JP2012088902A - Positional relation determination device, positional relation determination method and positional relation determination program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the accuracy of the inner/outer determination of an arbitrary point with respect to a polygon on the earth.SOLUTION: Selection means 1b selects sides 2a to 2d crossing a line 3 passing an object point P as the determination object of a positional relation between itself and a polygon 2 defined on the earth from among the sides of the polygon 2. Direction determination means 1c performs exterior product calculation using a first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the object point. Then, the direction determination means 1c determines the direction of the object point P with respect to each of all the selected sides according to the result of the exterior product calculation. The direction to be determined is either the inner direction of the internal side of the polygon 2 or the outer direction of the external side of the polygon with the selected side as a boundary. Inner/outer determination means 1d determines whether or not the object point is present at the internal side of the polygon 2 based on the number of times when it is determined that the direction to be determined is the inner direction and the number of times when it is determined that the direction to be determined is the outer direction.

Description

  The present invention relates to a positional relationship determination device, a positional relationship determination method, and a positional relationship determination program that determine the positional relationship between polygons and points on the earth.

  There is a technique for defining a polygonal region on the earth and determining whether a certain point is inside or outside the polygonal region. This technique is used, for example, for emergency rescue signal area identification and observation satellite observation area determination. When the area of the emergency rescue signal is specified, the rescue target area of each country is defined by a polygon, and it is determined whether or not the rescue signal transmission point is within the rescue target area. In the case of determining the observation satellite target area, the observation target area is defined by a polygon, and it is determined whether or not a point that can be observed by the observation satellite is within the observation target area.

  In the conventional inside / outside determination of a polygonal area on the earth, for example, a polygonal area whose apex is defined by latitude and longitude is projected onto a plane that expresses parallels and meridians as straight lines orthogonal to each other. An example of such a projection method onto a plane is the Mercator projection. The projected polygonal area is approximated to a polygon whose side is a straight line. Then, it is determined whether the point to be examined is inside or outside the approximated polygon. For example, count the number of intersections of polygons with axes extending north, south, east, and west from the input position.If the number of intersections of all axes is odd, it is within territorial waters, and if it is even, it is Determined.

JP 2000-99900 A

  However, the conventional polygon inside / outside determination method lacks accuracy because the sides of the polygon are approximated to a straight line. That is, the polygonal shape is defined by the coordinates (latitude, longitude) of the vertex. And the shortest path | route which connects between adjacent vertices along the surface of the earth becomes a polygon side. Strictly speaking, the shortest path connecting two points on the surface of the earth that is spherical is a curve, and if a side is approximated to a straight line on the projection plane, an error occurs in the polygonal region. Due to this error, the accuracy of the polygon inside / outside determination is insufficient.

  The present invention has been made in view of such points, and a positional relationship determination device, a positional relationship determination method, and a positional relationship that can improve the accuracy of internal / external determination of an arbitrary point with respect to a polygon on the earth. An object is to provide a judgment program.

In order to solve the above-described problem, a positional relationship determination apparatus having a selection unit, a direction determination unit, and an inside / outside determination unit is provided.
The selection means refers to a storage means for storing information on polygons defined on the earth, and among the sides of the polygon, a line passing through a target point that is a determination target of a positional relationship with the polygon Select the side that intersects with. The direction determining means includes a first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and the center of the earth to the target point. By calculating the outer product using the third vector, the position of the target point with respect to the selected side is determined by the inner side of the polygon and the outer side of the polygon from the selected side as a boundary. Which direction is determined for each of all selected sides. The inside / outside determining means determines whether or not the target point is inside the polygon based on the number of times determined to be the inward direction and the number of times determined to be the outward direction.

  In addition, there is provided a positional relationship determination method in which a computer executes a process similar to that of the positional relationship determination device. Furthermore, a positional relationship determination program for causing a computer to execute the same processing as that of the positional relationship determination device is provided.

  The accuracy of the inside / outside determination of an arbitrary point with respect to a polygon on the earth is improved.

It is a figure which shows the function of 1st Embodiment. It is a figure which shows the system configuration example of 2nd Embodiment. It is a figure which shows the observation range by an observation satellite. It is a figure which shows the example of 1 structure of the hardware of the satellite management apparatus used for 2nd Embodiment. It is a block diagram which shows the function of a satellite management apparatus. It is a figure which shows the example of a data structure of a satellite information storage part. It is a flowchart which shows the procedure of an object point calculation process. It is a figure which shows the example of a data structure of a target point memory | storage part. It is a figure which shows the example of a data structure of an observation object area | region memory | storage part. It is a figure which shows the example of the defined great circle. It is a figure which shows the example of inside / outside determination. It is a figure which shows the 1st example of a spherical triangle. It is a figure which shows the direction of the vector which the calculation result of the outer product of a 1st example shows. It is a figure which shows the 2nd example of a spherical triangle. It is a figure which shows the direction of the vector which the calculation result of the outer product of a 2nd example shows. It is a flowchart which shows the procedure of an inside / outside determination process. It is a figure which shows the example of the target point memory | storage part after an inside / outside determination. It is a figure which shows the example of the control command produced | generated. It is a figure which shows the precision of right-and-left determination.

Hereinafter, the present embodiment will be described with reference to the drawings.
[First Embodiment]
In the first embodiment, the sides of the polygon defined on the earth are not approximated to a straight line, and the point for which the positional relationship between the polygon and the polygon is determined is inside or outside the polygon. It is to determine whether there is.

  FIG. 1 is a diagram illustrating functions of the first embodiment. The positional relationship determination apparatus 1 according to the first embodiment includes a storage unit 1a, a selection unit 1b, a direction determination unit 1c, and an inside / outside determination unit 1d.

  The storage means 1a stores information on the polygon 2 defined on the earth. For example, the storage unit 1a stores coordinates indicating the position of the vertex of the polygon 2. The coordinates of the vertex are indicated by, for example, latitude and longitude. Each side of the polygon 2 is, for example, a curve obtained by connecting adjacent vertices with the shortest path along the ground surface. This curve is the arc of the great circle of the earth.

  The selection unit 1b refers to the storage unit 1a, and selects the sides 2a to 2d that intersect the line 3 passing through the target point P, which is the target of determination of the positional relationship with the polygon 2, out of the sides of the polygon 2 To do. Line 3 is, for example, the great circle of the earth. For example, a meridian passing through the target point P can be used as the line 3.

  The direction determination unit 1c determines the direction of the target point P with respect to the selected side for each of all the selected sides 2a to 2d. Specifically, the direction determining means 1c includes a first vector to one end of the selected side from the center of the earth, a second vector to the other end of the selected side from the center of the earth, and the center of the earth. The direction of the target point P is determined by calculating the outer product using the third vector 4c for the target point P.

  For example, the direction determination unit 1c sets a vector from the center of the earth to the front end with respect to the investigation direction in the selected side as the first vector. Moreover, the direction determination means 1c sets the vector from the center of the earth to the previous end with respect to the investigation direction in the selected side as the second vector. Further, the direction determining means 1c calculates a cross product obtained by multiplying the third vector 4c from the right of the first vector to generate a fourth vector. The direction determining unit 1c calculates a cross product obtained by multiplying the third vector 4c from the right by the second vector to generate a fifth vector. Then, the direction determining unit 1c determines the direction of the target point P with respect to the selected side based on the calculation result of the outer product obtained by multiplying the fourth vector from the right to the fifth vector.

  Note that the third vector 4c used in the direction determination of the target point P is common to all the selected sides 2a to 2d. The first vector and the second vector are individually generated for each of the selected sides 2a to 2d. For example, a first vector 4a and a second vector 4b are generated for the side 2a, and a first vector 4f and a second vector 4g are generated for the side 2c.

  The direction determining means 1c determines the position of the target point P with respect to the selected side based on the direction of the vector obtained as a result of the outer product calculation, and the inner direction and the polygon on the inner side of the polygon 2 with the selected side as a boundary. It is possible to determine which direction is the outer direction of the outer side of 2. For example, the direction determination means 1c determines the direction of investigation of the sides of the polygon. When the direction in which the side of the polygon is traced counterclockwise is determined as the investigation direction, the left side of the selected side is the inward direction, and the right side of the selected side is the outward direction. Further, when the direction in which the polygon side is traced clockwise is determined as the investigation direction, the right side of the selected side is the inward direction, and the left side of the selected side is the outward direction.

  When the direction in which the side of the polygon is traced in the counterclockwise direction is determined as the investigation direction, the direction determination unit 1c calculates the outer product calculated by multiplying the fourth vector from the right to the fifth vector by a vector in the geocentric direction. If there is, it is determined that the target point P is in the inward direction (left side). In addition, the direction determination unit 1c determines that the target point P is in the outer direction (right side) if the calculation result of the outer product obtained by multiplying the fourth vector by the fifth vector from the right is the vector in the zenith direction.

  When the direction in which the polygon side is traced clockwise is determined as the investigation direction, the direction determination unit 1c determines that the calculation result of the outer product obtained by multiplying the fourth vector from the right by the fifth vector is the zenith direction vector. It is determined that the target point P is in the inward direction (right side). The direction determining means 1c determines that the target point P is in the outer direction (left side) if the calculation result of the outer product obtained by multiplying the fourth vector by the fifth vector from the right is the vector in the geocentric direction.

  The inside / outside determination means 1d determines whether or not the target point P is inside the polygon 2 based on the number of times determined to be the inner direction and the number of times determined to be the outer direction. For example, the inside / outside determination unit 1d determines that the target point P is inside the polygon 2 if the number of times determined to be inward is greater than the number of times determined to be outward. The inside / outside determination means 1d determines that the target point P is outside the polygon 2 if the number of times determined to be the inner direction is equal to the number of times determined to be the outer direction.

  According to such a positional relationship determination apparatus 1, first, the selection means 1b selects the sides 2a to 2d that intersect the line 3 passing through the target point P. In the example of FIG. 1, four sides 2a to 2d are selected. Next, the direction determination unit 1c determines the direction of the target point P with respect to the selected side for each of the selected sides 2a to 2d. FIG. 1 shows a determination example for the sides 2a and 2c. In this example, the investigation direction is the counterclockwise direction.

  When determining the side 2a, the first vector 4a from the center of the earth to the end on the near side of the side 2a with respect to the survey direction, and the front side of the side 2a with respect to the survey direction from the center of the earth To the end of the second vector 4b. Next, a fourth vector 4d is generated by calculating an outer product obtained by multiplying the third vector 4c from the right of the first vector 4a. Further, a fifth vector 4e is generated by calculating an outer product obtained by multiplying the second vector 4b from the right of the third vector 4c. Then, the outer product obtained by multiplying the fourth vector 4d from the right by the fifth vector 4e is calculated. The calculation result of the outer product of the fourth vector 4d and the fifth vector 4e is a vector in the geocentric direction. Therefore, it is determined that the target point P is in the inward direction of the selected side 2a.

  When determining the side 2c, the first vector 4f from the center of the earth to the end on the near side of the side 2c with respect to the survey direction, and the front side of the side 2c with respect to the survey direction from the center of the earth To the end of the second vector 4g. Next, a fourth vector 4h is generated by calculating an outer product obtained by multiplying the third vector 4c from the right of the first vector 4f. Furthermore, a fifth vector 4i is generated by calculating an outer product obtained by multiplying the second vector 4g from the right of the third vector 4c. Then, the outer product of the fourth vector 4h multiplied by the fifth vector 4i from the right is calculated. The calculation result of the outer product of the fourth vector 4h and the fifth vector 4i is a vector in the zenith direction. Therefore, it is determined that the target point P is in the outward direction of the selected side 2c.

  Such a direction determination is performed for all of the selected sides 2a to 2d. Then, it is determined that the target point P is in the inner direction with respect to the sides 2a, 2b, and 2d, and the target point P is determined to be in the outer direction with respect to the side 2c.

  Thereafter, the inside / outside determination unit 1d determines whether or not the target point P is inside the polygon 2 based on the number of times determined to be the inner direction and the number of times determined to be the outer direction. In the example of FIG. 1, the number of times determined to be inward is three, and the number of times determined to be outward is one. Then, since the number of times determined to be the inner direction is greater than the number of times determined to be the outer direction, it is determined that the target point P is inside the polygon 2.

  In this way, by calculating the outer product with the vectors from both ends of the side from the center of the earth and the target point P, it is possible to perform the inside / outside determination without approximating the side to a straight line. As a result, the accuracy of the inside / outside determination is improved.

  Further, the vector outer product can be obtained by four arithmetic operations using components in the respective axial directions of the vector (for example, components in the X, Y, and Z axial directions of the orthogonal coordinate system), that is, an intersection of three-dimensional curves is obtained. Compared to a complicated calculation, the calculation is extremely simple. Therefore, it is possible to calculate at high speed.

  In addition, when observing the earth with observation satellites, polygons indicating the observation target region sometimes have vertices ranging from several hundred to thousands. In addition, when the target point to be determined is position information on the ground orbit traced from the satellite orbit, the number of repeated processing becomes enormous and the processing performance becomes a problem. Thus, as the number of repetitions increases, the efficiency of the inside / outside determination process for one target point becomes more important. That is, the positional relationship determination apparatus 1 according to the first embodiment is extremely useful for applications that perform internal / external determination of a huge number of target points.

[Second Embodiment]
In the second embodiment, the observation target area of the observation satellite is determined using the function of the positional relationship determination apparatus 1 shown in the first embodiment.

  FIG. 2 is a diagram illustrating a system configuration example according to the second embodiment. The satellite management apparatus 100 is connected to the transmission / reception station 21 via the network 10. The transmission / reception station 21 performs wireless communication with the observation satellite 22, transmits information such as a control command to the observation satellite 22, and receives information transmitted from the observation satellite 22. In the example of FIG. 2, the transmission / reception station 21 has the functions of a transmission station and a reception station, but the transmission station and the reception station may be provided separately.

  The satellite management apparatus 100 transmits a control command for the observation satellite 22 to the transmission / reception station 21 via the network 10. The control command is transmitted from the transmission / reception station 21 to the observation satellite 22. The observation satellite 22 performs attitude control and observation according to the control command sent from the transmission / reception station 21.

  The observation satellite 22 is equipped with an observation device such as a visible near infrared radiometer or a stereoscopic sensor. Visible and near-infrared radiometers are used to observe land and coastal areas using visible and near-infrared wavelengths. The stereoscopic sensor is an optical sensor that observes a visible range, and simultaneously acquires images in three directions of front view, direct view, and rear view. The observation satellite 22 observes the earth 20 using observation equipment in accordance with a control command sent from the ground transmitting / receiving station 21.

  In such a system, the observation target region by the observation satellite 22 may be limited to a predetermined polygonal region. For example, the observation target area may be limited to the Sea of Okhotsk for monitoring drift ice. In addition, in order to observe crustal deformation, the region where the crustal plate exists may be set as the observation target region. In addition, in order to monitor deforestation, the Amazon river basin may be the observation area. In addition, in order to explore underground resources, there are cases where areas where underground resources are expected to be buried are set as observation areas.

  When performing observation in the observation target region on the earth 20 using the observation satellite 22, the observation satellite 22 only needs to observe the region. At this time, when the observation target region cannot be accurately determined, the observation satellite 22 observes a wide range including the observation target region. When the observation range is widened, the amount of data such as image data collected by the observation satellite 22 increases, and the data collected by the observation satellite 22 may not be retained. In this case, leakage occurs in the observation result transmitted from the observation satellite 22 to the transmission / reception station 21. In order to suppress the occurrence of such observation omissions, it is appropriate to accurately determine the observation target area and to observe as little as possible in areas other than the observation target area.

  Therefore, in the second embodiment, in the satellite management apparatus 100, the position where the observation satellite 22 can be observed is set as the target point for the inside / outside determination, and it is accurately determined whether the target point is within the observation target region or outside the observation target region. to decide. Then, the satellite management apparatus 100 generates a control command indicating an observation instruction for the observation satellite 22 based on the determination result. By transmitting the generated control command to the observation satellite 22 via the transmission / reception station 21, it is possible to cause the observation satellite 22 to accurately observe only the observation target region.

  FIG. 3 is a diagram showing an observation range by the observation satellite. The observation satellite 22 orbits the earth. The trajectory of the point where the line drawn from the observation satellite 22 orbiting the orbit toward the center of the earth (the geocentric direction) intersects the ground surface is the ground trajectory 23.

  The observation satellite 22 can observe a range of a predetermined observation width D around the ground locus 23. While the observable range based on the ground trajectory 23 is in the observation target region 24, the observation satellite 22 is caused to perform the observation. The ground locus of the observation satellite 22 moves by the rotation of the earth every time the observation satellite 22 goes around the earth. For example, every time the observation satellite 22 goes around the earth, the ground locus 23 moves in the direction perpendicular to the ground locus 23 by the earth rotation speed × satellite period. As a result, when the observation satellite 22 orbits the earth by the number of times of return, the entire observation target region 24 can be observed by performing observation on the ground when the observation satellite 22 is above the observation target region 24.

  FIG. 4 is a diagram illustrating a configuration example of hardware of the satellite management device used in the second embodiment. The entire satellite management apparatus 100 is controlled by a CPU (Central Processing Unit) 101. A RAM (Random Access Memory) 102 and a plurality of peripheral devices are connected to the CPU 101 via a bus 108.

  The RAM 102 is used as a main storage device of the satellite management device 100. The RAM 102 temporarily stores at least part of an OS (Operating System) program and application programs to be executed by the CPU 101. The RAM 102 stores various data necessary for processing by the CPU 101.

  Peripheral devices connected to the bus 108 include a hard disk drive (HDD) 103, a graphic processing device 104, an input interface 105, an optical drive device 106, and a communication interface 107.

  The HDD 103 magnetically writes and reads data to and from the built-in disk. The HDD 103 is used as a secondary storage device of the satellite management device 100. The HDD 103 stores an OS program, application programs, and various data. Note that a semiconductor storage device such as a flash memory can also be used as the secondary storage device.

  A monitor 11 is connected to the graphic processing device 104. The graphic processing device 104 displays an image on the screen of the monitor 11 in accordance with a command from the CPU 101. Examples of the monitor 11 include a display device using a CRT (Cathode Ray Tube) and a liquid crystal display device.

  A keyboard 12 and a mouse 13 are connected to the input interface 105. The input interface 105 transmits a signal sent from the keyboard 12 or the mouse 13 to the CPU 101. The mouse 13 is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

  The optical drive device 106 reads data recorded on the optical disk 14 using laser light or the like. The optical disk 14 is a portable recording medium on which data is recorded so that it can be read by reflection of light. The optical disk 14 includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (ReWritable), and the like.

  The communication interface 107 is connected to the network 10. The communication interface 107 transmits and receives data to and from the transmission / reception station 21 and other computers via the network 10.

With the hardware configuration as described above, the processing functions of the present embodiment can be realized.
FIG. 5 is a block diagram illustrating functions of the satellite management apparatus. The satellite management apparatus 100 includes a satellite information storage unit 110, a target point calculation unit 120, a target point storage unit 130, an observation target region storage unit 140, a positional relationship determination unit 150, and a control command generation unit 160.

  The satellite information storage unit 110 stores information such as the orbit and attitude of the observation satellite 22 and the orientation of the observation device. For example, a part of the storage area of the RAM 102 or the HDD 103 is used as the satellite information storage unit 110.

  The target point calculation unit 120 calculates the target point based on information such as the orbit in the satellite information storage unit 110. The target point is a point on the ground trajectory 23 corresponding to the position of the observation satellite 22 for each observation time interval. The satellite management apparatus 100 generates a control command so that the observation satellite 22 performs observation when the target point falls within the observation target region. The target point calculation unit 120 stores the calculated target points in the target point storage unit 130.

  The target point storage unit 130 stores information regarding target points at each time at predetermined time intervals. The information regarding the target point includes information regarding the position of the target point and whether the target point is inside or outside the observation target region. For example, a part of the storage area of the RAM 102 or the HDD 103 is used as the target point storage unit 130.

  The observation target area storage unit 140 stores polygon definition information indicating the observation target area. The polygon indicating the observation target area is defined by, for example, coordinates of vertices constituting the polygon. Vertex coordinates can be indicated, for example, by latitude, longitude, and altitude. For example, a part of the storage area of the RAM 102 or HDD 103 is used as the observation target area storage unit 140.

  The positional relationship determination unit 150 determines whether the target point is inside or outside the observation target region. At that time, the positional relationship determination unit 150 recognizes the polygonal shape indicating the observation target region by referring to the information in the observation target region storage unit 140. Further, the positional relationship determination unit 150 recognizes the coordinates of the target point by referring to the information in the target point storage unit 130. When the inside / outside determination of the target point is completed, the positional relationship determination unit 150 stores the determination result in the target point storage unit 130. Note that the positional relationship determination unit 150 performs determination without approximating the sides of the polygon indicating the observation target area to a straight line when determining the inside / outside of the target point.

  The control command generation unit 160 generates a control command to be transmitted to the observation satellite 22. For example, the control command generation unit 160 generates a control command that performs observation during a period in which the target point is inside the observation target region and instructs to stop the observation when the target point is outside the observation target region. When observing forward observation or backward observation of the observation target region from the observation satellite 22, the control command generation unit 160 performs control so that observation is performed for a predetermined time before and after the time when the target point is inside the observation target region, for example. Commands can also be generated. The control command generation unit 160 transmits the generated control command to the transmission / reception station 21 via the network 10.

  For such a satellite management apparatus 100, the user operates an input device such as the keyboard 12 to input information related to the observation satellite 22 into the satellite information storage unit 110. In addition, the user operates an input device such as the keyboard 12 to input information on the vertexes of a polygon indicating the observation target area into the observation target area storage unit 140. When the user inputs a control command generation instruction, the target point calculation unit 120 first calculates the coordinates of the target point based on the positions of the observation satellites 22 at regular time intervals. For example, when observation is performed one week later, the coordinates of the target point are calculated from the orbit information of the observation satellite 22 one week later. The calculated coordinates of the target point are stored in the target point storage unit 130.

  When the calculation of the coordinates of the target point is completed, the positional relationship determination unit 150 determines whether the target point is inside or outside the observation target region. At this time, the polygon side indicating the observation target region remains a curve, and a highly accurate determination is performed. Based on whether each target point is inside or outside the observation target region, the control command generation unit 160 generates a control command for observing the inside of the observation target region.

  5 has the functions of the selection unit 1b, the direction determination unit 1c, and the inside / outside determination unit 1d in the first embodiment shown in FIG. Further, the observation target area storage unit 140 illustrated in FIG. 5 has the function of the storage unit 1a illustrated in FIG.

Next, each element of the satellite management apparatus 100 will be described in detail.
FIG. 6 is a diagram illustrating a data structure example of the satellite information storage unit. In the satellite information storage unit 110, observation condition information 111 and an orbital calendar file 112 are stored. The observation condition information 111 is information indicating conditions for causing the observation satellite 22 to observe the earth. The observation condition information 111 includes an orbital calendar file name, start / end times, calculation steps, satellite attitude, and sensor viewing angle.

  The orbital calendar file name is the name of the orbital calendar file including information defining the orbit of the observation satellite 22. The orbital calendar is position information of the observation satellite 22 at a desired time. The orbital calendar file includes information (orbital elements) necessary for calculating the orbit, for example.

  The start / end times are the observation start time and end time. A future time is set as the start time. The end time is a time later than the start time. The calculation step is a time interval for calculating the target point. The target point calculation unit 120 calculates target points at times for each calculation step from the start time to the end time.

  The attitude of the satellite is information indicating the attitude of the observation satellite 22. The posture is indicated by an angle around each axis of roll, pitch, and yaw. The sensor viewing angle is an angle in a direction perpendicular to the traveling direction of the observation satellite 22 that can be observed by the sensor.

  The orbital calendar file 112 includes orbital calendar information and the like. The orbital calendar information is information indicating the position of the observation satellite 22 at predetermined time intervals within a predetermined future time zone. The position of the observation satellite 22 is indicated by, for example, coordinates in the earth center inertial coordinate system.

The target point calculation unit 120 can calculate the target point with reference to the satellite information storage unit 110.
FIG. 7 is a flowchart showing the procedure of the target point calculation process. In the following, the process illustrated in FIG. 7 will be described in order of step number.

[Step S11] The target point calculation unit 120 acquires orbital calendar information from the start time to the end time indicated in the observation condition information 111 from the satellite information storage unit 110.
[Step S12] The target point calculation unit 120 sets the start time indicated in the observation condition information 111 as the calculation target time of the target point.

  [Step S13] The target point calculation unit 120 calculates the coordinates of the target point in the fixed earth coordinate system based on the orbital calendar information, the attitude of the satellite, and the sensor viewing angle. The fixed earth coordinate system is a three-dimensional orthogonal coordinate fixed to the earth with the center of the earth (for example, the center of gravity of the earth) as the origin.

  [Step S14] The target point calculation unit 120 converts the coordinates of the target point from the fixed earth coordinate system to the coordinates of the geodetic coordinate system. The geodetic coordinate system is a coordinate system defined by each country as a reference for map creation. In the geodetic coordinate system, the position is expressed using latitude, longitude, and altitude. The conversion from the earth fixed coordinate system to the geodetic coordinate system can be performed using a conversion matrix from orthogonal coordinates to polar coordinates. The altitude is a value obtained by correcting the distance from the origin represented by polar coordinates to the height from the sea level.

  [Step S15] The target point calculation unit 120 associates the coordinates (X, Y, Z) of the target point in the earth fixed coordinate system and the coordinates (latitude, longitude, altitude) in the geodetic coordinate system with the current calculation target time. To the target point storage unit 130.

  [Step S16] The target point calculation unit 120 determines whether or not the calculation target time has reached the end time indicated in the observation condition information 111. The target point calculation unit 120 ends the target point calculation process when the end time is reached. If the end time has not been reached, the target point calculation unit 120 proceeds with the process to step S17.

  [Step S17] The target point calculation unit 120 updates the calculation target time. For example, the target point calculation unit 120 adds the calculation step time indicated in the observation condition information 111 to the current calculation target time. Thereafter, the target point calculation unit 120 proceeds with the process to step S13.

In this way, the coordinates of the target point for each calculation step are calculated and stored in the target point storage unit 130.
FIG. 8 is a diagram illustrating a data structure example of the target point storage unit. The target point storage unit 130 stores a target point management table 131. The target point management table 131 includes columns for time, fixed earth coordinates, geodetic coordinates, right determination count, left determination count, and determination result. Information associated with the horizontal direction of each column is associated with each other and becomes information regarding one target point.

  In the time column, a time at which the target point can be observed is set. The time is expressed, for example, in International Atomic Time (TAI: Temps Atomique International (French)) counted from Modified Julian Day (MJD).

The coordinates of the target point in the fixed earth coordinate system are set in the fixed earth coordinate field. In the fixed earth coordinate system, the position of the target point is indicated by the coordinate values of the X axis, the Y axis, and the Z axis.
The coordinates of the target point in the geodetic coordinate system are set in the geodetic coordinate column. In the geodetic coordinate system, the position of the target point is indicated by latitude, longitude, and altitude.

The number of times that the target point is determined to be on the right side with respect to the polygonal side indicating the observation target region is set in the right determination number column.
In the left determination count column, the number of times that the target point is determined to be on the left side with respect to the polygonal side indicating the observation target region is set.

In the determination result column, a determination result indicating whether the target point is inside or outside the observation target region is set.
When the coordinates of the target point are calculated, the positional relationship determination unit 150 determines whether each target point is within the observation target region. The observation target area is defined in the observation target area storage unit 140.

  In the example of FIG. 8, information for one target point is set for one time, but information for a plurality of target points for one time is set in the target point management table 131. Also good. For example, the positions of both ends of the observation width D shown in FIG. 3 can be registered as target points in the target point management table 131. Further, when the observation satellite performs not only direct view but also forward view and backward view, the four corner points of the rectangular area including the front-rear direction can be registered as target points in the target point management table 131. When information on a plurality of target points is registered for the same time, for example, the control command generation unit 160 determines that at least one of the plurality of target points at the same time is inside the observation target region at that time. Generate control commands to perform observations.

  FIG. 9 is a diagram illustrating an example of the data structure of the observation target area storage unit. The observation target area storage unit 140 stores polygon data 141 indicating the shape of the observation target area. In the polygon data 141, columns of vertex number, latitude, longitude, and altitude are set.

  In the vertex number column, an identification number (vertex number) of each vertex constituting the polygon is set. In the latitude column, the latitude of the vertex is set. In the column of longitude, the longitude of the vertex is set. In the altitude column, the altitude from the top of the sea level is set.

Next, details of the determination process performed by the positional relationship determination unit 150 will be described.
When determining whether the target point is inside or outside the observation target region, the positional relationship determination unit 150 first defines a great circle (meridian) passing through the target point and the pole of the earth. The great circle of the earth is a circle formed by the intersection of the surface of the earth and a plane passing through the center of the earth.

  FIG. 10 is a diagram illustrating an example of a defined great circle. In the example of FIG. 10, the earth 31 is represented on the earth fixed coordinate system. The fixed earth coordinate system has an origin O at the center of the earth. The Z-axis is the conventional international origin (CIO) direction. The customary international origin is the average position of the Arctic 34 over the six years from 1900 to 1905. The direction from the origin O to the point where the prime meridian 32 and the equator 33 intersect is the X axis. The Y-axis is set to be a right-handed orthogonal coordinate system with respect to the Z-axis and the X-axis. The right-hand system is a coordinate system in which when the right hand thumb, index finger, and middle finger are bent so as to be orthogonal, the thumb is aligned with the X axis, the index finger is aligned with the Y axis, and the middle finger is aligned with the Z axis.

  Here, a great circle 37 passing through the target point P <b> 1, the north pole 34 and the south pole 35 is defined by the positional relationship determination unit 150. The angle from the prime meridian 32 to the great circle 37 is the longitude. Further, the angle formed between the equator plane (XY plane) and the zenith direction of the target point P1 is the latitude.

  The positional relationship determination unit 150 detects a side that intersects the great circle 37 among the polygonal sides indicating the observation target region 36. Then, the positional relationship determination unit 150 determines a side survey direction, and determines whether the target point P1 is on the right side or the left side with respect to the detected side survey direction. The positional relationship determination unit 150 counts the number of times determined to be the right side and the number of times determined to be the left side. The positional relationship determination unit 150 determines whether the target point is inside or outside the observation target region 36 by comparing the number of times determined to be the right side and the number of times determined to be the left side.

  For example, when the side investigation direction is counterclockwise, the positional relationship determination unit 150 determines that the target point P1 is inside the observation target region if the number of times determined to be the left side is large. The positional relationship determination unit 150 determines that the target point P1 is outside the observation target region if the number of determinations on the right side and the left side is the same.

  On the other hand, if the side direction is clockwise, the positional relationship determination unit 150 determines that the target point P1 is inside the observation target region if the number of times determined to be the right side is large. The positional relationship determination unit 150 determines that the target point P1 is outside the observation target region if the number of determinations on the right side and the left side is the same.

  FIG. 11 is a diagram illustrating an internal / external determination example. In FIG. 11, vertex numbers are shown beside each vertex of the polygon indicating the shape of the observation target region 36. In addition, an arrow next to the side of the polygon indicates the investigation direction of the side. In the example of FIG. 11, the observation target region 36 is a polygon represented by 20 vertices from the vertices V1 to V20. Therefore, the polygon indicating the observation target region 36 has 20 sides 41 to 60.

  First, consider a case where it is determined whether the target point P1 is inside or outside the observation target region 36. In this case, the positional relationship determination unit 150 detects a side that intersects the great circle 37 passing through the target point P <b> 1 among the polygonal sides 41 to 60. In the example of FIG. 11, there are a side 41 connecting the vertex V1 and the vertex V2, a side 53 connecting the vertex V13 and the vertex V14, a side 57 connecting the vertex V17 and the vertex V18, and a side 59 connecting the vertex V19 and the vertex V20. Detected.

  In the example of FIG. 11, it is determined whether the target point P1 is on the right side or the left side with respect to the detected sides 41, 53, 57, and 59 with the counterclockwise direction as the investigation direction. As a result, the target point P1 is on the left side with respect to the side 41, the target point P1 is on the left side with respect to the side 53, the target point P1 is on the right side with respect to the side 57, and the target point P1 with respect to the side 59 Is determined to be on the right. Then, the number of times determined to be the right side is 2, and the number of times determined to be the left side is 2, which is the same number. Therefore, it is determined that the target point P1 is outside the observation target region 36.

  Next, consider a case where it is determined whether the target point P2 is inside or outside the observation target region 36. In this case, the positional relationship determination unit 150 detects a side that intersects the great circle 38 that passes through the target point P2 from among the sides 41 to 60 of the polygon. In the example of FIG. 11, there are a side 43 connecting the vertex V3 and the vertex V4, a side 47 connecting the vertex V7 and the vertex V8, a side 49 connecting the vertex V9 and the vertex V10, and a side 51 connecting the vertex V11 and the vertex V12. Detected.

  Then, it is determined whether the target point P2 is on the right side or the left side with respect to the detected sides 43, 47, 49, 51 with the counterclockwise direction as the investigation direction. As a result, the target point P2 is on the left side with respect to the side 43, the target point P1 is on the right side with respect to the side 47, the target point P2 is on the left side with respect to the side 49, and the target point P2 with respect to the side 51 Is determined to be on the left. Then, the number of times determined as the right side is 1, the number of times determined as the left side is 3, and the number of times determined as the left side is larger. Therefore, it is determined that the target point P2 is inside the observation target region 36.

  By the way, polygonal sides 41 to 60 indicating the observation target region 36 are curves connecting the two vertices on the earth surface with the shortest distance. This curve is a great circle arc passing through the vertices at both ends of the side. The positional relationship determination unit 150 can accurately determine whether the target point is on the right side or the left side of the side (left / right determination) without approximating the side to a straight line.

Hereinafter, the method of left / right determination will be described in detail.
The positional relationship determination unit 150 generates a spherical triangle with the vertices at both ends of the sides (arcs) of the polygon where the great circles passing through the target point intersect and the target point.

FIG. 12 is a diagram illustrating a first example of a spherical triangle. In the example of FIG. 12, the side c between the vertex A and the vertex B is an investigation target. The direction from the vertex A to the vertex B is the investigation direction.
The target point C shown in FIG. 12 is located on the right side with respect to the survey direction of the side to be surveyed. In order to determine such a positional relationship, a spherical triangle composed of side c, side b between vertex A and target point C, and side a between target point C and vertex B is considered. Note that the side c is a great circle arc passing through the vertex A and the vertex B. The side b is an arc of a great circle passing through the vertex A and the target point C. The side a is an arc of a great circle passing through the target point C and the vertex B.

Here, a vector from the origin O to the vertex A aligned with the center of the earth is assumed to be a vector A. A vector from the origin O to the vertex B is defined as a vector B. A vector from the origin O to the target point C is a vector C. At this time, the positional relationship determination unit 150 calculates the following outer product.
Vector D = (Vector A × Vector C) × (Vector C × Vector B)
(1) FIG. 13 is a diagram illustrating the direction of a vector indicated by the outer product calculation result of the first example. FIG. 13 shows the orientation of each vector when looking down from the zenith direction of the target point C toward the origin O. That is, the direction of the vector C is from the back of FIG.

  “Vector A × Vector C” is a normal vector of a great circle passing through the vertex A and the target point C, and faces the direction in which the right-hand thread advances when the vector A is rotated from the vector A to the vector C. “Vector C × Vector B” is a normal vector of a great circle passing through the target point C and the vertex B, and is directed in the direction in which the right-handed screw advances when the vector C is rotated from the vector C to the vector B.

  The vector obtained as a result of the outer product of Expression (1) is directed in the direction in which the right-hand thread advances when the vector obtained by “vector A × vector C” is rotated to the vector obtained by “vector C × vector B”. Yes. Then, in the example of FIG. 13, it becomes a zenith direction vector. That is, if the calculation result of Expression (1) is a zenith direction vector, it can be determined that the target point C is on the right side with respect to the side c to be investigated.

  FIG. 14 is a diagram illustrating a second example of a spherical triangle. In the example of FIG. 14, the side c between the vertex A and the vertex B is the investigation target. The direction from the vertex A to the vertex B is the investigation direction.

  The target point C shown in FIG. 14 is located on the left side with respect to the survey direction of the side to be surveyed. In order to determine such a positional relationship, as in the first example shown in FIG. 12, the side c, the side b between the vertex A and the target point C, and the range between the target point C and the vertex B Consider a spherical triangle composed of side a. Then, the positional relationship determination unit 150 defines vectors from the origin O to the vertices A, B, and C, and calculates the outer product of Expression (1).

  FIG. 15 is a diagram illustrating the vector direction indicated by the outer product calculation result of the second example. FIG. 15 shows the direction of each vector when looking down from the zenith direction of the target point C toward the origin O. In the example of FIG. 15, the vector obtained as a result of the outer product of Expression (1) is the geocentric direction vector. That is, if the calculation result of Equation (1) is a geocentric direction vector, it can be determined that the target point C is on the left side with respect to the side c to be investigated.

  In this way, if the calculation result of Equation (1) is a zenith direction vector, the target point is on the right side of the side to be investigated, and conversely if the geocentric direction vector, the target point is on the left side of the side to be examined. I understand that there is.

Next, the procedure of the inside / outside determination process will be described.
FIG. 16 is a flowchart showing the procedure of the inside / outside determination process. In the following, the process illustrated in FIG. 16 will be described in order of step number. In the following processing, it is assumed that the polygon indicating the observation target region is investigated counterclockwise whether the target point is the right side or the left side of the side.

  [Step S21] The positional relationship determining unit 150 selects one target point. For example, the positional relationship determination unit 150 selects target points in order from the top of the target point management table 131 (see FIG. 8).

  [Step S22] The positional relationship determination unit 150 selects one side of the polygon that indicates the observation target region. For example, the positional relationship determination unit 150 first selects a side in the counterclockwise direction from the vertex of the vertex number “V1” of the polygon data 141 (see FIG. 9), and then sequentially selects the sides in the counterclockwise direction. To do.

  [Step S23] The positional relationship determination unit 150 determines whether the selected side intersects with a meridian passing through the target point. For example, the positional relationship determination unit 150 compares the longitudes of the vertices at both ends of the selected side with the longitude of the target point. For example, when the longitudes of the vertices at both ends of the selected side are u and v and the longitude of the target point is w, and the relationship of u <w ≦ v is satisfied, the positional relationship determination unit 150 targets the selected side. It is determined that it intersects the meridian passing through the point. When east longitude is represented by “+” and west longitude is represented by “−”, u, v, and w are real numbers of −180 or more and +180 or less, respectively.

  If the selected side intersects the meridian passing through the target point, the positional relationship determination unit 150 proceeds with the process to step S24. If the selected side does not intersect the meridian passing through the target point, the positional relationship determination unit 150 proceeds with the process to step S29.

[Step S24] The positional relationship determination unit 150 generates a spherical triangle by connecting the selected target point and the vertices at both ends of the selected side.
[Step S25] The positional relationship determination unit 150 calculates the outer product shown in Expression (1) for the generated spherical triangle.

  [Step S26] The positional relationship determination unit 150 determines whether or not the vector D obtained as a result of calculating the outer product of the equation (1) is a geocentric direction vector. For example, the positional relationship determination unit 150 generates a unit vector in the geocentric direction from the target point. Next, the positional relationship determination unit 150 calculates the inner product of the vector D and the unit vector in the geocentric direction. If the inner product calculation result is a positive value, the positional relationship determination unit 150 determines that the vector D is a geocentric direction vector. If the inner product calculation result is a negative value, the positional relationship determination unit 150 determines that the vector D is a zenith direction vector.

  If the outer product calculation result is the geocentric direction vector, the positional relationship determination unit 150 proceeds to step S27. If the outer product calculation result is the zenith direction vector, the positional relationship determination unit 150 proceeds to step S28.

  [Step S27] The positional relationship determination unit 150 determines that the target point is on the left side of the side if the result of the outer product of Equation (1) is a geocentric direction vector. Then, the positional relationship determination unit 150 increments the left determination count corresponding to the selected target point in the target point management table 131 (see FIG. 8) by one. The positional relationship determination unit 150 then advances the process to step S29.

  [Step S28] If the result of the outer product of Equation (1) is the zenith direction vector, the positional relationship determination unit 150 determines that the target point is on the right side of the side. Then, the positional relationship determination unit 150 increments the right determination count corresponding to the selected target point by 1 in the target point management table 131 (see FIG. 8).

  [Step S29] The positional relationship determination unit 150 determines whether or not all the sides of the polygon indicating the observation target region have been examined for the selected target point. If all sides have been examined, the positional relationship determination unit 150 proceeds with the process to step S30. If there is an unexamined side, the positional relationship determination unit 150 proceeds with the process to step S22.

  [Step S30] When the survey of all sides for the selected target point is completed, the positional relationship determination unit 150 refers to the target point management table 131 and compares the left determination count and the right determination count for the selected target point. . If the number of left determinations is greater, the positional relationship determination unit 150 proceeds with the process to step S31. If the left determination count is equal to the right determination count, the positional relationship determination section 150 advances the process to step S32.

  [Step S31] When the left determination count is larger, the positional relationship determination unit 150 determines that the selected target point is inside the observation target region. Then, the positional relationship determination unit 150 sets the determination result “inside” in the target point management table 131 in association with the selected target point. Thereafter, the positional relationship determination unit 150 proceeds with the process to step S33.

  [Step S32] The positional relationship determination unit 150 determines that the selected target point is outside the observation target region when the left determination count and the right determination count are the same. Then, the positional relationship determination unit 150 sets the determination result “outside” in the target point management table 131 in association with the selected target point.

  [Step S33] The positional relationship determination unit 150 determines whether or not all target points have been investigated. When the investigation of all target points is completed, the positional relationship determination unit 150 ends the inside / outside determination process. If there is an uninvestigated target point, the positional relationship determination unit 150 proceeds with the process to step S21.

In this manner, the inside / outside determination of all target points can be performed.
FIG. 17 is a diagram illustrating an example of the target point storage unit after the inside / outside determination. As a result of the inside / outside determination, the determination result is registered in the right determination, left determination, and determination result fields for each target point in the target point management table 131. The control command generation unit 160 refers to the target point management table 131 and generates a control command for the observation satellite 22.

  For example, in the example of FIG. 17, the target point at time T1 is outside the observation target region, but the target point at time T2 is inside the observation target region. Therefore, the control command generation unit 160 generates a control command for starting observation at time T2. The target point at time T11 is inside the observation target area, but the target point at time T12 is outside the observation target area. Therefore, the control command generator 160 generates a control command for ending the observation at time T12.

  FIG. 18 is a diagram illustrating an example of the generated control command. FIG. 18 shows a control command sequence 61 in which a plurality of control commands are arranged in the order of execution. An execution time is set in the control command. For example, the execution time of the control command for instructing the start of observation is T2. In addition, the execution time of the control command for instructing the observation stop is T12.

  Such a control command sequence 61 is transmitted to the observation satellite 22 via the transmission / reception station 21. The observation satellite 22 stores the received control command sequence 61 in the memory. Then, the observation satellite 22 sequentially executes the control commands that have reached the execution time.

  As described above, when the observation satellite 22 performs the observation, the inside / outside determination of the target point is accurately performed, and therefore the observation satellite 22 can be accurately observed only in the observation target region. That is, when determining whether the target point is inside or outside the observation target region, the side of the polygon is handled as an arc, so that no error occurs when the side is approximated to a straight line. Therefore, even when the target point is in the vicinity of the side to be investigated, the right / left determination can be performed accurately.

  FIG. 19 is a diagram illustrating the accuracy of the left / right determination. FIG. 19A is a diagram showing a positional relationship represented by the Mercator projection. FIG. 19B is a diagram illustrating a positional relationship when looking down from the zenith direction of the target point in the geocentric direction.

  In the Mercator projection, latitude and meridians are represented by straight lines. In the example of FIG. 19A, the vertex A and the vertex B are on the same latitude line 71. A side 72 between the vertex A and the vertex B is an investigation target. The direction from the vertex A to the vertex B is the investigation direction. Here, the side 72 is an arc of a great circle. Therefore, if the vertex A and the vertex B are in the northern hemisphere of the earth, the side 72 curves upward from the latitude line 71.

  In the example of FIG. 19, the target point C is slightly above the latitude line 71 (near north) and below the side 72 (south south). If the side 72 connecting the vertex A and the vertex B is approximated to a straight line on the Mercator projection, the target point C is determined to be on the right side of the side 72 to be investigated.

  On the other hand, as in the second embodiment, if the left / right determination is performed with the side 72 left in an arc, the target point C can be determined to be on the left side of the side 72 to be investigated. In this way, an accurate left / right determination result can be obtained by performing left / right determination with the side being in an arc. As a result, the inside / outside determination result is also accurate.

In addition, since the left / right determination can be performed by vector cross product calculation, high-speed arithmetic processing is possible. In other words, the outer product calculation of the vector of equation (1) can be calculated in detail as follows.
First, each vector is represented by a component in each axial direction in the orthogonal coordinate system. For example, suppose that vector A = (A _x , A _y , A _z ), vector B = (B _x , B _y , B _z ), vector C = (C _x , C _y , C _z ). Further, “vector A × vector C = vector E = (E _x , E _y , E _z )” and “vector C × vector B = vector F = (F _x , F _y , F _z )” are assumed. In this case, the vector E and the vector F are expressed by the following equations using the components of the vectors A, B, and C in the respective axial directions.
Vector E = (E _x , E _y , E _z )
_{= (A y C z -C y} A z, A z C x -C z A x, A x C y -C x A y) ··· (2)
Vector F = (F _x , F _y , F _z )
_{= (C y B z -B y} C z, C z B x -B z C x, C x B y -B x C y) ··· (3)
Then, the vector D shown in Formula (1) is represented as follows from Formula (2) and Formula (3).
Vector D = (D _x , D _y , D _z )
_{= (E y F z -F y} E z, E z F x -F z E x, E x F y -F x E y) ··· (4)
When the components in the axial direction of the vector D are replaced with the components in the axial directions of the vector A, the vector B, and the vector C, the following is obtained.
_{D x = (A z C x} -C z A x) (C x B y -B x C y) - (C z B x -B z C x) (A x C y -C x A y)
... (5)
_{D y = (A x C y} -C x A y) (C y B z -B y C z) - (C x B y -B x C y) (A y C z -C y A z)
... (6)
D _z = (A _y C _z −C _y A _z ) (C _z B _x −B _z C _x ) − (C _y B _z −B _y C _z ) (A _z C _x −C _z A _x )
... (7)
Thus, the vector D, which is the calculation result of the outer product of the expression (1), is expressed by the expressions (4) to (7) using the components of the vectors A, B, and C in the respective axial directions. These equations are numerical arithmetic operations, and can be calculated at high speed by the CPU 101. Therefore, the inside / outside determination of each target point can be executed at high speed.

  In addition, Formula (4)-Formula (7) are the examples which calculated the outer product with the coordinate value of the orthogonal coordinate system. In this way, when calculating the outer product in the orthogonal coordinate system, the positional relationship determination unit 150 replaces the altitude of the vertex shown in the polygon data 141 shown in FIG. 9 with the distance from the center of the earth, and the latitude / longitude / altitude Is converted to a value in the earth fixed coordinate system which is an orthogonal coordinate system.

Also, the vector outer product can be calculated using components in the polar coordinate system.
[Other Embodiments]
In the second embodiment, altitude information is also included in the coordinates of the target point and the vertex of the polygon indicating the observation target area, but all the altitudes are unified at a predetermined value (for example, 0 m above sea level). May be. Since the direction of the vector D, which is the outer product calculation result of the expression (1) shown in the second embodiment, is not affected by the altitude value, the same result for the left / right determination even if the altitude is unified to a predetermined value Can be obtained.

  Further, the inside / outside determination technique shown in the second embodiment can be used in various fields other than the determination of the observation target region by the observation satellite. For example, it can be used for area identification technology for emergency rescue signals.

  Currently, a ship rescue signal is transmitted as a digital signal from a buoy with a GPS (Global Positioning System) function. Rescue signals transmitted from buoys are caught by artificial satellites and transmitted to marine rescue organizations in neighboring countries. Then, in each country's maritime rescue organization, it is determined which country the responsible signal is transmitted from. The responsible area in each country is defined by a polygon whose vertex is a point designated by latitude and longitude. Therefore, the inside / outside determination process described in the first or second embodiment can be applied to the determination of whether the source of the rescue signal is inside or outside the polygon indicating the assigned area. By applying the internal / external determination processing described in the first or second embodiment to the determination of which country the rescue signal is in the area in charge, it is possible to quickly and accurately determine the country in charge of the rescue operation. Can do.

  The above processing functions can be realized by a computer. In that case, a program describing the processing contents of the functions that the positional relationship determination device and the satellite management device should have is provided. By executing the program on a computer, the above processing functions are realized on the computer. The program describing the processing contents can be recorded on a computer-readable recording medium. Examples of the computer-readable recording medium include a magnetic storage device, an optical disk, a magneto-optical recording medium, and a semiconductor memory. Examples of the magnetic storage device include a hard disk device (HDD), a flexible disk (FD), and a magnetic tape. Optical discs include DVD, DVD-RAM, CD-ROM / RW, and the like. Magneto-optical recording media include MO (Magneto-Optical disc).

  When distributing the program, for example, a portable recording medium such as a DVD or a CD-ROM in which the program is recorded is sold. It is also possible to store the program in a storage device of a server computer and transfer the program from the server computer to another computer via a network.

  The computer that executes the program stores, for example, the program recorded on the portable recording medium or the program transferred from the server computer in its own storage device. Then, the computer reads the program from its own storage device and executes processing according to the program. The computer can also read the program directly from the portable recording medium and execute processing according to the program. Further, each time the program is transferred from the server computer, the computer can sequentially execute processing according to the received program.

  In addition, at least a part of the above processing functions can be realized by an electronic circuit such as a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), or a PLD (Programmable Logic Device).

  As mentioned above, although embodiment was illustrated, the structure of each part shown by embodiment can be substituted by the other thing which has the same function. Moreover, other arbitrary structures and processes may be added. Further, any two or more configurations (features) of the above-described embodiments may be combined.

The techniques disclosed in the above embodiments include the techniques shown in the following supplementary notes.
(Supplementary note 1) A line passing through a target point that is a target of determination of a positional relationship with the polygon, among the sides of the polygon, with reference to storage means for storing information on the polygon defined on the earth A selection means for selecting an edge intersecting with
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. Direction determination means for determining whether each of the selected sides is a direction of
An inside / outside determination means for determining whether or not the target point is inside the polygon, based on the number of times determined to be an inward direction and the number of times determined to be an outward direction;
The positional relationship determination apparatus characterized by having.

  (Supplementary Note 2) The direction determining means generates a fourth vector by calculating a cross product obtained by multiplying the third vector from the right of the first vector, and generates the fourth vector from the right of the third vector. The target product for the selected edge is calculated based on the calculation result of the outer product multiplied by the fifth vector from the right of the fourth vector. The positional relationship determination apparatus according to appendix 1, wherein the direction of the position is determined.

  (Additional remark 3) The said direction determination means makes the direction which follows the side of the said polygon counterclockwise, and makes the vector from the center of the earth to the near end with respect to this investigation direction in the selected side. The first vector, the vector from the center of the earth to the end of the selected side toward the end of the survey direction is the second vector, and the fifth vector from the right of the fourth vector If the calculated cross product is a vector in the geocentric direction, it is determined that the target point is in the inward direction, and if the cross product is a vector in the zenith direction, the target point is determined to be in the outward direction. The positional relationship determination apparatus according to any one of appendix 1 or 2, wherein:

  (Supplementary Note 4) The direction determination means uses a direction in which the sides of the polygon are traced clockwise as a survey direction, and a vector from the center of the earth to the front end with respect to the survey direction in the selected side. The first vector, the vector from the center of the earth to the end of the selected direction on the selected side to the previous end is the second vector, and the fifth vector is multiplied from the right of the fourth vector. If the outer product calculation result is a vector in the zenith direction, it is determined that the target point is in the inward direction. If the outer product calculation result is a vector in the geocentric direction, it is determined that the target point is in the outer direction. The positional relationship determination apparatus according to any one of Supplementary Note 1 or 2, wherein:

  (Additional remark 5) The said inside / outside determination means will determine with the said target point being inside the said polygon, if the frequency | count determined to be an inner direction is more than the frequency | count determined to be an outer direction, and the frequency | count determined as an inner direction and outer The positional relationship determination apparatus according to any one of Supplementary notes 1 to 4, wherein if the number of times determined as a direction is the same, the target point is determined to be outside the polygon.

(Supplementary note 6) The positional relationship determination device according to any one of supplementary notes 1 to 5, wherein the line passing through the target point is a great circle of the earth passing through the target point.
(Appendix 7) Based on information indicating the orbit of the future observation satellite, for each future time at a predetermined time interval, a point where the observation satellite can be observed is calculated at that time, and the calculated point is set as the target point. The positional relationship determination apparatus according to any one of appendices 1 to 6, further comprising target point calculation means for storing in the storage means.

(Appendix 8) The computer
Reference is made to storage means for storing polygon information defined on the earth, and among the sides of the polygon, the side that intersects the line passing through the target point that is the target of the positional relationship with the polygon Select
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. For each of the selected sides, and
Based on the number of times determined to be inward and the number of times determined to be outward, it is determined whether or not the target point is inside the polygon.
The positional relationship determination method characterized by this.

(Supplementary note 9)
Reference is made to storage means for storing polygon information defined on the earth, and among the sides of the polygon, the side that intersects the line passing through the target point that is the target of the positional relationship with the polygon Select
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. For each of the selected sides, and
Based on the number of times determined to be inward and the number of times determined to be outward, it is determined whether or not the target point is inside the polygon.
A positional relationship determination program characterized by causing a process to be executed.

DESCRIPTION OF SYMBOLS 1 Position relationship determination apparatus 1a Memory | storage means 1b Selection means 1c Direction determination means 1d Inside / outside determination means 2 Polygon 2a-2d Side 3 Line 4a, 4f 1st vector 4b, 4g 2nd vector 4c 3rd vector 4d, 4h 4th vector 4e, 4i 5th vector P Target point

Claims (7)

Reference is made to storage means for storing polygon information defined on the earth, and among the sides of the polygon, the side that intersects the line passing through the target point that is the target of the positional relationship with the polygon A selection means for selecting
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. Direction determination means for determining whether each of the selected sides is a direction of
An inside / outside determination means for determining whether or not the target point is inside the polygon, based on the number of times determined to be an inward direction and the number of times determined to be an outward direction;
The positional relationship determination apparatus characterized by having.   The direction determining means calculates a cross product obtained by multiplying the third vector from the right of the first vector to generate a fourth vector, and multiplies the second vector from the right of the third vector. The fifth product is generated by calculating the outer product, and the direction of the target point with respect to the selected side is determined based on the calculation result of the outer product obtained by multiplying the fifth vector from the right of the fourth vector. The positional relationship determination apparatus according to claim 1, wherein:   The direction determining means uses a direction in which the sides of the polygon are traced in the counterclockwise direction as a survey direction, and a vector from the center of the earth to a front end of the selected side with respect to the survey direction. A vector that is a vector from the center of the earth to the previous end in the selected direction on the selected side as the second vector, and the right product of the fourth vector multiplied by the fifth vector If the calculation result of is a vector in the geocentric direction, it is determined that the target point is in the inner direction, and if the calculation result of the outer product is a vector in the zenith direction, it is determined that the target point is in the outer direction. The positional relationship determination apparatus according to claim 2, wherein   The direction determining means uses a direction in which the sides of the polygon are traced clockwise as a survey direction, and a vector from the center of the earth to a front end with respect to the survey direction in the selected side is the first vector. And the vector from the center of the earth to the end of the selected side in the selected direction is the second vector, and the outer product of the right side of the fourth vector multiplied by the fifth vector If the calculation result is a vector in the zenith direction, it is determined that the target point is in the inward direction, and if the calculation result of the outer product is a vector in the geocentric direction, it is determined that the target point is in the outer direction. The positional relationship determination apparatus according to claim 2.   The inside / outside determining means determines that the target point is inside the polygon if the number of times determined to be inward is greater than the number of times determined to be outward, and determines the number of times determined to be inward and the outward direction. The positional relationship determination apparatus according to claim 1, wherein if the number of times is the same, the target point is determined to be outside the polygon. Computer
Reference is made to storage means for storing polygon information defined on the earth, and among the sides of the polygon, the side that intersects the line passing through the target point that is the target of the positional relationship with the polygon Select
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. For each of the selected sides, and
Based on the number of times determined to be inward and the number of times determined to be outward, it is determined whether or not the target point is inside the polygon.
The positional relationship determination method characterized by this. On the computer,
Reference is made to storage means for storing polygon information defined on the earth, and among the sides of the polygon, the side that intersects the line passing through the target point that is the target of the positional relationship with the polygon Select
A first vector from the center of the earth to one end of the selected side, a second vector from the center of the earth to the other end of the selected side, and a third vector from the center of the earth to the point of interest The position of the target point with respect to the selected side is calculated as either the inner direction on the inner side of the polygon or the outer direction on the outer side of the polygon with the selected side as a boundary. For each of the selected sides, and
Based on the number of times determined to be inward and the number of times determined to be outward, it is determined whether or not the target point is inside the polygon.
A positional relationship determination program specially characterized by causing processing to be executed.

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