determination on the basis of the position of the target F detected by the sensor  20 . The determination unit  30   a  determines whether or not the operation surface  5  is operated by the target F on the basis of position data input from the sensor  20 . The determination unit  30   a  determines whether the distance D between the target F and the sensor  20  is equal to or less than a threshold value T. When determining that the distance D is equal to or less than the threshold value T, the determination unit  30   a  determines that the target F arrives at a virtual determination surface  6 , and the operation surface  5  is operated. 
     When the determination unit  30   a  determines that the operation surface  5  is operated, for example, the above-described in-vehicle back camera operates. The determination surface  6  is a virtual plane formed at a site in which a distance from the sensor  20  is constant, and is provided at a proximity position of the operation surface  5 . In this embodiment, the position of the determination surface  6  matches the position of the operation surface  5 . That is, the determination surface  6  overlaps the operation surface  5 . However, the position of the determination surface  6  may be a position spaced apart from the operation surface  5  by a predetermined distance. 
     The operation detection device  2  configured as described above sets a reference position that becomes a reference for detecting the operation on the operation surface  5  by the target F. Setting of the reference position is executed, for example, at an initial operation of the operation detection device  2 , or at the time of maintenance of the operation detection device  2 . The operation detection device  2  sets the reference position by bringing the target F close to the operation surface  5  displayed by the display unit  10 . Hereinafter, setting of the reference position may be referred to as calibration. An execution procedure of the calibration will be described in detail with reference to  FIG.  3   ,  FIG.  4   ,  FIG.  5   , and  FIG.  6   . 
       FIG.  3    is a view for describing a process of setting the reference position by the operation detection device  2 . First, as illustrated in  FIG.  3   , the display unit  10  displays three markers M 1 , M 2 , and M 3  on the operation surface  5  as the virtual image K. Then, a user brings the target F close to each of the three markers M 1 , M 2 , and M 3  displayed on the operation surface  5 . Each of the markers M 1 , M 2 , and M 3  is a reference point for performing calibration, and has, for example, a circular shape. In this embodiment, a position of each of the markers M 1 , M 2 , and M 3  represents a central point of each of the markers M 1  M 2 , and M 3 . 
     The markers M 1 , M 2 , and M 3  are displayed at positions which are not aligned on the same straight line in the operation surface  5 . That is, the markers M 1 , M 2 , and M 3  are displayed to form vertices of a triangle in the operation surface  5 . In this embodiment, the markers M 1 , M 2 , and M 3  are displayed to form vertices of a right triangle in the operation surface  5 . The marker M 1  is located at a vertex connecting two right-angled sides of the right triangle in the operation surface  5 . A straight line connecting the markers M 1  and M 2 , and a straight line connecting the markers M 1  and M 3  are orthogonal to each other. Hereinafter, “the markers M 1 , M 2 , and M 3 ” may be collectively referred to as “markers M” for easy explanation. 
     When the target F approaches the markers M, the sensor  20  detects positions of the target F that has approached the markers M to acquire positions of the markers M as coordinate values in a sensor coordinate system C 1 . The sensor coordinate system C 1  is an XYZ orthogonal coordinate system with a position of the sensor  20  set as a reference. The sensor coordinate system C 1  has an origin S 1  at the position of the sensor  20 , and includes an X1-axis (first X-axis), a Y1-axis (first Y-axis), and a Z1-axis (first Z-axis) which are orthogonal to each other. The Z1-axis extends from the origin S 1  toward the operation surface  5 . For example, a direction in which the Z1-axis extends is a direction orthogonal to the operation surface  5 . For example, directions in which the X1-axis and the Y1-axis respectively extend are directions along a plane parallel to the operation surface  5 . For example, a unit of each of the X1-axis, the Y1-axis, and the Z1-axis is meter (m). 
     The coordinate values of the markers M in the sensor coordinate system C 1  are transformed into coordinate values of the markers M in a temporary coordinate system C 2 , and then are transformed into coordinate values of the markers M in a screen coordinate system C 3 . The temporary coordinate system C 2  is a virtual XYZ orthogonal system that is used in a process of transforming the coordinate values of the markers M in the sensor coordinate system C 1  into the coordinate values of the markers M in the screen coordinate system C 3 . The temporary coordinate system C 2  includes the origin S 2  on the operation surface  5 , and includes an X2-axis (second X-axis), a Y2-axis (second Y-axis), and a Z2-axis orthogonal to each other. For example, a position of the origin S 2  is a position of one of the three markers M 1 , M 2 , and M 3  displayed on the operation surface  5 . In this embodiment, the position of the origin S 2  of the temporary coordinate system C 2  is a position of the marker M 1 . 
     The Z2-axis of the temporary coordinate system C 2  extends from the origin S 2  to a side opposite to the sensor  20 . For example, a direction in which the Z2-axis extends is a direction orthogonal to the operation surface  5 , and matches the direction in which the Z1-axis of the sensor coordinate system C 1  extends. The X2-axis and the Y2-axis are located on a plane parallel to the operation surface  5 . In this embodiment, a position of the parallel plane is a position overlapping the operation surface  5 . The X2-axis is parallel to an X3-axis of the screen coordinate system C 3  on the operation surface  5 , and deviates from the X3-axis on the operation surface  5  in a direction orthogonal to the X3-axis by a predetermined distance. 
     The X2-axis of the temporary coordinate system C 2  passes through the markers M 1  and M 2  on the operation surface  5 . That is, the X2-axis is located on a straight line connecting the markers M 1  and M 2 . The Y2-axis of the temporary coordinate system C 2  is parallel to a Y3-axis of the screen coordinate system C 3  on the operation surface  5 , and deviates from the Y3-axis on the operation surface  5  in a direction orthogonal to the Y3-axis by a predetermined distance. The Y2-axis passes through the markers M 1  and M 3  on the operation surface  5 . That is, the Y2-axis is located on a straight line connecting the markers M 1  and M 3 . 
     The screen coordinate system C 3  includes an origin S 3  on the operation surface  5 , and includes the X3-axis (third X-axis), the Y3-axis (third Y-axis), and a Z3-axis orthogonal to each other. For example, the origin S 3  of the screen coordinate system C 3  is located at a vertex (in  FIG.  3   , a vertex on an upper-left side of the operation surface  5 ) displayed near the marker M 3  among four vertices of the rectangular operation surface  5 . The vertex is a vertex connecting a long side  5   b  and a short side  5   c  of the operation surface  5 . The Z3-axis extends from the origin S 3  to a side opposite to the sensor  20 . For example, a direction in which the Z3-axis extends is a direction orthogonal to the operation surface  5 , and matches the direction in which the Z1-axis of the sensor coordinate system C 1  extends and the direction in which the Z2-axis of the temporary coordinate system C 2  extends. The X3-axis overlaps the long side  5   b  of the operation surface  5 , and the Y3-axis overlaps the short side  5   c  of the operation surface  5 . 
     The control unit  30  performs transformation from the coordinate values of the markers M in the sensor coordinate system C 1  into the coordinate values of the Markers M in the temporary coordinate system C 2 , and transformation from the coordinate values of the markers M in the temporary coordinate system C 2  into the coordinate values of the markers M in the screen coordinate system C 3 .  FIG.  4    is a block diagram illustrating a functional configuration of the control unit  30 . As illustrated in  FIG.  4   , the control unit  30  includes a first coordinate transformation unit  31 , and a second coordinate transformation unit  32 . When receiving the coordinate values of the markers M in the sensor coordinate system C 1  from the sensor  20 , the first coordinate transformation unit  31  transforms the coordinate values of the markers M in the sensor coordinate system C 1  into the coordinate values of the markers M in the temporary coordinate system C 2 . The second coordinate transformation unit  32  transforms the coordinate values of the Markers M in the temporary coordinate system C 2  into the coordinate values of the markers M in the screen coordinate system C 3 . 
       FIG.  5    is a view for describing a process of transforming the coordinate values of the markers M in the sensor coordinate system C 1  into the coordinate values of the markers M in the temporary coordinate system C 2 . Transformation from the coordinate values of the markers M in the sensor coordinate system C 1  into the coordinate values of the markers M in the temporary coordinate system C 2  is performed by congruent affine transformation. By the way, the affine transformation is transformation that performs processing including rotation, parallel movement, scaling, and skew (that is, shearing) with respect to a coordinate system. Linearity is maintained before and after the affine transformation. That is, a straight line defined in a coordinate system before the affine transformation is maintained as the straight line without being bent in a coordinate system after the affine transformation. The congruent affine transformation is transformation that performs only rotation and parallel movement excluding scaling and skew in the above-described processing with respect to the coordinate system. The above-described “scaling” represents enlargement or reduction of scales of the coordinate system. 
     The first coordinate transformation unit  31  performs, for example, congruent affine transformation that performs only rotation and parallel movement with respect to the sensor coordinate system C 1  to transform the sensor coordinate system C 1  into the temporary coordinate system C 2 . Specifically, the first coordinate transformation unit  31  performs at least one of the parallel movement and the rotation with respect to the sensor coordinate system C 1  to transform the sensor coordinate system C 1  into the temporary coordinate system C 2 . For example, the above-described parallel movement represents movement from the origin S 1  of the sensor coordinate system C 1  to the origin S 2  of the temporary coordinate system C 2 . For example, the above-described rotation represents rotation around the origin  1 I of the sensor coordinate system C 1  before the parallel movement or after the parallel movement. When at least one of the above-described parallel movement and rotation is performed with respect to the sensor coordinate system C 1 , the sensor coordinate system C 1  is transformed into the temporary coordinate system C 2  including the X2-axis and the Y2-axis located on a plane (in this embodiment, a plane overlapping the operation surface  5 ) parallel to the operation surface  5 . 
     The congruent affine transformation from the sensor coordinate system C 1  to the temporary coordinate system C 2  will be described in more detail. As illustrated in  FIG.  3   , the coordinate values of the markers M 1 , M 2 , and M 3  in the sensor coordinate system C 1  are respectively set as P 1 , P 2 , and P 3 , and the coordinate values of the markers M 1 , M 2 , and M 3  in the temporary coordinate system C 2  are respectively set as Q 1 , Q 2 , and Q 3 . Components of the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  are acquired by detecting the target F by the sensor  20 . Components of the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  are obtained from the components of the coordinate values P 1 , P 2 , and P 3 . 
     In this embodiment, since the origin S 2  of the temporary coordinate system C 2  is located at the marker M 1 , components of the coordinate value Q 1  corresponding to the marker M 1  are expressed as (0, 0, 0). Since the X2-axis of the temporary coordinate system C 2  passes through the marker M 2 , components of the coordinate value Q 2  are expressed as (X2 q , 0, 0) when a component of the X2-axis of the coordinate value Q 2  corresponding to the marker M 2  is set as X2 q . Since the Y2-axis of the temporary coordinate system C 2  passes through the marker M 3 , components of the coordinate value Q 3  are expressed as (0, Y2 q , 0) when a component of the Y2-axis of a coordinate value Q 3  corresponding to the marker M 3  is set as Y2 q . 
     The first coordinate transformation unit  31  Obtains unknown X2 q  and Y2 q  from a positional relationship between the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1 . Specifically, the first coordinate transformation unit  31  obtains X2 q  by using the following Expression (1), and obtains Y2 q  by using the following Expression (2).
 
[Mathematical Formula 1]
 
 X 2 q −| |  (1)
 
[Mathematical Formula 2]
 
 Y 2 q =| |  (2)
 
     The first coordinate transformation unit  31  obtains components of the coordinate values Q 2  and Q 3  in the temporary coordinate system C 2  by obtaining X2 q  and Y2 q . When the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  before transformation, and the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  after transformation are obtained, a transformation coefficient matrix (details will be described later) for performing the congruent affine transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2  can be obtained. The first coordinate transformation unit  31  transforms the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  into the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  by obtaining the transformation coefficient matrix. 
       FIG.  6    is a view for describing a process of transforming the coordinate values Q 1 , Q 2 , and Q 3  of the markers M 1 , M 2 , and M 3  in the temporary coordinate system C 2  into coordinate values R 1 , R 2 , and R 3  of the markers M 1 , M 2 , and M 3  in the screen coordinate system C 3 . Due to the congruent affine transformation by the first coordinate transformation unit  31 , the sensor coordinate system C 1  is transformed into the temporary coordinate system C 2  including the X2-axis and the Y2-axis located on the operation surface  5 . As a result, the origin S 2  of the temporary coordinate system C 2  and the origin S 3  of the screen coordinate system C 3  are located on the operation surface  5  in combination. Accordingly, it is not necessary to perform the parallel movement in a direction in which the Z2-axis extends with respect to the temporary coordinate system C 2  so as to transform the temporary coordinate system C 2  into the screen coordinate system C 3 , and it is also not necessary to preform scaling of the Z2-axis. 
     However, the X2-axis and the Y2-axis of the temporary coordinate system C 2  respectively deviate from the X3-axis and the Y3-axis of the screen coordinate system C 3  on the operation surface  5 . Accordingly, in order to transform the temporary coordinate system C 2  into the screen coordinate system C 3 , it is necessary to match the positions of the X2-axis and the Y2-axis and the positions of the X3-axis and the Y3-axis in the screen coordinate system C 3  with each other. In addition, in order to match a scale of the X2-axis and a scale of the Y2-axis with a scale of the X3-axis and a scale of the Y3-axis, respectively, it is necessary to perform scaling of the X2-axis and the Y2-axis. 
     Here, with respect to the temporary coordinate system C 2 , the second coordinate transformation unit  32  performs movement in a direction parallel to a plane including the X2-axis and the Y2-axis, and scaling of the temporary coordinate system C 2  to transform the temporary coordinate system C 2  into the screen coordinate system C 3 . For example, in a case where components of the coordinate value R 1  are (100, 300, 0), and components of the coordinate value R 2  are (700, 300, 0), transformation from X2 including components (X2 q , 0, 0) of the coordinate value Q 2  into X3 is performed by using the following Expression (3), when a value on the X2-axis of the temporary coordinate system C 2  is set as X2, and a value on the X3-axis of the screen coordinate system C 3  is set as X3. 
     
       
         
           
             
               
                 
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     Transformation from the Y2-axis of the temporary coordinate system C 2  into the Y3-axis of the screen coordinate system C 3  is also performed in a similar manner. In this manner, the second coordinate transformation unit  32  transforms the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  into the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3 . 
     Next, the reference position setting method according to this embodiment will be described with reference to  FIG.  7   .  FIG.  7    is a flowchart illustrating an example of the reference position setting method according to this embodiment. The reference position setting method is performed by using the operation detection device  2 . First, the display unit  10  displays three markers M 1 , M 2 , and M 3  on the operation surface  5  (process W 1 ). At this time, the display unit  10  displays the three markers M 1 , M 2 , and M 3  on the operation surface  5  to form vertices of a triangle (refer to  FIG.  3   ). Then, a user brings the target F such as a finger close to each of the three markers M 1 , M 2 , and M 3 . 
     When the target F approaches the markers M, the sensor  20  detects the target F (process W 2 ). Specifically, the sensor  20  detects position data including the distance D between the sensor  20  and the target F, and outputs the position data to the control unit  30  (refer to  FIG.  2   ). When the control unit  30  receives the position data output from the sensor  20 , the determination unit  30   a  determines whether or not the distance D is equal to or less than the threshold value T. The determination unit  30   a  recognizes approaching of the target F to the markers M when determining that the distance D is equal to or less than the threshold value T. Detection of the target F by the sensor  20  is performed in accordance with recognition of approaching of the target F to the markers M by the determination unit  30   a . When the sensor  20  detects the target F, the control unit  30  acquires the coordinate values P 1 , P 2 , and P 3  of the markers M 1 , M 2 , and M 3  in the sensor coordinate system C 1  which are included in the position data output from the sensor  20 . 
     When the control unit  30  acquires the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1 , the first coordinate transformation unit  31  transforms the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  into the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  (process W 3 ). Specifically, the first coordinate transformation unit  31  performs the congruent of affine transformation that performs only rotation and parallel movement with respect to the sensor coordinate system C 1  to transform the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  into the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2 . 
     In this embodiment, as illustrated in  FIG.  5   , the first coordinate transformation unit  31  performs parallel movement and rotation with respect to the sensor coordinate system C 1 . When the first coordinate transformation unit  31  performs the above-described parallel movement and rotation, the sensor coordinate system C 1  is transformed into the temporary coordinate system C 2  including the X2-axis and the Y2-axis located on a plane (in this embodiment, a plane overlapping the operation surface  5 ) parallel to the operation surface  5 . 
     Next, the second coordinate transformation unit  32  transforms the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  into the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  (process W 4 ). Specifically, with respect to the temporary coordinate system C 2 , the second coordinate transformation unit  32  performs movement in a direction parallel to a plane including the X2-axis and the Y2-axis, and scaling of the temporary coordinate system C 2  to transform the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  into the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3 . 
     As described above, the first coordinate transformation unit  31  transforms the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  into the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2 , and the second coordinate transformation unit  32  transforms the coordinate values Q 1 , Q 2 , and Q 3  in the temporary coordinate system C 2  into the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3 . As a result, the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1 , and the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  are associated with each other, and thus a reference position for determining coordinate values of respective positions placed on the operation surface  5  are set (process W 5 ). Then, a series of processes are completed, and the calibration is completed. When the calibration is completed, the operation detection device  2  can be used to cause respective devices to operate. 
     Next, an operational effect of the reference position setting method and the operation detection device  2  according to this embodiment will be described in combination with a problem in the affine transformation. In the case of performing the affine transformation with respect to an arbitrary XYZ orthogonal coordinate system, the affine transformation from the coordinate value P into the coordinate value Q is expressed by the following Expression (4), when components of the coordinate value P before the affine transformation are set as (Xp, Yp, Zp), and components of the coordinate value Q after the affine transformation are set as (Xq, Yq, Zq). 
     
       
         
           
             
               
                 
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     In Expression (4), b is a transformation coefficient matrix representing parallel movement of the XYZ orthogonal coordinate system, and A is a transformation coefficient matrix representing rotation, scaling, and skew of the XYZ orthogonal coordinate system. In order to perform the affine transformation from the coordinate value P into the coordinate value Q, it is necessary to obtain respective coefficients (a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , and a 33 ) of the transformation coefficient matrix A, and respective coefficients (b 1 , b 2 , and b 3 ) of the transformation coefficient matrix b. 
     With regard to an X-axis, a Y-axis, and a Z-axis of the XYZ orthogonal coordinate system, four unknowns (that is, three coefficients of the transformation coefficient matrix A, and one coefficient of the transformation coefficient matrix b) exist. Accordingly, when four sets of combination of the coordinate value P and the coordinate value Q are present, all of the unknowns relating to the X-axis, the Y-axis, and the Z-axis can be obtained. That is, when acquiring four coordinate values P before the affine transformation, and four coordinate values Q after the affine transformation, the transformation coefficient matrices A and b can be obtained. It is conceivable to perform the calibration by using the affine transformation. For example, it is considered that four markers as a reference are displayed on the same plane, and respective coordinate values P representing positions of the respective markers in an arbitrary coordinate system are affine-transformed into respective coordinate values Q representing positions of respective markers in an additional coordinate system to perform association between the respective coordinate values P and the respective coordinate values Q. 
     However, even when performing the affine transformation from four coordinate values P located on the same plane (for example, a plane including an X-axis and a Y-axis of an arbitrary coordinate system) into four coordinate values Q, components of the Z-axis become the same as each other, and thus conditions for obtaining unknowns relating to each of the X-axis, the Y-axis, and the Z-axis become deficient. Accordingly, it is difficult to obtain the transformation coefficient matrices A and b. Accordingly, as described above, even when directly performing the affine transformation from the sensor coordinate system C 1  into the screen coordinate system C 3 , it is difficult to obtain the transformation coefficient matrices A and b, and thus it is difficult to directly transform the sensor coordinate system C 1  into the screen coordinate system C 3 . 
     In contrast, in the reference position setting method and the operation detection device  2  according to this embodiment, at least one of parallel movement and rotation is performed with respect to the sensor coordinate system C 1  to perform congruent affine transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2 . In addition, with respect to the temporary coordinate system C 2 , movement in a direction parallel to a plane including the X2-axis and the Y2-axis, and scaling of the temporary coordinate system C 2  are performed to transform the temporary coordinate system C 2  into the screen coordinate system C 3 . That is, in each of the process W 3  of transforming the sensor coordinate system C 1  into the temporary coordinate system C 2 , and the process W 4  of transforming the temporary coordinate system C 2  into the screen coordinate system C 3 , a process of performing rotation of the coordinate system and a process of performing scaling of the coordinate system are performed, respectively. 
     In this manner, when performing scaling and the like by using Expression (3) described above after performing transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2  by the congruent affine transformation, transformation from the temporary coordinate system C 2  into the screen coordinate system C 3  becomes possible. That is, when performing two-stage transformation including transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2  and transformation from the temporary coordinate system C 2  into the screen coordinate system C 3 , transformation into the screen coordinate system C 3  that becomes a reference of an operation on the operation surface  5  becomes possible. 
     As described above, since the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  are obtained from the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1 , another measurement instrument for actually measuring the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  is not necessary when performing the calibration. That is, in this embodiment, only the sensor  20  is the measurement instrument for performing the calibration. Accordingly, a device configuration can be simplified. 
     As an example in the case of using another measurement instrument, a method of actually measuring the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  by using a ruler, and of writing the coordinate values R 1 , R 2 , and R 3  in a program as an integer is considered. However, due to a normal measurement error in actual measurement of the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3 , or the like, a positional relationship of the markers M 1 , M 2 , and M 3  may be distorted before and after the coordinate system transformation. 
     As another factor that the positional relationship of the markers M 1 , M 2 , and M 3  is distorted, an accuracy difference that occurs between a length in the X1-axis and a length in the Y1-axis in the sensor coordinate system C 1  is considered. The operation surface  5  on which the markers M 1 , M 2 , and M 3  are displayed is displayed by the AI plate  11 . When the AI plate  11  displays the operation surface  5 , vector transformation by scaling and skew may be performed with respect to the operation surface  5 . 
     Even under the condition, according to the reference position setting method and the operation detection device  2  according to this embodiment, since the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  are obtained from the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1 , the positional relationship of the markers M 1 , M 2 , and M 3  before and after the coordinate system transformation is not distorted. That is, the transformation coefficient matrices A and b which are used in the coordinate system transformation can be obtained with accuracy. Accordingly, the coordinate values P 1 , P 2 , and P 3  in the sensor coordinate system C 1  can be transformed into the coordinate values R 1 , R 2 , and R 3  in the screen coordinate system C 3  with accuracy, and the calibration can be performed with accuracy. 
     A case where resolution in a longitudinal direction (that is, a direction in which the X3-axis of the screen coordinate system C 3  extends) of the operation surface  5  and resolution in a lateral direction (that is, a direction in which the Y3-axis of the screen coordinate system C 3  extends) are different from each other is also considered. However, according to the reference position setting method and the operation detection device  2  according to this embodiment, even in a case where a difference in the resolution exists, the positional relationship of the markers M 1 , M 2 , and M 3  is not distorted. 
     In this embodiment, the coordinate value P 1  of the marker M 1  in the sensor coordinate system C 1  is set as the origin S 2  of the temporary coordinate system C 2 . Accordingly, a component of the coordinate value P 1  of the marker M 1  in the temporary coordinate system C 2  becomes zero. According to this, it is possible to reduce a processing load in accordance with transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2 , and a processing load in accordance with transformation from the temporary coordinate system C 2  into the screen coordinate system C 3 . 
     In this embodiment, the coordinate value P 2  of the marker M 2  in the sensor coordinate system C 1  is set as the coordinate value Q 2  on the X2-axis of the temporary coordinate system C 2 , and the coordinate value P 3  of the marker M 3  in the sensor coordinate system C 1  is set as the coordinate value Q 3  on the Y2-axis of the temporary coordinate system C 2 . Accordingly, components of the Y2-axis and the Z2-axis of the coordinate value Q 2  in the temporary coordinate system C 2  become zero, respectively. In addition, components of the X2-axis and the Z2-axis of the coordinate value Q 3  in the temporary coordinate system C 2  become zero, respectively. According to this, it is possible to reduce the processing load in accordance with transformation from the sensor coordinate system C 1  into the temporary coordinate system C 2 , and the processing load in accordance with transformation from the temporary coordinate system C 2  into the screen coordinate system C 3 , respectively. 
     Hereinbefore, description has been given of an embodiment of the reference position setting method and the operation detection device according to the present disclosure. However, the present disclosure is not limited to the above-described embodiment, and may be modified or applied to another configuration within a range not departing from the gist described in the appended claims. For example, the content and procedure of the processes of the reference position setting method, and configuration of respective parts of the operation detection device can be appropriately modified within a range not departing from the gist of the appended claims. 
     For example, in the above-described embodiment, description has been given of an example in which the three markers M 1 , M 2 , and M 3  having a circular shape are displayed. However, the number of the markers may be greater than three. The shape of the markers is not particularly limited. For example, the shape of the markers may be a polygonal shape such as a triangular shape, a square shape, a hexagonal shape, or an octagonal shape, or an elongated circular shape such as an elliptical shape. 
     In the above-described embodiment, description has been given of an example in which the sensor coordinate system C 1 , the temporary coordinate system C 2 , and the screen coordinate system C 3  are orthogonal coordinate systems. However, it is not necessary for the X1-axis, the Y1-axis, and the Z1-axis of the sensor coordinate system C 1  to be orthogonal to each other, and the axes may intersect each other. Similarly, the X2-axis, the Y2-axis, and the Z2-axis of the temporary coordinate system C 2  may intersect each other, and the X3-axis, the Y3-axis, and the Z3-axis of the screen coordinate system C 3  may intersect each other. In the above-described embodiment, description has been given of an example in which the direction in which the Z1-axis of the sensor coordinate system C 1  extends is a direction orthogonal to the operation surface  5 . However, the direction in which the Z1-axis extends may be a direction inclined with respect to a direction orthogonal to the operation surface  5 . Directions in which the X1-axis and the Y1-axis of the sensor coordinate system C 1  extend may be directions intersecting the operation surface  5 . 
     In the above-described embodiment, description has been given of an example in which the position of the origin S 2  of the temporary coordinate system C 2  is the position of the marker M 1 . However, the position of the origin S 2  may be a position other than the marker M 1  on the operation surface  5 , and may be a position other than the operation surface  5 . In the above-described embodiment, description has been given of an example in which the direction in which the Z2-axis of the temporary coordinate system C 2  extends is a direction orthogonal to the operation surface  5  and matches the direction in which the Z1-axis of the sensor coordinate system C 1  extends. However, the direction in which the Z2-axis of the temporary coordinate system C 2  extends may be direction inclined with respect to a direction orthogonal to the operation surface  5 . 
     In the above-described embodiment, description has been given of an example in which the X2-axis and the Y2-axis of the temporary coordinate system C 2  are located on a plane parallel to the operation surface  5 , and a position of the parallel plane is a position overlapping the operation surface  5 . However, the position of the parallel plane may be a position deviating from the operation surface  5 . That is, it is not necessary for the X2-axis and the Y2-axis to be located on the operation surface  5 , and the axes may deviate from the operation surface  5  to a direction in which the Z2-axis extends. 
     In the above-described embodiment, description has been given of an example in which the X2-axis of the temporary coordinate system C 2  deviates from the X3-axis of the screen coordinate system C 3  in a direction orthogonal to the X3-axis by a predetermined distance on the operation surface  5 . However, the X2-axis may overlap the X3-axis, and may pass through a position other than the markers M 1  and M 2  on the operation surface  5 . Similarly, the Y2-axis of the temporary coordinate system C 2  may overlap the Y3-axis of the screen coordinate system C 3 , and may pass through a position other than the markers M 1  and M 3  on the operation surface  5 . 
     In the above-described embodiment, description has been given of an example in which the direction in which the Z3-axis of the screen coordinate system C 3  extends is, for example, a direction orthogonal to the operation surface  5 , and Matches the direction in which the Z1-axis of the sensor coordinate system C 1  extends and the direction in which the Z2-axis of the temporary coordinate system C 2  extends. However, the direction in which the Z3-axis extends may be a direction inclined with respect to a direction orthogonal to the operation surface  5 . 
     In the above-described embodiment, description has been given of an example in which the aerial imaging element is the AI plate  11  that images an image in the air. However, for example, the aerial imaging element may be a three-dimensional imaging element such as a hologram that images a three-dimensional virtual image in front of a user when viewed from the user, or may be an element other than the AI plate. 
     In the above-described embodiment, description has been given of the operation detection device  2  including the display unit  10 , the sensor  20 , and the control unit  30 . However, the kind, the shape, the size, the number, the material, and the arrangement aspect of the display unit, the sensor, and the control unit can be appropriately changed. For example, in the above-described embodiment, description has been given of the sensor  20  that is a depth sensor configured to detect the distance D from the target F. However, the operation detection device may include a sensor other than the depth sensor. That is, the operation detection device may include an infrared sensor, an ultrasonic sensor, or the like instead of the sensor, and the kind of the sensor can be appropriately changed. 
     In the above-described embodiment, description has been given of an example in which the sensor  20  measures the distance between the sensor  20  and respective points on an object by the TOF method. However, a method of measuring the distance between the sensor and respective points on the object is not limited to the TOF method. For example, the sensor may measure the distance between the sensor and respective points on the object by a light coding method. In the light coding method, the sensor irradiates respective points on the object existing within an imaging region including the target with light beams in a random dot pattern. Then, the sensor receives the light beams reflected from the respective points on the object, and detects deformation of the pattern of the reflected light beams to measure the distance between the sensor and the respective points on the object. 
     The operation detection device may be mounted on an apparatus other than a vehicle. In addition, the operation detection device may be a device that displays an operation surface for causing respective devices other than the vehicle to operate as a virtual image. The reference position setting method and the operation detection device are also applicable to various apparatuses other than the vehicle. The reference position setting method may be carried out by using a device other than the operation detection device. 
     REFERENCE SIGNS LIST 
       1 : display apparatus,  2 : operation detection device,  3 : image display device,  5 : operation surface,  10 : display unit,  20 : sensor,  30 : control unit,  31 : first coordinate transformation unit,  32 : second coordinate transformation unit, C 1 : sensor coordinate system, C 2 : temporary coordinate system, C 3 : screen coordinate system, F: target, K: virtual image, M 1 , M 2 , M 3 : marker, P 1 , P 2 , P 3 , Q 1 , Q 2 , Q 3 , R 1 , R 2 , R 3 : coordinate value, S 1 , S 2 , S 3 : origin, X1-axis: first X-axis, X2-axis: second X-axis, X3-axis: third X-axis, Y1-axis: first Y-axis, Y2-axis: second Y-axis, Y3-axis: third Y-axis, Z1-axis: first Z-axis.