WO2018083859A1 - Geographical information processor, geographical information processing method and computer-readable medium - Google Patents

Geographical information processor, geographical information processing method and computer-readable medium Download PDF

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Publication number
WO2018083859A1
WO2018083859A1 PCT/JP2017/029801 JP2017029801W WO2018083859A1 WO 2018083859 A1 WO2018083859 A1 WO 2018083859A1 JP 2017029801 W JP2017029801 W JP 2017029801W WO 2018083859 A1 WO2018083859 A1 WO 2018083859A1
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points
true sphere
interpolation
plane
path
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PCT/JP2017/029801
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French (fr)
Japanese (ja)
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雅彦 石田
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日本電気株式会社
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G5/00—Traffic control systems for aircraft, e.g. air-traffic control [ATC]
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B29/00—Maps; Plans; Charts; Diagrams, e.g. route diagram

Definitions

  • the present invention relates to a geographic information processing apparatus, a geographic information processing method, and a computer-readable medium.
  • Patent Document 1 a method of calculating a route by projecting a point or route on the earth having a spheroid shape onto a true sphere.
  • this method necessary arithmetic processing is performed using coordinates projected onto a true sphere.
  • the route connecting the two points is handled as being set on the great circle.
  • FIG. 24 shows a geodesic path connecting Manila (14 degrees north latitude 121 degrees east longitude) and Naha (26 degrees north latitude 128 degrees east longitude) on the spheroid, and the latitude of 36 degrees north latitude is obtained by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path which interpolated the projected geodesic path with the great circle on a true sphere with respect to the projected geodesic path projected on the true sphere. As shown in FIG. 24, it can be seen that an error of a maximum of 322 m occurs at 19 degrees north latitude in the great circle interpolation path with respect to the projected geodesic path.
  • FIG. 25 shows a projected geodesic path obtained by projecting a geodesic path connecting Manila and Naha on a spheroid onto a true sphere having a reference latitude of 18 degrees north latitude by the method described in Patent Document 1. It is a figure which shows the error of a great circle interpolation path
  • the error of the great circle interpolation path with respect to the projected geodesic path projected on the true sphere with 36 degrees north latitude shown in FIG. 24 as the reference latitude is indicated by a solid line, and projected on the true sphere with 18 degrees north latitude as the reference latitude.
  • the error of the great circle interpolation path with respect to the projected geodesic path is shown by a broken line. As shown by the broken line in FIG. 25, in this case, it is understood that an error of maximum 12 m occurs at 22 degrees north latitude in the great circle interpolation path with respect to the projected geodesic path.
  • FIG. 26 shows two geodesic paths that project a geodesic path connecting Manila and Naha on a spheroid onto a true sphere having a reference latitude of 36 degrees north latitude by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path
  • the error of the great circle interpolation path with respect to the projected geodesic path projected on the true sphere with the latitude of 36 degrees north shown in FIG. 24 as the reference latitude is indicated by a solid line, and projected on the true sphere with the latitude of 36 degrees north as the reference latitude.
  • the error of the two-round great circle interpolation path with respect to the projected geodesic path is indicated by a broken line.
  • an error of a maximum of 116 m occurs at the latitude of 16 degrees 45 minutes north on the great circle interpolation path of the two sections.
  • the error can be reduced by dividing the route as compared with FIG.
  • 20 degrees north latitude it is recognized that there is a point where the great circle interpolation path bends.
  • the present invention has been made in view of the above circumstances, and an object of the present invention is to set a path that is accurately interpolated with respect to a geodesic line between two points on a spheroid projected onto a true sphere.
  • the purpose is to do.
  • the geographic information processing apparatus reads a storage device storing information indicating two points on a spheroid, and information on the two points on the spheroid from the storage device.
  • Two points on the read ellipsoid are projected on a true sphere defined by a reference latitude, and a plane to which a great circle connecting the two points projected on the true sphere belongs is placed on the true sphere.
  • a calculation unit that rotates using a straight line connecting the two projected points as a rotation axis and uses an intersection line between the rotated plane and the surface of the true sphere as an interpolation path.
  • the geographic information processing method reads information on two points on a spheroid from a storage device, and places the two points on the read spheroid on a true sphere defined by a reference latitude. Projecting and rotating the plane to which the great circle connecting the two points projected on the true sphere belongs to a straight line connecting the two points projected on the true sphere as a rotation axis, An intersection line with the surface of the true sphere is set as an interpolation path.
  • the geographic information processing program includes a process of reading information on two points on a spheroid from a storage device, and a true latitude defined by reference latitudes on the two points on the read spheroid.
  • a process of setting a line of intersection between the rotated plane and the surface of the true sphere as an interpolation path is a process of reading information on two points on a spheroid from a storage device, and a true latitude defined by reference latitudes on the two points on the read spheroid.
  • a route obtained by accurately interpolating a route obtained by projecting a geodesic line between two points on a spheroid onto a true sphere can be set.
  • FIG. 1 is a block diagram schematically showing a configuration of a geographic information processing apparatus according to a first embodiment.
  • 1 is a block diagram schematically showing a basic configuration of a geographic information processing apparatus according to a first embodiment.
  • FIG. 2 is a block diagram schematically showing a configuration of a calculation unit according to the first exemplary embodiment.
  • 4 is a flowchart showing a method for setting an interpolation path for a geodesic line in the geographic information processing apparatus according to the first embodiment; It is a figure which shows the outline
  • FIG. 6 is an XZ plan view when a projection interpolation point in the coordinate system Sn is viewed from the Y-axis direction.
  • the coordinate system Sn it is a figure which shows the plane which rotated the plane which a great circle belongs to around the axis
  • an XZ plan view of a plane rotated by a rotation angle ⁇ around an axis connecting a start point and an end point projected on a true sphere to a plane to which a great circle belongs is viewed from the Y-axis direction.
  • the geodesic path connecting Manila and Naha on the spheroid is divided into two sections with respect to the projected geodesic path projected onto a true sphere with the latitude of 36 degrees north as the reference latitude by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path
  • Embodiment 1 A geographic information processing apparatus 100 according to the first embodiment will be described.
  • control and navigation calculation of a moving body that moves on the earth such as an aircraft needs to perform calculation processing by converting map information into a numerical value.
  • the shape of the Earth is not a true sphere, but is a spheroid that is crushed in the north-south direction and has a maximum radius near the equator. Therefore, a process for setting a path in the spheroid as a path on the true sphere is performed. And by performing calculation processing using projected coordinates on the true sphere, the processing is simplified and speeded up, and the control and navigation calculation of a moving body moving on the earth is realized with small hardware resources.
  • the geographic information processing apparatus 100 is configured using hardware resources such as a computer system.
  • FIG. 1 is a block diagram schematically illustrating the configuration of the geographic information processing apparatus 100 according to the first embodiment.
  • the geographic information processing apparatus 100 includes an input device 1, a storage device 2, a calculation unit 3, a display device 4, and a bus 5.
  • the input device 1, the storage device 2, the arithmetic unit 3, and the display device 4 are connected via the bus 5 and can exchange data with each other.
  • FIG. 2 is a block diagram schematically illustrating a basic configuration of the geographic information processing apparatus 100 according to the first embodiment.
  • the input device 1, the display device 4, and the bus 5 are displayed for understanding the overall configuration of the geographic information processing device 100, and the basic configuration of the geographic information processing device 100 is as shown in FIG. 2.
  • the input device 1 is used when inputting data to the geographic information processing device 100 from the outside.
  • various data input means such as a keyboard, a mouse, a DVD (Digital Versatile Disc) drive, and a network connection can be applied.
  • the storage device 2 can store a database in which data provided via the input device 1 is stored, a database output by the calculation unit 3 and a program used for processing by the calculation unit 3. .
  • various storage devices such as a hard disk drive and a flash memory can be applied.
  • FIG. 3 is a block diagram schematically illustrating a configuration of the calculation unit 3 according to the first embodiment.
  • the calculation unit 3 includes a true sphere projection conversion formula generation unit 31, a geodesic information input unit 32, a coordinate system definition unit 33, an interpolation point generation unit 34, an interpolation point projection unit 35, and a separation distance function determination.
  • FIG. 4 is a flowchart illustrating a method for setting an interpolation route for a geodesic line in the geographic information processing apparatus 100 according to the first embodiment.
  • the plane to which the path on the great circle connecting the start point and the end point on the true sphere belongs is rotated by a predetermined amount about the line connecting the start point and the end point, so that the error relative to the geodesic line of the interpolation path Is minimized.
  • the following is a breakdown by item.
  • Step S1 Generation of true spherical projection conversion formula
  • the true sphere projection conversion formula generation unit 31 reads the reference latitude for projecting the coordinates on the spheroid onto the true sphere, generates a true sphere conversion formula, and writes it into the storage device 2.
  • the reference latitude read by the true sphere projection conversion formula generation unit 31 is stored in the storage device 2, for example.
  • Step S2 Geodesic information input
  • geodesic information input unit 32 to read the coordinates of the end point p e of the starting point p s geodesic path on a rotating ellipsoid stored in the storage device 2 sequentially, the data to be read is present Is determined (step S21). If the data to be read is present, coordinates of the starting point P s on the sphericity using a sphere projection conversion formula stored in the storage device 2, for projecting the coordinates of the end point P e (step S22).
  • FIG. 5 shows an outline of projection from the spheroid SP to the true sphere TS. If there is no data to be read, the process ends.
  • the geodesic path connecting the start point p s and the end point p e on the spheroid by the same method be projected as a projection geodesic path connecting the start point P s and the end point P e of the sphericity Is also possible.
  • the geographic information processing apparatus 100 sets a path obtained by interpolating the projected geodesic path on the true sphere, it is not necessary to project the geodesic path on the spheroid as a projected geodesic path on the true sphere.
  • the projected geodesic path when referring to the projected geodesic path, it does not mean that the projected geodesic path is actually projected onto the true sphere, but for comparison with the interpolation path set in the present embodiment. It should be noted that this is only referred to for convenience of explanation.
  • Step S3 Coordinate system definition on true sphere
  • Coordinate system definition unit 33 based on the starting point P s and the end point P e projected onto a sphere TS, assume a coordinate system Sn according to a sphere TS.
  • FIG. 6 is a diagram showing a true sphere TS in the coordinate system Sn.
  • the coordinate system Sn is set as follows. First, to set a great circle GC on a sphere TS which belongs to the true sphere TS origin P s and the end point is projected onto P e.
  • a vector indicating a middle point between the start point P s and the end point P e on the great circle GC And here, are the position vectors of the start point P s and the end point Pe, respectively.
  • an arrow is placed on the upper side of a character such as an alphabet, a position vector of a point related to the character or a vector along a direction indicated by the character is indicated.
  • Vector in the direction perpendicular to And The normal vector of the plane to which the great circle GC belongs And From the above, It becomes. That is, these three vectors are orthogonal to each other and each defines the direction of the X, Y, and Z axes.
  • FIG. 7 is a diagram showing the true sphere TS in the coordinate system Sn in more detail.
  • the distance L between the starting point P s and the end point P e on sphericity TS is the R as the radius of the true sphere is expressed by the following equation.
  • the angle [Phi 0 formed by the start point P s or end point P e with respect to the X-axis as viewed from the center O of a sphere TS is expressed by the following equation.
  • the interpolation point generation unit 34 generates the coordinates of the interpolation point (partition point) on the geodesic path on the spheroid SP. First, the actual azimuth ⁇ and actual distance ⁇ from the starting point p s on spheroid SP to the end point p e. Then, as the point to interpolate the starting point p s and the end point P e on spheroid SP, the actual azimuth from the start point P s on the spheroid SP theta, interpolation point p of actual distance a ⁇ : (a) Ask.
  • a is an arbitrary real number between 0 and 1.
  • FIG. 8 shows an outline of the interpolation point.
  • These data read by the interpolation point generation unit 34 are stored in the storage device 2, for example.
  • Step S5 Interpolation point projection
  • the interpolation point projection unit 35 projects the interpolation point on the generated spheroid SP onto the coordinate system Sn of the true sphere TS. That is, the projection interpolation point Pn (a) in the coordinate system Sn of the true sphere TS corresponding to the point p (a) on the spheroid SP is obtained.
  • FIG. 9 is a diagram showing projection interpolation points in the coordinate system Sn.
  • the position vector Pn (a) of the projection interpolation point in the coordinate system Sn can be expressed by the following equation.
  • the separation distance function determination unit 36 determines the separation distance function in the following manner. Range of the X component of each projection interpolation point Pn (a) in the coordinate system and Sn range of cos ⁇ 0 ⁇ 1, Y component is -sin ⁇ 0 ⁇ sin ⁇ 0.
  • the Z component is a parameter representing the separation between the projection interpolation point located on the projected geodesic path and the great circle GC on the true sphere TS, and the separation distance d is represented by the following equation.
  • the spherical coordinates ⁇ (a) and ⁇ (a) in the coordinate system Sn are defined as shown by the following equations. At this time, the range of ⁇ (a) is ⁇ 0 to ⁇ 0 .
  • the projection interpolation point Pn (a) in the coordinate system Sn is expressed by the following equation.
  • ⁇ (a) is a dividing point of the great circle GC connecting the start point P s and the end point P e of the true sphere TS
  • ⁇ (a) is a parameter representing the distance in the projection interpolation point Pn (a) .
  • ⁇ (a) is uniquely determined by ⁇ (a)
  • sin ⁇ and cos ⁇ can be expressed as the following equation as a function of ⁇ .
  • ⁇ and ⁇ are functions representing the separation distance that satisfies the relationship shown in the following formula (1).
  • FIG. 10 is a diagram showing the projection interpolation point Pn ( ⁇ ) in the coordinate system Sn. As shown in FIG. 10, the projection interpolation point Pn ( ⁇ ) is set on the projected geodesic path GL.
  • an interpolation point on the spheroid is converted into a coordinate system Sn on a true sphere.
  • the point p i on the spheroid is projected to the coordinate system Sn on sphericity, consider the N sampling points Pn i.
  • Each spherical coordinate in the coordinate system Sn sampling point Pn i ( ⁇ i, ⁇ i ) are as follows.
  • the above equation (2) must be established at each of the N sampling points. Therefore, the following formula is obtained.
  • N coefficients can be determined by multiplying the above equation by an inverse matrix from the left.
  • the inverse matrix calculation method for example, a sweeping out method or the like can be used. Therefore, the separation functions ⁇ ( ⁇ ) and ⁇ ( ⁇ ) shown in the equation (2) can be determined by 2N constants ⁇ i and ⁇ i.
  • 15 to 18 are diagrams showing approximation accuracy when the number of samplings (N) is 1, 3, 5, and 7.
  • the error of the great circle interpolation path is 322 m at the maximum.
  • Rotation angle calculator 37 calculates the rotation angle ⁇ is rotated about an axis connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the perfect sphere.
  • FIG. 11 is an XZ plan view when the projection interpolation point Pn ( ⁇ ) in the coordinate system Sn is viewed from the Y-axis direction.
  • the separation distance d which is the distance from the projection interpolation point Pn ( ⁇ ) to the great circle GC, is the length of the arc in FIG. 11 and is expressed by the following equation.
  • a plane PL2 which is rotated around an axis AX by rotation angle ⁇ connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the sphericity Y It is an XZ plan view seen from the axial direction. As shown in FIG. 13, this means that the plane is rotated around the Y axis in the coordinate system Sn. In the coordinate system centered at the origin, the projected interpolation point after the rotation is converted as follows.
  • FIG. 14 is a diagram showing arcs constituting the rotational separation distance.
  • the rotation separation distance RD is It can be expressed by a formula.
  • the above equation can be approximated as the following equation (4) when the rotational separation RD ( ⁇ , ⁇ ) is extremely small compared to the normalized radius of the earth.
  • the rotation separation distance RD ( ⁇ , ⁇ ) can be minimized by appropriately selecting the rotation angle ⁇ .
  • FIG. 19 shows an error when interpolation is performed based on the rotation angle obtained by the midpoint method.
  • the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere
  • the broken line indicates the error of the interpolation path obtained by the midpoint method with respect to the projected geodesic path.
  • the maximum value of the rotational separation is 49.2 m south of latitude 20 degrees north and 34.9 m north of latitude 20 degrees north.
  • the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere
  • the broken line indicates the error of the interpolation path obtained by the maximum separation point method with respect to the projected geodesic path.
  • the maximum value of the separation distance is 38.0 m south of latitude 20 degrees north and 48.8 m north of latitude 20 degrees north.
  • FIG. 21 shows an error when interpolation is performed based on the rotation angle obtained by the averaging method.
  • the solid line shows the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere
  • the broken line shows the error of the interpolation path obtained by the averaging method with respect to the projected geodesic path.
  • the maximum value of the rotational separation distance is 45.5 m south of latitude 20 degrees north and 39.2 m north of latitude 20 degrees north.
  • the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere
  • the broken line indicates the error of the interpolation path obtained by the weighted average method with respect to the projected geodesic path.
  • the maximum value of the rotation separation distance is 72.4 m south of latitude 20 degrees north and 34.6 m north of latitude 20 degrees north.
  • the rotation angle ⁇ is calculated such that the root mean square of the rotation separation distance RD in the section [ ⁇ 0 , ⁇ 0 ] is minimized.
  • the value I integrated in the interval [ ⁇ 0 , ⁇ 0 ] is obtained by squaring Equation (5).
  • Each term of the above equation is integrated in the interval [ ⁇ 0 , ⁇ 0 ].
  • k m is not selected.
  • the portions excluding cos ⁇ and sin ⁇ from the terms of the square I of the rotational separation distance RD described above are denoted by I 1 to I 8 , respectively.
  • the root mean square I of the rotation separation distance is expressed by the following equation.
  • Integrated value I 1 is given by the following equation.
  • Integrated value I 2 is given by the following equation.
  • Integrated value I 3 is given by the following equation. If we further calculate, The integral value I 4 is given by the following equation.
  • the integral value I 5 is given by the following equation.
  • the integral value I 6 is given by the following equation.
  • the integral value I 7 is given by the following equation.
  • Integrated value I 8 is given by the following equation.
  • FIG. 23 shows an error when interpolation is performed based on the rotation angle obtained by the method of least squares.
  • the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere
  • the broken line indicates the error of the interpolation path obtained by the least square method with respect to the projected geodesic path.
  • the maximum value of the rotational separation distance is 46.5 m south of latitude 20 degrees north and 38.1 m north of latitude 20 degrees north.
  • the error can be reduced as compared with FIG. 24, and the path obtained after the interpolation can be a smooth continuous line.
  • the type of solution method may be stored in the storage device 2 as the optimum rotation angle calculation method database D1, for example.
  • the calculating part 3 can read the solution used for calculation of a rotation angle from the memory
  • the optimum rotation angle calculation method database D1 includes information, algorithms, or programs related to calculation processing methods used in accordance with the optimum rotation angle calculation method.
  • Step S8 Interpolation path information output
  • the interpolation path information output unit 38 sets an interpolation path for interpolating the projected geodesic path using the calculated rotation angle ⁇ .
  • P GC point on a subject is rotated great circle, defining a vector V, it is represented by the equation below.
  • the interpolation path constituted by the plane to which the great circle rotated at the rotation angle ⁇ belongs is redefined as follows. If this is described in a normal coordinate system with the polar direction as the Z axis, the following equation is obtained.
  • the vector V is a unit normal vector with respect to the above-described plane PL2 that intersects the plane to which the interpolation path belongs, that is, the surface of the true sphere TS.
  • Each component value and inner product value of the unit normal vector are stored in the storage device 2 as data representing interpolation path information on the true sphere of the geodesic path read in step S2. Thereafter, the process returns to step S2.
  • the geographic information processing apparatus 100 converts the great circle path on the true sphere to the start point of the great circle path with respect to the route obtained by projecting the geodesic path on the spheroid onto the true sphere.
  • the error of both paths can be minimized. This makes it possible to improve interoperability between maps set on a true sphere even when the reference latitude is different.
  • the interpolation path on the true sphere shown in the above formula is formally expressed as an intersection of a plane and a true sphere, as in a general method. Therefore, according to the present embodiment, it is possible to improve the interpolation accuracy without significantly increasing the amount of calculation as compared with a general method.
  • the present invention is not limited to the above-described embodiments, and can be appropriately changed without departing from the spirit of the present invention.
  • a moving body such as an aircraft moving on the earth
  • the geographical information processing apparatus according to the above-described embodiment includes, for example, a moving body other than an aircraft flying in the air, a vehicle moving on the land, a ship moving on the sea, a submarine moving on the sea, and the like moving on the earth. Can be mounted on any mobile body.
  • the geographical information processing apparatus according to the above-described embodiment is not limited to a mobile object, but can be incorporated in an operation management system for a mobile object such as a control system that uses an aircraft for control.
  • the geographic information processing apparatus and the geographic information processing method performed by this apparatus have been described.
  • the present invention is not limited to this.
  • the present invention can also realize arbitrary processing by causing a CPU (Central Processing Unit) to execute a computer program.
  • a CPU Central Processing Unit
  • Non-transitory computer readable media include various types of tangible storage media (tangible storage medium). Examples of non-transitory computer-readable media include magnetic recording media (eg flexible disks, magnetic tapes, hard disk drives), magneto-optical recording media (eg magneto-optical discs), CD-ROMs (Read Only Memory), CD-Rs, CD-R / W, semiconductor memory (for example, mask ROM, PROM (Programmable ROM), EPROM (Erasable ROM), flash ROM, RAM (random access memory)) are included.
  • the program may also be supplied to the computer by various types of temporary computer-readable media. Examples of transitory computer readable media include electrical signals, optical signals, and electromagnetic waves.
  • the temporary computer-readable medium can supply the program to the computer via a wired communication path such as an electric wire and an optical fiber, or a wireless communication path.

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Abstract

An accurately interpolated path is set to a path consisting of a geodesic line between two points on an ellipsoid of revolution that is projected on to a true sphere. A geographical information processor (100) has a storage device (2) and a computation unit (3). The storage device (2) has stored therein information that indicates two points on the ellipsoid of revolution. The computation unit (3) reads the information pertaining to the two points on the ellipsoid of revolution from the storage unit (2) and rotates a plane to which a path on a great circle linking the two points projected to the true sphere belongs by a prescribed amount around a line linking the start and end points on the true sphere and thereby minimizes the error of an interpolated path after rotation against the geodesic line projected to the true sphere.

Description

地理情報処理装置、地理情報処理方法及びコンピュータ可読媒体Geographic information processing apparatus, geographical information processing method, and computer-readable medium
　本発明は、地理情報処理装置、地理情報処理方法及びコンピュータ可読媒体に関する。 The present invention relates to a geographic information processing apparatus, a geographic information processing method, and a computer-readable medium.
　今日、地球上での移動体監視を行うため、様々なナビゲーションシステムが運用されている。輸送機械の中でも移動距離が長大である航空機の運航を管理するには、広範囲での方位、距離の算出を行う必要が有る。航空機のナビゲーションシステムでは、一般に、国家の領土及び領空、又は飛行情報区（ＦＩＲ：Flight Information Region）程度における広域の範囲で、大縮尺の空間情報を正確かつ効率的に処理することが求められる。更に、地球全体の範囲をカバーできるナビゲーションシステムを構築できることが望ましいことは、言うもでもない。 Today, various navigation systems are used to monitor moving objects on the earth. In order to manage the operation of an aircraft that has a long movement distance among transport machines, it is necessary to calculate the azimuth and distance over a wide range. In an aircraft navigation system, it is generally required to accurately and efficiently process large-scale spatial information in a wide area such as a national territory and airspace, or a flight information area (FIR). Furthermore, it goes without saying that it is desirable to be able to build a navigation system that can cover the entire globe.
　このようなナビゲーションシステムの例として、回転楕円（だえん）体形状を有する地球上の地点や経路を真球上に投影して、経路計算を行う手法が提案されている（特許文献１）。この手法では、必要な演算処理を真球上に投影した座標を用いて行う。また、真球上においては、２地点の間を結ぶ経路は、真球の大円上に設定されるものとして取り扱われる。これにより、回転楕円体上の座標を用いて演算する場合と比べて、演算量を低減することができ、比較的簡易な計算リソースで演算処理を実現することができる。 As an example of such a navigation system, a method of calculating a route by projecting a point or route on the earth having a spheroid shape onto a true sphere has been proposed (Patent Document 1). In this method, necessary arithmetic processing is performed using coordinates projected onto a true sphere. On the true sphere, the route connecting the two points is handled as being set on the great circle. Thereby, compared with the case where it calculates using the coordinate on a spheroid, a calculation amount can be reduced and a calculation process can be implement | achieved by a comparatively simple calculation resource.
国際公開第２０１４／１０８９５７号International Publication No. 2014/108957
　しかしながら、特許文献１に記載の手法では、真球上の２地点間の経路を真球の大円上に設定する。しかし、大円上の経路は、回転楕円体上の最短経路である測地線を真球上に投影した経路とは異なるため、誤差が生じることとなる。これに対し、特許文献１では、真球上をいくつかのエリアに分割して、それぞれのエリアについて計算の基準となる基準緯度を変更して計算を行うことで、各エリア内の誤差を許容範囲内に収めている。このとき、基準緯度の異なる２つのエリアを通過するときの接続部における各エリアでの誤差が異なるので、相互に許容し得ない差異が生じるおそれがある。 However, in the method described in Patent Document 1, a route between two points on the true sphere is set on the great circle of the true sphere. However, since the route on the great circle is different from the route obtained by projecting the geodesic line, which is the shortest route on the spheroid, onto the true sphere, an error occurs. On the other hand, in Patent Document 1, an error in each area is allowed by dividing the true sphere into several areas and performing calculation by changing the reference latitude that is the calculation reference for each area. It is within the range. At this time, since the error in each area in the connecting portion when passing through two areas having different reference latitudes is different, there is a possibility that a difference that cannot be allowed is generated.
　図２４は、回転楕円体上においてマニラ（北緯１４度東経１２１度）と那覇（北緯２６度東経１２８度）とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯３６度を基準緯度とする真球上に投影した投影測地線経路に対する、投影測地線経路を真球上の大円で補間した大円補間経路の誤差を示す図である。図２４に示すように、投影測地線経路に対する大円補間経路には、北緯１９度で最大３２２ｍの誤差が生じることがわかる。 FIG. 24 shows a geodesic path connecting Manila (14 degrees north latitude 121 degrees east longitude) and Naha (26 degrees north latitude 128 degrees east longitude) on the spheroid, and the latitude of 36 degrees north latitude is obtained by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path which interpolated the projected geodesic path with the great circle on a true sphere with respect to the projected geodesic path projected on the true sphere. As shown in FIG. 24, it can be seen that an error of a maximum of 322 m occurs at 19 degrees north latitude in the great circle interpolation path with respect to the projected geodesic path.
　一方、図２５は、回転楕円体上におけるマニラと那覇とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯１８度を基準緯度とする真球上に投影した投影測地線経路に対する、大円補間経路の誤差を示す図である。図２５では、図２４に示した北緯３６度を基準緯度として真球上に投影した投影測地線経路に対する大円補間経路の誤差を実線で示し、北緯１８度を基準緯度として真球上に投影した投影測地線経路に対する大円補間経路の誤差を破線で示した。図２５の破線で示すように、この場合、投影測地線経路に対する大円補間経路には、北緯２２度で最大１２ｍの誤差が生じることがわかる。 On the other hand, FIG. 25 shows a projected geodesic path obtained by projecting a geodesic path connecting Manila and Naha on a spheroid onto a true sphere having a reference latitude of 18 degrees north latitude by the method described in Patent Document 1. It is a figure which shows the error of a great circle interpolation path | route. In FIG. 25, the error of the great circle interpolation path with respect to the projected geodesic path projected on the true sphere with 36 degrees north latitude shown in FIG. 24 as the reference latitude is indicated by a solid line, and projected on the true sphere with 18 degrees north latitude as the reference latitude. The error of the great circle interpolation path with respect to the projected geodesic path is shown by a broken line. As shown by the broken line in FIG. 25, in this case, it is understood that an error of maximum 12 m occurs at 22 degrees north latitude in the great circle interpolation path with respect to the projected geodesic path.
　このように、基準緯度の異なる真球上に投影した投影測地線経路に対する大円補間経路の間には、３００ｍ程度の差異が生じることとなる。この差異が許容できない場合には、上記の条件で投影した２枚の地図を同時に参照して差異の影響を回避する、又は、２地点間に中継点を設けるなど、運用面での対応策をとることが求められる。以上より、特許文献１の手法では、基準緯度の異なる真球上の地図の相互運用性が低いことを示されている。 Thus, there will be a difference of about 300 m between the great circle interpolation path with respect to the projected geodesic path projected onto a true sphere with different reference latitudes. If this difference is unacceptable, refer to the two maps projected under the above conditions at the same time to avoid the effect of the difference, or provide a relay point between the two points. It is required to take. From the above, the technique of Patent Document 1 shows that the interoperability of maps on a true sphere with different reference latitudes is low.
　これに対し、誤差を低減するため、回転楕円体上の２地点間の測地線経路を複数の区間に分割して、各区間に真球上の大円補間経路を設定する方法も考え得る。しかし、この方法では、誤差を縮小しようとすると分割数を多くしなければならず、かつ、各区間の接続点において経路が屈曲し、滑らかな連続線にならないという問題が生じてしまう。 On the other hand, in order to reduce the error, a method of dividing the geodesic path between two points on the spheroid into a plurality of sections and setting a great circle interpolation path on a true sphere in each section may be considered. However, in this method, if the error is to be reduced, the number of divisions must be increased, and a problem arises that the path is bent at the connection point of each section and does not become a smooth continuous line.
　例えば、測地線経路をｎ（ｎは、正の整数）個の区間に等間隔に分割する場合、区間の接続点である（ｎ－１）個の経由地点が存在する。このとき、測地線上の始点から終点への方位θと距離ｄを求め、測地線上において始点から距離ｄi＝ｄ×ｉ／ｎ（ｉは、０＜ｉ＜ｎの整数）、方位θの地点の緯度、経度を求めることで、各経由地点の回転楕円体上の緯度、経度を求めることができる。これには、測地学の第一問題、第二問題の解法として知られる、例えばＳｏｄａｎｏの方法を用いることができる。 For example, when a geodesic route is divided into n (n is a positive integer) sections at equal intervals, there are (n−1) waypoints that are connection points of the sections. At this time, the azimuth θ and the distance d from the start point to the end point on the geodesic line are obtained, and the distance d i = d × i / n (i is an integer of 0 <i <n) and the azimuth θ point on the geodesic line. By calculating the latitude and longitude, it is possible to determine the latitude and longitude on the spheroid at each waypoint. For this, for example, Sodano's method known as a solution to the first and second problems of geodesy can be used.
　図２６は、回転楕円体上におけるマニラと那覇とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯３６度を基準緯度とする真球上に投影した投影測地線経路に対する、２つの区間に分けて補間した場合の大円補間経路の誤差を示す図である。図２６では、図２４に示した北緯３６度を基準緯度として真球上に投影した投影測地線経路に対する大円補間経路の誤差を実線で示し、北緯３６度を基準緯度として真球上に投影した投影測地線経路に対する２つの区間の大円補間経路の誤差を破線で示した。図２６に示すように、２つの区間の大円補間経路には、北緯１６度４５分で最大１１６ｍの誤差が生じている。これにより、経路を分割することで、図２４に比べて誤差を少なくすることができることがわかる。しかしながら、北緯２０度では、大円補間経路が屈曲する点があることが認められる。 FIG. 26 shows two geodesic paths that project a geodesic path connecting Manila and Naha on a spheroid onto a true sphere having a reference latitude of 36 degrees north latitude by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path | route at the time of interpolating by dividing into an area. In FIG. 26, the error of the great circle interpolation path with respect to the projected geodesic path projected on the true sphere with the latitude of 36 degrees north shown in FIG. 24 as the reference latitude is indicated by a solid line, and projected on the true sphere with the latitude of 36 degrees north as the reference latitude. The error of the two-round great circle interpolation path with respect to the projected geodesic path is indicated by a broken line. As shown in FIG. 26, an error of a maximum of 116 m occurs at the latitude of 16 degrees 45 minutes north on the great circle interpolation path of the two sections. Thus, it can be seen that the error can be reduced by dividing the route as compared with FIG. However, at 20 degrees north latitude, it is recognized that there is a point where the great circle interpolation path bends.
　区分点（経由地点）を適切に設定することで誤差をより小さくできる可能性は有るものの、この場合の各区間の近似は一次近似に相当するので、誤差の収束は比較的緩やかである。そのため、補間精度を向上させようとすると、区分点を密に設定しなければならず、区分点の増大に伴い計算量が増加するという問題が生じてしまう。 Although there is a possibility that the error can be made smaller by appropriately setting the dividing points (route points), the approximation of each section in this case corresponds to a first-order approximation, so the error convergence is relatively gradual. Therefore, when trying to improve the interpolation accuracy, it is necessary to set the dividing points densely, which causes a problem that the amount of calculation increases as the number of dividing points increases.
　本発明は、上記の事情に鑑みて成されたものであり、本発明の目的は、真球上に投影した回転楕円体上の２地点間の測地線に対して精度よく補間した経路を設定することを目的とする。 The present invention has been made in view of the above circumstances, and an object of the present invention is to set a path that is accurately interpolated with respect to a geodesic line between two points on a spheroid projected onto a true sphere. The purpose is to do.
　本発明の一態様である地理情報処理装置は、回転楕円体上の２つの地点を示す情報が格納された記憶装置と、前記記憶装置から前記回転楕円体上の２つの地点の情報を読み込み、読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影し、前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転し、回転された平面と前記真球の表面との交線を補間経路とする演算部と、を有するものである。 The geographic information processing apparatus according to one aspect of the present invention reads a storage device storing information indicating two points on a spheroid, and information on the two points on the spheroid from the storage device. Two points on the read ellipsoid are projected on a true sphere defined by a reference latitude, and a plane to which a great circle connecting the two points projected on the true sphere belongs is placed on the true sphere. And a calculation unit that rotates using a straight line connecting the two projected points as a rotation axis and uses an intersection line between the rotated plane and the surface of the true sphere as an interpolation path.
　本発明の一態様である地理情報処理方法は、記憶装置から回転楕円上の２つの地点の情報を読み込み、読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影し、前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転し、回転された平面と前記真球の表面との交線を補間経路として設定する、ものである。 The geographic information processing method according to one aspect of the present invention reads information on two points on a spheroid from a storage device, and places the two points on the read spheroid on a true sphere defined by a reference latitude. Projecting and rotating the plane to which the great circle connecting the two points projected on the true sphere belongs to a straight line connecting the two points projected on the true sphere as a rotation axis, An intersection line with the surface of the true sphere is set as an interpolation path.
　本発明の一態様である地理情報処理プログラムは、記憶装置から回転楕円体上の２つの地点の情報を読み込む処理と、読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影する処理と、前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転する処理と、回転された平面と前記真球の表面との交線を補間経路として設定する処理と、をコンピュータに実行させる、ものである。 The geographic information processing program according to one aspect of the present invention includes a process of reading information on two points on a spheroid from a storage device, and a true latitude defined by reference latitudes on the two points on the read spheroid. A process of projecting on a sphere and a process of rotating a plane to which a great circle connecting two points projected on the true sphere belongs to a straight line connecting the two points projected on the true sphere as a rotation axis And a process of setting a line of intersection between the rotated plane and the surface of the true sphere as an interpolation path.
　本発明によれば、回転楕円体上の２地点間の測地線を真球上に投影した経路に対して精度よく補間した経路を設定することができる。 According to the present invention, a route obtained by accurately interpolating a route obtained by projecting a geodesic line between two points on a spheroid onto a true sphere can be set.
実施の形態１にかかる地理情報処理装置の構成を模式的に示すブロック図である。1 is a block diagram schematically showing a configuration of a geographic information processing apparatus according to a first embodiment. 実施の形態１にかかる地理情報処理装置の基本的構成を模式的に示すブロック図である。1 is a block diagram schematically showing a basic configuration of a geographic information processing apparatus according to a first embodiment. 実施の形態１にかかる演算部の構成を模式的に示すブロック図である。FIG. 2 is a block diagram schematically showing a configuration of a calculation unit according to the first exemplary embodiment. 実施の形態１にかかる地理情報処理装置での測地線に対する補間経路の設定方法を示すフローチャートである。4 is a flowchart showing a method for setting an interpolation path for a geodesic line in the geographic information processing apparatus according to the first embodiment; 回転楕円体から真球への投影の概要を示す図である。It is a figure which shows the outline | summary of the projection to a true sphere from a spheroid. 座標系Ｓｎにおける真球を示す図である。It is a figure which shows the true sphere in coordinate system Sn. 座標系Ｓｎにおける真球をより詳細に示す図である。It is a figure which shows the true sphere in coordinate system Sn in detail. 補間地点の概要を示す図である。It is a figure which shows the outline | summary of an interpolation point. 座標系Ｓｎにおける補間地点を示す図である。It is a figure which shows the interpolation point in coordinate system Sn. 座標系Ｓｎにおける投影補間地点を示す図である。It is a figure which shows the projection interpolation point in coordinate system Sn. 座標系Ｓｎにおける投影補間地点をＹ軸方向から見た場合のＸ－Ｚ平面図である。FIG. 6 is an XZ plan view when a projection interpolation point in the coordinate system Sn is viewed from the Y-axis direction. 座標系Ｓｎにおいて、大円が属する平面を真球上の始点と終点とを結ぶ軸の周りに回転させた平面を示す図である。In the coordinate system Sn, it is a figure which shows the plane which rotated the plane which a great circle belongs to around the axis | shaft which connects the start point and end point on a perfect sphere. 座標系Ｓｎにおいて、大円が属する平面を真球上に投影された始点と終点とを結ぶ軸の周りに回転角φだけ回転させた平面をＹ軸方向から見たＸ－Ｚ平面図である。In the coordinate system Sn, an XZ plan view of a plane rotated by a rotation angle φ around an axis connecting a start point and an end point projected on a true sphere to a plane to which a great circle belongs is viewed from the Y-axis direction. . 回転離隔距離を構成する弧を示す図である。It is a figure which shows the arc which comprises a rotation separation distance. サンプリング数を１個としたときの近似精度を示す図である。It is a figure which shows the approximation precision when the number of sampling is set to one. サンプリング数を３個としたときの近似精度を示す図である。It is a figure which shows the approximation accuracy when the number of sampling is set to three. サンプリング数を５個としたときの近似精度を示す図である。It is a figure which shows the approximation accuracy when the sampling number is set to 5. サンプリング数を７個としたときの近似精度を示す図である。It is a figure which shows the approximation accuracy when the sampling number is set to 7. 中間点法で得られた回転角に基づいて補間した際の誤差を示す図である。It is a figure which shows the error at the time of interpolating based on the rotation angle obtained by the midpoint method. 最大離隔点法で得られた回転角に基づいて補間した際の誤差を示す図である。It is a figure which shows the error at the time of interpolating based on the rotation angle obtained by the maximum separation point method. 平均法で得られた回転角に基づいて補間した際の誤差を示す図である。It is a figure which shows the error at the time of interpolating based on the rotation angle obtained by the average method. 加重平均法で得られた回転角に基づいて補間した際の誤差を示す図である。It is a figure which shows the error at the time of interpolating based on the rotation angle obtained by the weighted average method. 最小自乗法で得られた回転角に基づいて補間した際の誤差を示す図である。It is a figure which shows the error at the time of interpolating based on the rotation angle obtained by the least square method. 回転楕円体上においてマニラ（北緯１４度東経１２１度）と那覇（北緯２６度東経１２８度）とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯３６度を基準緯度とする真球上に投影した投影測地線経路に対する、投影測地線経路を真球上の大円で補間した大円補間経路の誤差を示す図である。On the spheroid, a true sphere with a geodesic path connecting Manila (14 degrees north latitude 121 degrees east longitude) and Naha (26 degrees north latitude 128 degrees east longitude) with a reference latitude of 36 degrees north latitude by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path which interpolated the projected geodesic path with the great circle on a perfect sphere with respect to the projected geodesic path projected on the top. 回転楕円体上におけるマニラと那覇とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯１８度を基準緯度とする真球上に投影した投影測地線経路に対する、大円補間経路の誤差を示す図である。The error of the great circle interpolation path with respect to the projected geodesic path obtained by projecting the geodesic path connecting Manila and Naha on the spheroid onto the true sphere with the latitude of 18 degrees north as the reference latitude by the method described in Patent Document 1. FIG. 回転楕円体上におけるマニラと那覇とを結ぶ測地線経路を、特許文献１に記載の手法によって北緯３６度を基準緯度とする真球上に投影した投影測地線経路に対する、２つの区間に分けて補間した場合の大円補間経路の誤差を示す図である。The geodesic path connecting Manila and Naha on the spheroid is divided into two sections with respect to the projected geodesic path projected onto a true sphere with the latitude of 36 degrees north as the reference latitude by the method described in Patent Document 1. It is a figure which shows the error of the great circle interpolation path | route at the time of interpolating.
　以下、図面を参照して本発明の実施の形態について説明する。各図面においては、同一要素には同一の符号が付されており、必要に応じて重複説明は省略される。 Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted as necessary.
　実施の形態１
　実施の形態１にかかる地理情報処理装置１００について説明する。一般に、航空機などの地球上を移動する移動体の管制や航法計算は、地図情報を数値化して演算処理を行う必要が有る。ところが、地球の形状は真球ではなく、南北方向に押しつぶされ、半径が赤道付近で最大となる回転楕円体である。そのため、回転楕円体における経路を真球上における経路として設定する処理を行う。そして真球上の投影座標を用いて演算処理を行うことで、処理を簡略化、高速化し、小規模なハードウェア資源により、地球上を移動する移動体の管制や航法計算を実現する。 Embodiment 1
A geographic information processing apparatus 100 according to the first embodiment will be described. In general, control and navigation calculation of a moving body that moves on the earth such as an aircraft needs to perform calculation processing by converting map information into a numerical value. However, the shape of the Earth is not a true sphere, but is a spheroid that is crushed in the north-south direction and has a maximum radius near the equator. Therefore, a process for setting a path in the spheroid as a path on the true sphere is performed. And by performing calculation processing using projected coordinates on the true sphere, the processing is simplified and speeded up, and the control and navigation calculation of a moving body moving on the earth is realized with small hardware resources.
　地理情報処理装置１００は、例えばコンピュータシステムなどのハードウェア資源を用いて構成される。図１は、実施の形態１にかかる地理情報処理装置１００の構成を模式的に示すブロック図である。地理情報処理装置１００は、入力装置１、記憶装置２、演算部３、表示装置４及びバス５を有する。入力装置１、記憶装置２、演算部３、表示装置４は及びバス５を介して接続され、相互にデータの受け渡しを行うことが可能である。 The geographic information processing apparatus 100 is configured using hardware resources such as a computer system. FIG. 1 is a block diagram schematically illustrating the configuration of the geographic information processing apparatus 100 according to the first embodiment. The geographic information processing apparatus 100 includes an input device 1, a storage device 2, a calculation unit 3, a display device 4, and a bus 5. The input device 1, the storage device 2, the arithmetic unit 3, and the display device 4 are connected via the bus 5 and can exchange data with each other.
　図２は、実施の形態１にかかる地理情報処理装置１００の基本的構成を模式的に示すブロック図である。図１において、入力装置１、表示装置４及びバス５は、地理情報処理装置１００の全体構成を理解するために表示したものであり、地理情報処理装置１００の基本的構成は、図２のように表すことができる。 FIG. 2 is a block diagram schematically illustrating a basic configuration of the geographic information processing apparatus 100 according to the first embodiment. In FIG. 1, the input device 1, the display device 4, and the bus 5 are displayed for understanding the overall configuration of the geographic information processing device 100, and the basic configuration of the geographic information processing device 100 is as shown in FIG. 2. Can be expressed as
　入力装置１は、地理情報処理装置１００に対して外部からデータの入力を行う際に用いられる。例えば、入力装置１としては、キーボード、マウス、ＤＶＤ（Digital Versatile Disc）ドライブ、ネットワーク接続などの、各種のデータ入力手段を適用することが可能である。 The input device 1 is used when inputting data to the geographic information processing device 100 from the outside. For example, as the input device 1, various data input means such as a keyboard, a mouse, a DVD (Digital Versatile Disc) drive, and a network connection can be applied.
　記憶装置２は、入力装置１を介して提供されるデータが格納されたデータベースや、演算部３で出力されるデータベースや演算部３での処理に供されるプログラムを記憶することが可能である。記憶装置２は、例えばハードディスクドライブ、フラッシュメモリなどの各種の記憶装置を適用することが可能である。 The storage device 2 can store a database in which data provided via the input device 1 is stored, a database output by the calculation unit 3 and a program used for processing by the calculation unit 3. . As the storage device 2, various storage devices such as a hard disk drive and a flash memory can be applied.
　演算部３についてより詳細に説明する。図３は、実施の形態１にかかる演算部３の構成を模式的に示すブロック図である。図３に示すように、演算部３は、真球投影変換式生成部３１、測地線情報入力部３２、座標系定義部３３、補間地点生成部３４、補間地点投影部３５、離隔距離関数決定部３６、回転角算出部３７、及び、補間経路情報出力部３８を有する。真球投影変換式生成部３１、測地線情報入力部３２、座標系定義部３３、補間地点生成部３４、補間地点投影部３５、離隔距離関数決定部３６、回転角算出部３７、及び、補間経路情報出力部３８のそれぞれについては、後述する。 The calculation unit 3 will be described in more detail. FIG. 3 is a block diagram schematically illustrating a configuration of the calculation unit 3 according to the first embodiment. As shown in FIG. 3, the calculation unit 3 includes a true sphere projection conversion formula generation unit 31, a geodesic information input unit 32, a coordinate system definition unit 33, an interpolation point generation unit 34, an interpolation point projection unit 35, and a separation distance function determination. A unit 36, a rotation angle calculation unit 37, and an interpolation path information output unit 38. True spherical projection conversion formula generation unit 31, geodesic information input unit 32, coordinate system definition unit 33, interpolation point generation unit 34, interpolation point projection unit 35, separation distance function determination unit 36, rotation angle calculation unit 37, and interpolation Each of the route information output unit 38 will be described later.
　次いで、本実施の形態１にかかる、測地線に対する補間経路の設定方法について説明する。図４は、実施の形態１にかかる地理情報処理装置１００での測地線に対する補間経路の設定方法を示すフローチャートである。本実施の形態では、真球上の始点と終点とを結ぶ大円上の経路が属する平面を、始点と終点とを結ぶ線を軸として所定量回転させることで、補間経路の測地線に対する誤差を最小化するものである。以下、項目別に分説する。 Next, a method for setting an interpolation path for a geodesic line according to the first embodiment will be described. FIG. 4 is a flowchart illustrating a method for setting an interpolation route for a geodesic line in the geographic information processing apparatus 100 according to the first embodiment. In this embodiment, the plane to which the path on the great circle connecting the start point and the end point on the true sphere belongs is rotated by a predetermined amount about the line connecting the start point and the end point, so that the error relative to the geodesic line of the interpolation path Is minimized. The following is a breakdown by item.
［ステップＳ１　真球投影変換式生成］
　以下では、回転楕円体上の座標を真球上に投影するにあたり、例えば上述の特許文献１に記載の手法を用いることができる。この場合、真球投影変換式生成部３１は、回転楕円体上の座標を真球上に投影するための基準緯度を読み込み、真球変換式を生成し記憶装置２に書き込む。真球投影変換式生成部３１に読み込まれる基準緯度は、例えば記憶装置２に格納されている。 [Step S1: Generation of true spherical projection conversion formula]
In the following, when the coordinates on the spheroid are projected onto the true sphere, for example, the technique described in Patent Document 1 described above can be used. In this case, the true sphere projection conversion formula generation unit 31 reads the reference latitude for projecting the coordinates on the spheroid onto the true sphere, generates a true sphere conversion formula, and writes it into the storage device 2. The reference latitude read by the true sphere projection conversion formula generation unit 31 is stored in the storage device 2, for example.
［ステップＳ２　測地線情報入力］
　測地線情報入力部３２は、記憶装置２に格納されている回転楕円体上の測地線経路の始点ｐｓの座標と終点ｐｅの座標とを順次読み込むために、読み込むべきデータが存在するかを判定する（ステップＳ２１）。読み込むべきデータが存在する場合は、記憶装置２に格納されている真球投影変換式を用いて真球上の始点Ｐｓの座標、終点Ｐｅの座標に投影する（ステップＳ２２）。図５に、回転楕円体ＳＰから真球ＴＳへの投影の概要を示す。読み込むべきデータが存在しない場合は処理を終了する。 [Step S2 Geodesic information input]
Or geodesic information input unit 32 to read the coordinates of the end point p e of the starting point p s geodesic path on a rotating ellipsoid stored in the storage device 2 sequentially, the data to be read is present Is determined (step S21). If the data to be read is present, coordinates of the starting point P s on the sphericity using a sphere projection conversion formula stored in the storage device 2, for projecting the coordinates of the end point P e (step S22). FIG. 5 shows an outline of projection from the spheroid SP to the true sphere TS. If there is no data to be read, the process ends.
　ここで、回転楕円体上の始点ｐｓと終点ｐｅとを結ぶ測地線経路を、同様の手法によって、真球上の始点Ｐｓと終点Ｐｅとを結ぶ投影測地線経路として投影することも可能である。しかし、地理情報処理装置１００が真球上の投影測地線経路を補間した経路を設定するにあたっては、回転楕円体上の測地線経路を、真球上に投影測地線経路として投影する必要はなく、真球上の始点Ｐｓと終点Ｐｅとに基づいて、以下の手順により補間経路を設定する。以下、投影測地線経路に言及する場合には、真球上への投影測地線経路の投影を実際に行うことを意味するものではなく、本実施の形態で設定する補間経路との比較のため、説明の便宜上参照しているに過ぎない点に留意すべきである。 Here, the geodesic path connecting the start point p s and the end point p e on the spheroid by the same method, be projected as a projection geodesic path connecting the start point P s and the end point P e of the sphericity Is also possible. However, when the geographic information processing apparatus 100 sets a path obtained by interpolating the projected geodesic path on the true sphere, it is not necessary to project the geodesic path on the spheroid as a projected geodesic path on the true sphere. , based on the starting point P s and the end point P e of the perfect sphere, sets the interpolation path by the following procedure. Hereinafter, when referring to the projected geodesic path, it does not mean that the projected geodesic path is actually projected onto the true sphere, but for comparison with the interpolation path set in the present embodiment. It should be noted that this is only referred to for convenience of explanation.
［ステップＳ３　真球上での座標系定義］
　座標系定義部３３は、真球ＴＳ上に投影された始点Ｐｓ及び終点Ｐｅに基づいて、真球ＴＳにかかる座標系Ｓｎを仮定する。図６は、座標系Ｓｎにおける真球ＴＳを示す図である。座標系Ｓｎは、以下の要領で設定する。まず、真球ＴＳ上に投影された始点Ｐｓと終点Ｐｅとが属する真球ＴＳ上の大円ＧＣを設定する。ここで、真球ＴＳの中心Ｏを基準として、大円ＧＣ上における始点Ｐｓと終点Ｐｅとの中点を示すベクトルを
Figure JPOXMLDOC01-appb-M000001
 とする。ここで、
Figure JPOXMLDOC01-appb-M000002
 は、それぞれ始点Ｐｓ及び終点Ｐｅの位置ベクトルである。以下、アルファベット等の文字の上側に矢印がつく場合には、その文字にかかる点の位置ベクトル又は文字が示す方向に沿ったベクトルを示すものとする。
　大円ＧＣが属する平面上で、
Figure JPOXMLDOC01-appb-M000003
 に垂直な方向のベクトルを
Figure JPOXMLDOC01-appb-M000004
 とする。
　大円ＧＣが属する平面の法線方向のベクトルを
Figure JPOXMLDOC01-appb-M000005
 とする。
　以上より、
Figure JPOXMLDOC01-appb-M000006
 となる。すなわち、これらの３つのベクトルは互いに直交し、それぞれがＸ軸、Ｙ軸及びＺ軸の方向を規定する。 [Step S3: Coordinate system definition on true sphere]
Coordinate system definition unit 33, based on the starting point P s and the end point P e projected onto a sphere TS, assume a coordinate system Sn according to a sphere TS. FIG. 6 is a diagram showing a true sphere TS in the coordinate system Sn. The coordinate system Sn is set as follows. First, to set a great circle GC on a sphere TS which belongs to the true sphere TS origin P s and the end point is projected onto P e. Here, with reference to the center O of a sphere TS, a vector indicating a middle point between the start point P s and the end point P e on the great circle GC
Figure JPOXMLDOC01-appb-M000001
 And here,
Figure JPOXMLDOC01-appb-M000002
 Are the position vectors of the start point P s and the end point Pe, respectively. Hereinafter, when an arrow is placed on the upper side of a character such as an alphabet, a position vector of a point related to the character or a vector along a direction indicated by the character is indicated.
On the plane to which the great circle GC belongs,
Figure JPOXMLDOC01-appb-M000003
 Vector in the direction perpendicular to
Figure JPOXMLDOC01-appb-M000004
 And
The normal vector of the plane to which the great circle GC belongs
Figure JPOXMLDOC01-appb-M000005
 And
From the above,
Figure JPOXMLDOC01-appb-M000006
 It becomes. That is, these three vectors are orthogonal to each other and each defines the direction of the X, Y, and Z axes.
　図７は、座標系Ｓｎにおける真球ＴＳをより詳細に示す図である。真球ＴＳ上での始点Ｐｓと終点Ｐｅとの間の距離Ｌは、Ｒを真球の半径として、以下の式で表される。
Figure JPOXMLDOC01-appb-M000007
 　また、真球ＴＳの中心Ｏから見たＸ軸に対する始点Ｐｓ又は終点Ｐｅがなす角度Φ０は、以下の式で表される。
Figure JPOXMLDOC01-appb-M000008
 FIG. 7 is a diagram showing the true sphere TS in the coordinate system Sn in more detail. The distance L between the starting point P s and the end point P e on sphericity TS is the R as the radius of the true sphere is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000007
 The angle [Phi 0 formed by the start point P s or end point P e with respect to the X-axis as viewed from the center O of a sphere TS is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000008
［ステップＳ４　補間地点の生成］
　補間地点生成部３４は、回転楕円体ＳＰ上の測地線経路上における補間地点（区分点）の座標を生成する。まず、回転楕円体ＳＰ上での始点ｐｓから終点ｐｅへの実方位θ及び実距離λを求める。そして、回転楕円体ＳＰ上での始点ｐｓと終点Ｐｅとを内挿する点として、回転楕円体ＳＰ上での始点Ｐｓから実方位θ、実距離ａλの補間地点ｐ（ａ）を求める。ここで、ａは、０から１の間の任意の実数である。図８に、補間地点の概要を示す。 [Step S4: Interpolation Point Generation]
The interpolation point generation unit 34 generates the coordinates of the interpolation point (partition point) on the geodesic path on the spheroid SP. First, the actual azimuth θ and actual distance λ from the starting point p s on spheroid SP to the end point p e. Then, as the point to interpolate the starting point p s and the end point P e on spheroid SP, the actual azimuth from the start point P s on the spheroid SP theta, interpolation point p of actual distance aλ: (a) Ask. Here, a is an arbitrary real number between 0 and 1. FIG. 8 shows an outline of the interpolation point.
　補間地点生成部３４に読み込まれるこれらのデータは、例えば記憶装置２に格納される。 These data read by the interpolation point generation unit 34 are stored in the storage device 2, for example.
［ステップＳ５　補間地点の投影］
　補間地点投影部３５は、生成した回転楕円体ＳＰ上の補間地点を真球ＴＳの座標系Ｓｎに投影する。つまりは、回転楕円体ＳＰ上の地点ｐ（ａ）に対応する真球ＴＳの座標系Ｓｎでの投影補間地点Ｐｎ（ａ）を求める。図９は、座標系Ｓｎにおける投影補間地点を示す図である。座標系Ｓｎにおける投影補間地点の位置ベクトルＰｎ（ａ）は、以下の式で表すことができる。
Figure JPOXMLDOC01-appb-M000009
 [Step S5: Interpolation point projection]
The interpolation point projection unit 35 projects the interpolation point on the generated spheroid SP onto the coordinate system Sn of the true sphere TS. That is, the projection interpolation point Pn (a) in the coordinate system Sn of the true sphere TS corresponding to the point p (a) on the spheroid SP is obtained. FIG. 9 is a diagram showing projection interpolation points in the coordinate system Sn. The position vector Pn (a) of the projection interpolation point in the coordinate system Sn can be expressed by the following equation.
Figure JPOXMLDOC01-appb-M000009
［ステップＳ６　離隔距離関数決定］
　離隔距離関数決定部３６は、以下の要領で離隔距離関数を決定する。座標系Ｓｎにおける各投影補間地点Ｐｎ（ａ）のＸ成分の値域はｃｏｓΦ０～１、Ｙ成分の値域は－ｓｉｎΦ０～ｓｉｎΦ０である。Ｚ成分は、投影測地線経路上に位置している投影補間地点と真球ＴＳ上の大円ＧＣとの離隔を表すパラメータであり、離隔距離ｄは以下の式で表される。
Figure JPOXMLDOC01-appb-M000010
 ここで、座標系Ｓｎにおける球座標Θ（ａ）、Φ（ａ）を、以下の式で示すように定義する。
Figure JPOXMLDOC01-appb-M000011
 このとき、Φ（ａ）の値域は、－Φ０～Φ０である。 [Step S6: Separation Distance Function Determination]
The separation distance function determination unit 36 determines the separation distance function in the following manner. Range of the X component of each projection interpolation point Pn (a) in the coordinate system and Sn range of cosΦ 0 ~ 1, Y component is -sinΦ 0 ~ sinΦ 0. The Z component is a parameter representing the separation between the projection interpolation point located on the projected geodesic path and the great circle GC on the true sphere TS, and the separation distance d is represented by the following equation.
Figure JPOXMLDOC01-appb-M000010
 Here, the spherical coordinates Θ (a) and Φ (a) in the coordinate system Sn are defined as shown by the following equations.
Figure JPOXMLDOC01-appb-M000011
 At this time, the range of Φ (a) is −Φ 0 to Φ 0 .
　球座標Θ（ａ）、Φ（ａ）を用いて、座標系Ｓｎにおける投影補間地点Ｐｎ（ａ）は、以下の式で表される。
Figure JPOXMLDOC01-appb-M000012
 Φ（ａ）は真球ＴＳ上の始点Ｐｓと終点Ｐｅとを結ぶ大円ＧＣの内分点であり、Θ（ａ）は投影補間地点Ｐｎ（ａ）における離隔距離を表すパラメータである。Θ（ａ）は、Φ（ａ）によって一意に決定されるので、ｓｉｎΘ及びｃｏｓΘを、Φの関数として、以下の式のように表すことができる。
Figure JPOXMLDOC01-appb-M000013
 但し、ε及びδは、以下の式（１）に示す関係を満たす離隔距離を表す関数である。
Figure JPOXMLDOC01-appb-M000014
 従って、座標系Ｓｎにおける投影補間地点Ｐｎ（Φ）を以下のように記述することができる。但し、以下の式では、Ｒ＝１として正規化した。
Figure JPOXMLDOC01-appb-M000015
 図１０は、座標系Ｓｎにおける投影補間地点Ｐｎ（Φ）を示す図である。図１０に示すように、投影補間地点Ｐｎ（Φ）は、投影測地線経路ＧＬ上に設定される。 Using the spherical coordinates Θ (a) and Φ (a), the projection interpolation point Pn (a) in the coordinate system Sn is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000012
 [Phi (a) is a dividing point of the great circle GC connecting the start point P s and the end point P e of the true sphere TS, Θ (a) is a parameter representing the distance in the projection interpolation point Pn (a) . Since Θ (a) is uniquely determined by Φ (a), sin Θ and cos Θ can be expressed as the following equation as a function of Φ.
Figure JPOXMLDOC01-appb-M000013
 However, ε and δ are functions representing the separation distance that satisfies the relationship shown in the following formula (1).
Figure JPOXMLDOC01-appb-M000014
 Therefore, the projection interpolation point Pn (Φ) in the coordinate system Sn can be described as follows. However, in the following formula | equation, it normalized as R = 1.
Figure JPOXMLDOC01-appb-M000015
 FIG. 10 is a diagram showing the projection interpolation point Pn (Φ) in the coordinate system Sn. As shown in FIG. 10, the projection interpolation point Pn (Φ) is set on the projected geodesic path GL.
近似係数定義
　離隔距離関数ε（Φ）、δ（Φ）について、区間［－Φ０, Φ０］での近似を行う。ここでは、近似を行うにあたり、以下の式（２）に示すように三角関数を用いる。
Figure JPOXMLDOC01-appb-M000016
 これにより、以下の式（３）が成立する。
Figure JPOXMLDOC01-appb-M000017
 始点Ｐｓ、終点Ｐｅでは、上述した式（１）が自動的に成立する。
Figure JPOXMLDOC01-appb-M000018
 ここで、αｋ、βｋは、それぞれＮ個の未知の定数である。 Approximation coefficient definition The separation function ε (Φ), δ (Φ) is approximated in the interval [−Φ 0 , Φ 0 ]. Here, for approximation, a trigonometric function is used as shown in the following equation (2).
Figure JPOXMLDOC01-appb-M000016
 Thereby, the following expression (3) is established.
Figure JPOXMLDOC01-appb-M000017
 At the start point P s and the end point Pe , the above-described equation (1) is automatically established.
Figure JPOXMLDOC01-appb-M000018
 Here, α k and β k are N unknown constants, respectively.
近似係数算出
　定数を決定するために、回転楕円体上の補間点を真球上の座標系Ｓｎに変換する。ここでは、補間は稠密に行わずとも、始点ｐｓから終点ｐｅまでをＮ＋１分割する地点ｐｉ（ｉ＝１～Ｎ）をサンプリングすることで、十分な精度を確保することができる。回転楕円体上の地点ｐｉを真球上の座標系Ｓｎに投影した、Ｎ個のサンプリング地点Ｐｎｉを考える。それぞれのサンプリング地点Ｐｎｉの座標系Ｓｎにおける球座標（Θｉ,Φｉ）は、以下の通りである。
Figure JPOXMLDOC01-appb-M000019
 このとき、Ｎ個のサンプリング地点のそれぞれで、上述の式（２）が成立しなければならない。よって、以下の式が得られる。
Figure JPOXMLDOC01-appb-M000020
 上式を行列で表すと、以下の式が得られる。
Figure JPOXMLDOC01-appb-M000021
 上式に、逆行列を左から乗じることで、Ｎ個の係数を決定することができる。逆行列の算出方法としては、例えば掃き出し法などを用いることができる。
Figure JPOXMLDOC01-appb-M000022
 従って、２Ｎ個の定数αｉ、βｉによって、式（２）に示した離隔距離関数ε（Φ）、δ（Φ）を決定することができる。 Approximation coefficient calculation In order to determine a constant, an interpolation point on the spheroid is converted into a coordinate system Sn on a true sphere. Here, interpolation without performing dense, by sampling the point p i (i = 1 ~ N ) for the N + 1 division from the start point p s to the end point p e, it is possible to secure a sufficient precision. The point p i on the spheroid is projected to the coordinate system Sn on sphericity, consider the N sampling points Pn i. Each spherical coordinate in the coordinate system Sn sampling point Pn i (Θ i, Φ i ) are as follows.
Figure JPOXMLDOC01-appb-M000019
 At this time, the above equation (2) must be established at each of the N sampling points. Therefore, the following formula is obtained.
Figure JPOXMLDOC01-appb-M000020
 When the above equation is expressed as a matrix, the following equation is obtained.
Figure JPOXMLDOC01-appb-M000021
 N coefficients can be determined by multiplying the above equation by an inverse matrix from the left. As the inverse matrix calculation method, for example, a sweeping out method or the like can be used.
Figure JPOXMLDOC01-appb-M000022
 Therefore, the separation functions ε (Φ) and δ (Φ) shown in the equation (2) can be determined by 2N constants αi and βi.
　ここで、サンプリングの近似精度について検証する。図１５～１８は、サンプリング数（Ｎ）を１、３、５、７個としたときの近似精度を示す図である。図１５～１８は、実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、点がサンプリング地点を示し、破線が上述の式（２）で表される近似誤差を示す。図１７からわかるように、サンプリング地点を５個以上とすることで、サンプリング地点と回転楕円体上の測地線経路をほぼ正確に真球に投影することができる。また、図１８の例では、大円補間経路の誤差が最大で３２２ｍであることがわかる。 Here, we will verify the approximate accuracy of sampling. 15 to 18 are diagrams showing approximation accuracy when the number of samplings (N) is 1, 3, 5, and 7. FIG. In FIGS. 15 to 18, the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, the point indicates the sampling point, and the broken line indicates the approximation error represented by the above equation (2). As can be seen from FIG. 17, by setting the number of sampling points to five or more, the sampling points and the geodesic path on the spheroid can be projected onto the true sphere almost accurately. In the example of FIG. 18, it can be seen that the error of the great circle interpolation path is 322 m at the maximum.
［ステップＳ７　回転角算出］
　回転角算出部３７は、大円ＧＣが属する平面ＰＬ１を真球上に投影された始点Ｐｓと終点Ｐｅとを結ぶ軸の周り回転させる回転角φを算出する。図１１は、座標系Ｓｎにおける投影補間地点Ｐｎ（Φ）をＹ軸方向から見た場合のＸ－Ｚ平面図である。この場合、投影補間地点Ｐｎ（Φ）から大円ＧＣまでの距離である離隔距離ｄは、図１１における弧の長さであり、以下の式で表される。
Figure JPOXMLDOC01-appb-M000023
 [Step S7 Rotation Angle Calculation]
Rotation angle calculator 37 calculates the rotation angle φ is rotated about an axis connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the perfect sphere. FIG. 11 is an XZ plan view when the projection interpolation point Pn (Φ) in the coordinate system Sn is viewed from the Y-axis direction. In this case, the separation distance d, which is the distance from the projection interpolation point Pn (Φ) to the great circle GC, is the length of the arc in FIG. 11 and is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000023
　本実施の形態では、以上の定義の下で、大円ＧＣが属する平面ＰＬ１を真球上に投影された始点Ｐｓと終点Ｐｅとを結ぶ軸の周りに回転角φだけ回転させることで、離隔距離を最小化する。　図１２は、座標系Ｓｎにおいて、大円ＧＣが属する平面ＰＬ１を真球上に投影された始点Ｐｓと終点Ｐｅとを結ぶ軸ＡＸの周りに回転角φだけ回転させた平面ＰＬ２を示す図である。図１３は、座標系Ｓｎにおいて、大円ＧＣが属する平面ＰＬ１を真球上に投影された始点Ｐｓと終点Ｐｅとを結ぶ軸ＡＸの周りに回転角φだけ回転させた平面ＰＬ２をＹ軸方向から見たＸ－Ｚ平面図である。このことは、図１３に示すように、座標系ＳｎにおいてＹ軸周りに平面を回転させることを意味し、原点中心の座標系では回転後の投影補間地点は、以下のように変換される。
Figure JPOXMLDOC01-appb-M000024
 In this embodiment, the above under the definition, by rotating by the rotation angle φ around the axis connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the sphericity Minimize separation distance. 12, in the coordinate system Sn, shows a plane PL2 which is rotated around an axis AX by rotation angle φ connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the sphericity FIG. 13, in the coordinate system Sn, a plane PL2 which is rotated around an axis AX by rotation angle φ connecting the start point P s and the end point P e of great circle GC is projected plane PL1 belonging to the sphericity Y It is an XZ plan view seen from the axial direction. As shown in FIG. 13, this means that the plane is rotated around the Y axis in the coordinate system Sn. In the coordinate system centered at the origin, the projected interpolation point after the rotation is converted as follows.
Figure JPOXMLDOC01-appb-M000024
　また、始点Ｐｓと終点Ｐｅとは、以下の式のように変換される。
Figure JPOXMLDOC01-appb-M000025
 Further, the starting point P s and the end point P e, are transformed by the following equation.
Figure JPOXMLDOC01-appb-M000025
　ここで、回転後の離隔距離である回転離隔距離ＲＤ（Φ,φ）を定義する。以下では、平面ＰＬ２と平行であり、かつ、真球ＴＳの中心を含む平面を平面ＰＬ３と定義する。図１４は、回転離隔距離を構成する弧を示す図である。図１４に示すように、投影補間地点Ｐｎ（Φ）と平面ＰＬ３との距離は、これらを結ぶ弧ＡＲＣ１であり、弧ＡＲＣ１は以下の式で示される。但し、以下の式では、上述の通り、Ｒ＝１として正規化されている。
Figure JPOXMLDOC01-appb-M000026
 Here, a rotation separation distance RD (Φ, φ) that is a separation distance after rotation is defined. Hereinafter, a plane parallel to the plane PL2 and including the center of the true sphere TS is defined as a plane PL3. FIG. 14 is a diagram showing arcs constituting the rotational separation distance. As shown in FIG. 14, the distance between the projection interpolation point Pn (Φ) and the plane PL3 is an arc ARC1 connecting these, and the arc ARC1 is expressed by the following equation. However, in the following expression, as described above, it is normalized as R = 1.
Figure JPOXMLDOC01-appb-M000026
　図１４に示すように、大円が属する平面を回転した平面（平面ＰＬ２）と平面ＰＬ３との距離は、これらを結ぶ弧ＡＲＣ２であり、弧ＡＲＣ２は以下の式で示される。但し、以下の式では、上述の通り、Ｒ＝１として正規化されている。
Figure JPOXMLDOC01-appb-M000027
 As shown in FIG. 14, the distance between the plane (plane PL2) obtained by rotating the plane to which the great circle belongs and the plane PL3 is an arc ARC2 connecting these, and the arc ARC2 is expressed by the following equation. However, in the following expression, as described above, it is normalized as R = 1.
Figure JPOXMLDOC01-appb-M000027
　投影補間地点Ｐｎ（Φ）と大円が属する平面を回転した平面（平面ＰＬ２）との間の距離は、上述の弧ＡＲＣと弧ＡＲＣ２との和であるので、回転離隔距離ＲＤは、以下の式で表すことができる。
Figure JPOXMLDOC01-appb-M000028
 上式は、回転離隔距離ＲＤ（Φ,φ）が正規化された地球の半径に比べて極めて小さい場合には、以下の式（４）の様に近似することができる。
Figure JPOXMLDOC01-appb-M000029
 上式において、回転角φを適切に選択することで、回転離隔距離ＲＤ（Φ,φ）を最小化することができる。これにより、回転角φを適切に設定することで、回転後の平面と真球の表面との交線が、投影測地線を補間する経路として設定されることとなる。
Since the distance between the projection interpolation point Pn (Φ) and the plane (plane PL2) rotated from the plane to which the great circle belongs is the sum of the arc ARC and the arc ARC2, the rotation separation distance RD is It can be expressed by a formula.
Figure JPOXMLDOC01-appb-M000028
 The above equation can be approximated as the following equation (4) when the rotational separation RD (Φ, φ) is extremely small compared to the normalized radius of the earth.
Figure JPOXMLDOC01-appb-M000029
 In the above equation, the rotation separation distance RD (Φ, φ) can be minimized by appropriately selecting the rotation angle φ. Thus, by appropriately setting the rotation angle φ, the intersection line between the rotated plane and the true sphere surface is set as a path for interpolating the projected geodesic line.
最適角導出
　上述の式（２）を式（４）に代入すると、回転離隔距離ＲＤは、以下の式（５）で近似できる。
Figure JPOXMLDOC01-appb-M000030
 Φ＝±Φ０でＲＤ＝０が成立するが、一般に、区間［－Φ０, Φ０］の全域にわたってＲＤ＝０が成立するφは存在しない。そこで、誤差が最小となるように回転角φを選択する。 Optimal angle derivation When the above equation (2) is substituted into equation (4), the rotational separation RD can be approximated by the following equation (5).
Figure JPOXMLDOC01-appb-M000030
 Although RD = 0 holds when Φ = ± Φ 0 , in general, there is no φ where RD = 0 holds across the entire section [−Φ 0 , Φ 0 ]. Therefore, the rotation angle φ is selected so that the error is minimized.
　以下、誤差を最小化するための回転角φの解法について説明する。
［解法１　中間点法］
　真球上の始点Ｐｓと終点Ｐｅとの中点において、回転離隔距離ＲＤが０となるような回転角φを選択する。このとき、以下の式が得られる。
Figure JPOXMLDOC01-appb-M000031
 したがって、回転角φは以下の式で表される。
Figure JPOXMLDOC01-appb-M000032
 中間点法で得られた回転角に基づいて補間した際の誤差を、図１９に示す。図１９では、実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、破線が投影測地線経路に対する、中間点法で得られた補間経路の誤差を示す。この補間方法においては、回転離隔距離の最大値は、北緯２０度以南で４９．２ｍ、北緯２０度以北で３４．９ｍである。 Hereinafter, a method of solving the rotation angle φ for minimizing the error will be described.
[Solution 1 Midpoint Method]
At the midpoint between the start point P s and the end point P e of the perfect sphere, it selects the rotation angle φ, as the rotational distance RD is zero. At this time, the following equation is obtained.
Figure JPOXMLDOC01-appb-M000031
 Therefore, the rotation angle φ is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000032
 FIG. 19 shows an error when interpolation is performed based on the rotation angle obtained by the midpoint method. In FIG. 19, the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, and the broken line indicates the error of the interpolation path obtained by the midpoint method with respect to the projected geodesic path. In this interpolation method, the maximum value of the rotational separation is 49.2 m south of latitude 20 degrees north and 34.9 m north of latitude 20 degrees north.
　以上より、中間点法によれば、図２４と比較して、誤差を低減することができ、かつ、補間後に得られる経路を滑らかな連続線とすることができる。 As described above, according to the midpoint method, it is possible to reduce the error as compared with FIG. 24 and to make the path obtained after the interpolation a smooth continuous line.
［解法２　最大離隔点法］
　本補間方法においては、真球上の始点Ｐｓと終点Ｐｅ間の補間点で離隔距離ｄが最大となる地点の回転離隔距離ＲＤが０になるような回転角φを選択する。離隔距離ｄが最大となる地点では、上述の式（３）より、以下の式が成立する。
Figure JPOXMLDOC01-appb-M000033
 離隔距離Ｄが最大となる地点ΦＭでは、以下の式が成立する。
Figure JPOXMLDOC01-appb-M000034
 式（６）を利用して、初期値をΦ＝０としてＮＥＷＴＯＮ（ニュートン）法を用いて式（７）を満たすΦＭを求めることができる。このときの回転角φは、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000035
 最大離隔点法で得られた回転角に基づいて補間した際の誤差を、図２０に示す。図２０では、実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、破線が投影測地線経路に対する、最大離隔点法で得られた補間経路の誤差を示す。この補間方法においては、離隔距離の最大値は、北緯２０度以南で３８．０ｍ、北緯２０度以北で４８．８ｍである。 [Solution 2 Maximum separation point method]
In this interpolation method selects the start point P s and the end point P e rotational angle as rotational distance RD of the point where the separation distance d is maximum interpolation point becomes 0 between φ on sphericity. At the point where the separation distance d is maximum, the following formula is established from the above formula (3).
Figure JPOXMLDOC01-appb-M000033
 In distance D point is maximum [Phi M, the following expression holds.
Figure JPOXMLDOC01-appb-M000034
 Using Equation (6), Φ M satisfying Equation (7) can be obtained using the NEWTON method with an initial value of Φ = 0. The rotation angle φ at this time is given by the following equation.
Figure JPOXMLDOC01-appb-M000035
 FIG. 20 shows an error when interpolation is performed based on the rotation angle obtained by the maximum separation point method. In FIG. 20, the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, and the broken line indicates the error of the interpolation path obtained by the maximum separation point method with respect to the projected geodesic path. In this interpolation method, the maximum value of the separation distance is 38.0 m south of latitude 20 degrees north and 48.8 m north of latitude 20 degrees north.
　以上より、最大離隔点法によれば、図２４と比較して、誤差を低減することができ、かつ、補間後に得られる経路を滑らかな連続線とすることができる。 As described above, according to the maximum separation point method, it is possible to reduce the error as compared with FIG. 24 and to make the path obtained after the interpolation a smooth continuous line.
［解法３　高精度化解法］
　上記で説明した中間点法及び最大離隔点法は、簡便な演算で回転角φを求めることができる点で有利である。しかし、中間点法及び最大離隔点法は、回転前の情報のみに基づいているため、回転後の補間精度が保証されない。そのため、更なる高精度化のため、回転離隔距離ＲＤについて、最適解を導く方法を説明する。 [Solution 3 High-precision solution]
The intermediate point method and the maximum separation point method described above are advantageous in that the rotation angle φ can be obtained by a simple calculation. However, since the midpoint method and the maximum separation point method are based only on information before rotation, interpolation accuracy after rotation is not guaranteed. Therefore, a method for deriving an optimal solution for the rotational separation distance RD will be described for further high accuracy.
［解法３－１　平均法］
　式（５）について、区間［－Φ０, Φ０］での回転離隔距離の平均ＲＤａは、以下の式で表される。
Figure JPOXMLDOC01-appb-M000036
 分母の計算は省略し、分子の計算について検討すると、
Figure JPOXMLDOC01-appb-M000037
 上式より、ＲＤａが０となる回転角φは、以下の式で求められる。
Figure JPOXMLDOC01-appb-M000038
 平均法で得られた回転角に基づいて補間した際の誤差を、図２１に示す。図２１では、実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、破線が投影測地線経路に対する、平均法で得られた補間経路の誤差を示す。この補間方法においては、回転離隔距離の最大値は、北緯２０度以南で４５．５ｍ、北緯２０度以北で３９．２ｍである。 [Solution 3-1 Average method]
Regarding the equation (5), the average RDa of the rotation separation distance in the section [−Φ 0 , Φ 0 ] is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000036
 Omitting the denominator calculation and considering the numerator calculation
Figure JPOXMLDOC01-appb-M000037
 From the above equation, the rotation angle φ at which RD a is 0 can be obtained by the following equation.
Figure JPOXMLDOC01-appb-M000038
 FIG. 21 shows an error when interpolation is performed based on the rotation angle obtained by the averaging method. In FIG. 21, the solid line shows the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, and the broken line shows the error of the interpolation path obtained by the averaging method with respect to the projected geodesic path. In this interpolation method, the maximum value of the rotational separation distance is 45.5 m south of latitude 20 degrees north and 39.2 m north of latitude 20 degrees north.
　以上より、平均法によれば、図２４と比較して、誤差を低減することができ、かつ、補間後に得られる経路を滑らかな連続線とすることができる。 As described above, according to the averaging method, it is possible to reduce errors as compared with FIG. 24 and to make the path obtained after interpolation a smooth continuous line.
［解法３－２　加重平均法］
　区間の中央部の重みづけを考慮した加重平均について検討する。式（５）に加重関数Ｗ（Φ）を乗じて、区間［－Φ０, Φ０］での回転離隔距離の加重平均ＲＤｗａを算出する。ここでは、加重関数Ｗ（Φ）は、北緯２０度以北で１、以南で０を与えるものとする。加重平均ＲＤｗａは、以下の式で求められる。
Figure JPOXMLDOC01-appb-M000039
 分母の計算は省略し、分子の計算について検討すると、
Figure JPOXMLDOC01-appb-M000040
 上式より、ＲＤｗａが０となる回転角φは、以下の式で求められる。
Figure JPOXMLDOC01-appb-M000041
 加重平均法で得られた回転角に基づいて補間した際の誤差を、図２２に示す。図２２では、実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、破線が投影測地線経路に対する、加重平均法で得られた補間経路の誤差を示す。この補間方法においては、回転離隔距離の最大値は、北緯２０度以南で７２．４ｍ、北緯２０度以北で３４．６ｍである。 [Solution 3-2 Weighted Average Method]
Examine the weighted average considering the weight of the central part of the section. The weighted average RDwa of the rotation separation distance in the section [−Φ 0 , Φ 0 ] is calculated by multiplying Expression (5) by the weighting function W (Φ). Here, it is assumed that the weighting function W (Φ) gives 1 for north of 20 degrees north latitude and 0 for south. The weighted average RDwa is obtained by the following formula.
Figure JPOXMLDOC01-appb-M000039
 Omitting the denominator calculation and considering the numerator calculation
Figure JPOXMLDOC01-appb-M000040
 From the above equation, the rotation angle φ at which RD wa becomes 0 is obtained by the following equation.
Figure JPOXMLDOC01-appb-M000041
 FIG. 22 shows an error when interpolation is performed based on the rotation angle obtained by the weighted average method. In FIG. 22, the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, and the broken line indicates the error of the interpolation path obtained by the weighted average method with respect to the projected geodesic path. In this interpolation method, the maximum value of the rotation separation distance is 72.4 m south of latitude 20 degrees north and 34.6 m north of latitude 20 degrees north.
　以上より、加重平均法によれば、図２４と比較して、誤差を低減することができ、かつ、補間後に得られる経路を滑らかな連続線とすることができる。 As described above, according to the weighted average method, it is possible to reduce the error as compared with FIG. 24 and to make the path obtained after the interpolation a smooth continuous line.
［解法３－３　最小自乗法］
　この方法では、区間［－Φ０, Φ０］における回転離隔距離ＲＤの自乗平均が最小となるような回転角φを算出する。式（５）を自乗して、区間［－Φ０, Φ０］で積分した値Ｉを求める。
Figure JPOXMLDOC01-appb-M000042
 上式の各項を、区間［－Φ０, Φ０］で積分する。上式では、
Figure JPOXMLDOC01-appb-M000043
 が含まれるが、ここではｋ＝ｍは選択しないものとする。ここで、上述の回転離隔距離ＲＤの自乗Ｉの各項から、ｃｏｓφ及びｓｉｎφを除いた部分を、それぞれＩ１～Ｉ８とする。すると、回転離隔距離の自乗平均Ｉは、以下の式で表される。
Figure JPOXMLDOC01-appb-M000044
 積分値Ｉ１は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000045
 積分値Ｉ２は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000046
 積分値Ｉ３は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000047
 更に計算を進めると、
Figure JPOXMLDOC01-appb-M000048
 積分値Ｉ４は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000049
 積分値Ｉ５は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000050
 積分値Ｉ６は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000051
 積分値Ｉ７は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000052
 積分値Ｉ８は、以下の式で与えられる。
Figure JPOXMLDOC01-appb-M000053
 [Solution 3-3 Least Squares Method]
In this method, the rotation angle φ is calculated such that the root mean square of the rotation separation distance RD in the section [−Φ 0 , Φ 0 ] is minimized. The value I integrated in the interval [−Φ 0 , Φ 0 ] is obtained by squaring Equation (5).
Figure JPOXMLDOC01-appb-M000042
 Each term of the above equation is integrated in the interval [−Φ 0 , Φ 0 ]. In the above formula,
Figure JPOXMLDOC01-appb-M000043
 Here, k = m is not selected. Here, the portions excluding cosφ and sinφ from the terms of the square I of the rotational separation distance RD described above are denoted by I 1 to I 8 , respectively. Then, the root mean square I of the rotation separation distance is expressed by the following equation.
Figure JPOXMLDOC01-appb-M000044
 Integrated value I 1 is given by the following equation.
Figure JPOXMLDOC01-appb-M000045
 Integrated value I 2 is given by the following equation.
Figure JPOXMLDOC01-appb-M000046
 Integrated value I 3 is given by the following equation.
Figure JPOXMLDOC01-appb-M000047
 If we further calculate,
Figure JPOXMLDOC01-appb-M000048
 The integral value I 4 is given by the following equation.
Figure JPOXMLDOC01-appb-M000049
 The integral value I 5 is given by the following equation.
Figure JPOXMLDOC01-appb-M000050
 The integral value I 6 is given by the following equation.
Figure JPOXMLDOC01-appb-M000051
 The integral value I 7 is given by the following equation.
Figure JPOXMLDOC01-appb-M000052
 Integrated value I 8 is given by the following equation.
Figure JPOXMLDOC01-appb-M000053
以上で、求めた自乗値Ｉを回転角φで微分すると、以下の式が得られる。
Figure JPOXMLDOC01-appb-M000054
 従って、自乗和を最小とするには、回転角φについて以下の式が成立すればよい。
Figure JPOXMLDOC01-appb-M000055
 最小自乗法で得られた回転角に基づいて補間した際の誤差を、図２３に示す。図２３では実線が真球上の投影測地線経路に対する大円補間経路の誤差を示し、破線が投影測地線経路に対する、最小自乗法で得られた補間経路の誤差を示す。この補間方法においては、回転離隔距離の最大値は、北緯２０度以南で４６．５ｍ、北緯２０度以北で３８．１ｍである。 When the square value I thus obtained is differentiated by the rotation angle φ, the following equation is obtained.
Figure JPOXMLDOC01-appb-M000054
 Therefore, in order to minimize the sum of squares, the following equation should be established for the rotation angle φ.
Figure JPOXMLDOC01-appb-M000055
 FIG. 23 shows an error when interpolation is performed based on the rotation angle obtained by the method of least squares. In FIG. 23, the solid line indicates the error of the great circle interpolation path with respect to the projected geodesic path on the true sphere, and the broken line indicates the error of the interpolation path obtained by the least square method with respect to the projected geodesic path. In this interpolation method, the maximum value of the rotational separation distance is 46.5 m south of latitude 20 degrees north and 38.1 m north of latitude 20 degrees north.
　以上より、最小自乗法によれば、図２４と比較して、誤差を低減することができ、かつ、補間後に得られる経路を滑らかな連続線とすることができる。 As described above, according to the least square method, the error can be reduced as compared with FIG. 24, and the path obtained after the interpolation can be a smooth continuous line.
　上記の解法の方式の種別については、例えば記憶装置２に、最適回転角算出方法データベースＤ１として格納されてもよい。これにより、演算部３は、回転角の算出に用いる解法を、記憶装置２から読み込むことができる。最適回転角算出方法データベースＤ１には、最適回転角算出方法に応じて用いる計算処理方法にかかる情報、アルゴリズム、又は、プログラムが含まれる。 The type of solution method may be stored in the storage device 2 as the optimum rotation angle calculation method database D1, for example. Thereby, the calculating part 3 can read the solution used for calculation of a rotation angle from the memory | storage device 2. FIG. The optimum rotation angle calculation method database D1 includes information, algorithms, or programs related to calculation processing methods used in accordance with the optimum rotation angle calculation method.
［ステップＳ８　補間経路情報出力］
　補間経路情報出力部３８は、算出した回転角φを用いて、投影測地線経路を補間する補間経路を設定する。ここで、回転される対象である大円上の点ＰＧＣは、ベクトルＶを定義すると、以下に式のように表される。
Figure JPOXMLDOC01-appb-M000056
 [Step S8: Interpolation path information output]
The interpolation path information output unit 38 sets an interpolation path for interpolating the projected geodesic path using the calculated rotation angle φ. Here, P GC point on a subject is rotated great circle, defining a vector V, it is represented by the equation below.
Figure JPOXMLDOC01-appb-M000056
　回転角φにて回転された大円が属する平面によって構成される補間経路は、上述の通り、以下のように再定義される。
Figure JPOXMLDOC01-appb-M000057
 これを、極方向をＺ軸とする通常の座標系で記述すると、以下の式の通りとなる。ここでは、ベクトルＶは、補間経路が属する平面、すなわち真球ＴＳの表面と交線を有する上述の平面ＰＬ２に対する単位法線ベクトルである。
Figure JPOXMLDOC01-appb-M000058
 単位法線ベクトルの各成分値と内積の値はステップＳ２で読み込んだ測地線経路の真球上の補間経路情報を表すデータとして記憶装置２に格納する。その後、ステップＳ２へ戻る。 As described above, the interpolation path constituted by the plane to which the great circle rotated at the rotation angle φ belongs is redefined as follows.
Figure JPOXMLDOC01-appb-M000057
 If this is described in a normal coordinate system with the polar direction as the Z axis, the following equation is obtained. Here, the vector V is a unit normal vector with respect to the above-described plane PL2 that intersects the plane to which the interpolation path belongs, that is, the surface of the true sphere TS.
Figure JPOXMLDOC01-appb-M000058
 Each component value and inner product value of the unit normal vector are stored in the storage device 2 as data representing interpolation path information on the true sphere of the geodesic path read in step S2. Thereafter, the process returns to step S2.
　以上説明した処理を行うことで、地理情報処理装置１００は、回転楕円体上の測地線経路を真球上に投影した経路に対して、真球上の大円経路を、大円経路の始点と終点とを結ぶ軸の周りに回転させることで、両経路の誤差を最小化することができる。これにより、基準緯度が異なる場合でも、真球上に設定した地図間の相互運用性を向上させることが可能となる。 By performing the processing described above, the geographic information processing apparatus 100 converts the great circle path on the true sphere to the start point of the great circle path with respect to the route obtained by projecting the geodesic path on the spheroid onto the true sphere. By rotating around the axis connecting the end point and the end point, the error of both paths can be minimized. This makes it possible to improve interoperability between maps set on a true sphere even when the reference latitude is different.
　また、上式で示した真球上の補間経路は、一般的な方法と同様に、形式的には平面と真球面の交線として表される。よって、本実施の形態によれば、一般的な方法と比べて、大幅に計算量を増加させることなく補間精度を向上することができる。  Also, the interpolation path on the true sphere shown in the above formula is formally expressed as an intersection of a plane and a true sphere, as in a general method. Therefore, according to the present embodiment, it is possible to improve the interpolation accuracy without significantly increasing the amount of calculation as compared with a general method.
その他の実施の形態
　なお、本発明は上記実施の形態に限られたものではなく、趣旨を逸脱しない範囲で適宜変更することが可能である。例えば、上述の実施の形態では、地理情報処理装置が、地球上を移動する航空機などの移動体に搭載される場合について説明したが、これは例示に過ぎない。上述の実施の形態にかかる地理情報処理装置は、例えば空中を飛行する航空機以外の移動体、陸上を移動する車両、海上を移動する船舶、海中を移動する潜水艇など、地球上を移動する他の移動体に搭載ができる。また、上述の実施の形態にかかる地理情報処理装置は、移動体に限らず、航空機を管制に用いる管制システムなど移動体の運航管理システムなどに組み込むことも可能である。 Other Embodiments The present invention is not limited to the above-described embodiments, and can be appropriately changed without departing from the spirit of the present invention. For example, in the above-described embodiment, the case where the geographic information processing apparatus is mounted on a moving body such as an aircraft moving on the earth has been described, but this is merely an example. The geographical information processing apparatus according to the above-described embodiment includes, for example, a moving body other than an aircraft flying in the air, a vehicle moving on the land, a ship moving on the sea, a submarine moving on the sea, and the like moving on the earth. Can be mounted on any mobile body. Moreover, the geographical information processing apparatus according to the above-described embodiment is not limited to a mobile object, but can be incorporated in an operation management system for a mobile object such as a control system that uses an aircraft for control.
　以上では、地理情報処理装置及びこの装置で行われる地理情報処理方法について説明した。しかし、本発明は、これに限定されるものではない。本発明は、任意の処理を、ＣＰＵ（Central Processing Unit）にコンピュータプログラムを実行させることにより実現することも可能である。 In the above, the geographic information processing apparatus and the geographic information processing method performed by this apparatus have been described. However, the present invention is not limited to this. The present invention can also realize arbitrary processing by causing a CPU (Central Processing Unit) to execute a computer program.
　プログラムは、様々なタイプの非一時的なコンピュータ可読媒体（non-transitory computer readable medium）を用いて格納され、コンピュータに供給することができる。非一時的なコンピュータ可読媒体は、様々なタイプの実体のある記録媒体（tangible storage medium）を含む。非一時的なコンピュータ可読媒体の例は、磁気記録媒体（例えばフレキシブルディスク、磁気テープ、ハードディスクドライブ）、光磁気記録媒体（例えば光磁気ディスク）、ＣＤ－ＲＯＭ（Read Only Memory）、ＣＤ－Ｒ、ＣＤ－Ｒ／Ｗ、半導体メモリ（例えば、マスクＲＯＭ、ＰＲＯＭ（Programmable ROM）、ＥＰＲＯＭ（Erasable PROM）、フラッシュＲＯＭ、ＲＡＭ（random access memory））を含む。また、プログラムは、様々なタイプの一時的なコンピュータ可読媒体（transitory computer readable medium）によってコンピュータに供給されてもよい。一時的なコンピュータ可読媒体の例は、電気信号、光信号、及び電磁波を含む。一時的なコンピュータ可読媒体は、電線及び光ファイバ等の有線通信路、又は無線通信路を介して、プログラムをコンピュータに供給できる。 The program can be stored and supplied to a computer using various types of non-transitory computer readable media. Non-transitory computer readable media include various types of tangible storage media (tangible storage medium). Examples of non-transitory computer-readable media include magnetic recording media (eg flexible disks, magnetic tapes, hard disk drives), magneto-optical recording media (eg magneto-optical discs), CD-ROMs (Read Only Memory), CD-Rs, CD-R / W, semiconductor memory (for example, mask ROM, PROM (Programmable ROM), EPROM (Erasable ROM), flash ROM, RAM (random access memory)) are included. The program may also be supplied to the computer by various types of temporary computer-readable media. Examples of transitory computer readable media include electrical signals, optical signals, and electromagnetic waves. The temporary computer-readable medium can supply the program to the computer via a wired communication path such as an electric wire and an optical fiber, or a wireless communication path.
　以上、実施の形態を参照して本願発明を説明したが、本願発明は上記によって限定されるものではない。本願発明の構成や詳細には、発明のスコープ内で当業者が理解し得る様々な変更をすることができる。 The present invention has been described above with reference to the embodiment, but the present invention is not limited to the above. Various changes that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the invention.
　この出願は、２０１６年１１月１日に出願された日本出願特願２０１６－２１４５２６を基礎とする優先権を主張し、その開示の全てをここに取り込む。 This application claims priority based on Japanese Patent Application No. 2016-214526 filed on November 1, 2016, the entire disclosure of which is incorporated herein.
１　入力装置
２　記憶装置
３　演算部
４　表示装置
５　バス
３１　真球投影変換式生成部
３２　測地線情報入力部
３３　座標系定義部
３４　補間地点生成部
３５　補間地点投影部
３６　離隔距離関数決定部
３７　回転角算出部
３８　補間経路情報出力部
１００　地理情報処理装置
ＡＲＣ１　投影補間地点Ｐｎ（Φ）と平面ＰＬ３とを結ぶ弧
ＡＲＣ２　大円が属する平面を回転した平面（平面ＰＬ２）と平面ＰＬ３とを結ぶ弧
ＧＣ　大円
ＧＬ　投影測地線経路
Ｐｅ　真球上の終点
ｐｅ　回転楕円体上の終点
ＰＬ１　真球上の始点と終点を結ぶ大円を含む平面
ＰＬ２　ＰＬ１を真球上の始点と終点を結ぶ軸で所定の角度回転した平面
ＰＬ３　ＰＬ２に平行であり、かつ、真球ＴＳの中心を含む平面
Ｐｓ　真球上の始点
ｐｓ　回転楕円体上の始点
ＴＳ　真球
ＳＰ　回転楕円体 DESCRIPTION OF SYMBOLS 1 Input device 2 Memory | storage device 3 Calculation part 4 Display apparatus 5 Bus 31 True spherical projection conversion type | mold production | generation part 32 Geodesic information input part 33 Coordinate system definition part 34 Interpolation point production | generation part 35 Interpolation point projection part 36 Separation distance function determination part 37 Rotation angle calculation unit 38 Interpolation path information output unit 100 Geographic information processing device ARC1 Arc ARC2 connecting projection interpolation point Pn (Φ) and plane PL3 A plane (plane PL2) obtained by rotating the plane to which the great circle belongs is connected to plane PL3. the start and end points on a plane PL2 PL1 sphericity including great circle connecting the start point and the end point of the end point on PL1 sphericity on the arc GC great circle GL projection geodesic path P e sphericity on the end point p e spheroidal connecting parallel to a predetermined angular rotation to a plane PL3 PL2 in the axial and the starting point TS true sphere SP spheroids on the starting point p s spheroid in the plane P s sphericity including the center of a sphere TS

Claims (9)

  1. 　回転楕円体上の２つの地点を示す情報が格納された記憶装置と、
    　前記記憶装置から前記回転楕円体上の２つの地点の情報を読み込み、読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影し、前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転し、回転された平面と前記真球の表面との交線を補間経路とする演算部と、を備える、
    　地理情報処理装置。     A storage device storing information indicating two points on the spheroid;
    The information of two points on the spheroid is read from the storage device, and the two points on the spheroid read are projected onto a true sphere defined by a reference latitude and projected onto the sphere. The plane to which the great circle connecting the two points belongs is rotated with the straight line connecting the two points projected on the true sphere as the rotation axis, and the line of intersection between the rotated plane and the surface of the true sphere An arithmetic unit as an interpolation path,
    Geographic information processing device.
  2. 　前記回転楕円体上の２つの地点を結ぶ前記回転楕円体上の測地線経路を補間する補間地点を生成し、
    　前記補間地点を前記真球上に投影した投影補間地点と、前記回転された平面と、の間の距離である回転離隔距離が所定の値となるように回転角を決定する、
    　請求項１に記載の地理情報処理装置。     Generating an interpolation point that interpolates a geodesic path on the spheroid that connects two points on the spheroid;
    A rotation angle is determined so that a rotation separation distance that is a distance between a projection interpolation point obtained by projecting the interpolation point on the true sphere and the rotated plane becomes a predetermined value.
    The geographic information processing apparatus according to claim 1.
  3. 　前記真球上に投影された２つの地点の中間点である前記投影補間地点において、前記回転離隔距離が０となるように、前記大円が属する平面を回転させる、
    　請求項２に記載の地理情報処理装置。     Rotating the plane to which the great circle belongs so that the rotation separation distance is 0 at the projection interpolation point which is an intermediate point between the two points projected onto the true sphere;
    The geographic information processing apparatus according to claim 2.
  4. 　前記真球上に投影された２つの地点の離隔距離が最大となる前記投影補間地点において、前記回転離隔距離が０となるように、前記大円が属する平面を回転させる、
    　請求項２に記載の地理情報処理装置。     Rotating the plane to which the great circle belongs so that the rotation separation distance is 0 at the projection interpolation point where the separation distance between the two points projected onto the true sphere is maximum;
    The geographic information processing apparatus according to claim 2.
  5. 　１以上の前記投影補間地点のそれぞれにおける回転離隔距離の平均が０となるように、前記大円が属する平面を回転させる、
    　請求項２に記載の地理情報処理装置。     Rotating the plane to which the great circle belongs so that the average rotation separation distance at each of the one or more projection interpolation points is 0;
    The geographic information processing apparatus according to claim 2.
  6. 　前記１以上の投影補間地点のそれぞれに重みづけをして、重みづけをした前記１以上の投影補間地点のそれぞれにおける回転離隔距離の平均が０となるように、前記大円が属する平面を回転させる、
    　請求項５に記載の地理情報処理装置。     Weighting each of the one or more projection interpolation points, and rotating the plane to which the great circle belongs so that the average rotation separation distance at each of the weighted one or more projection interpolation points is 0 Let
    The geographic information processing apparatus according to claim 5.
  7. 　前記１以上の投影補間地点のそれぞれにおける回転離隔距離の自乗平均が最小となるように、前記大円が属する平面を回転させる、
    　請求項２に記載の地理情報処理装置。     Rotating the plane to which the great circle belongs so that the root mean square of the rotation separation distance at each of the one or more projection interpolation points is minimized;
    The geographic information processing apparatus according to claim 2.
  8. 　記憶装置から回転楕円上の２つの地点の情報を読み込み、
    　読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影し、
    　前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転し、
    　回転された平面と前記真球の表面との交線を補間経路として設定する、
    　地理情報処理方法。　　　     Read the information of two points on the spheroid from the storage device,
    Project the two points on the read spheroid onto a sphere defined by the reference latitude,
    A plane to which a great circle connecting two points projected on the true sphere belongs is rotated with a straight line connecting the two points projected on the true sphere as a rotation axis,
    An intersection line between the rotated plane and the surface of the true sphere is set as an interpolation path;
    Geographic information processing method.
  9. 　記憶装置から回転楕円体上の２つの地点の情報を読み込む処理と、
    　読み込んだ前記回転楕円体上の２つの地点を基準緯度で定義される真球上に投影する処理と、
    　前記真球上に投影された２つの地点を結ぶ大円が属する平面を、前記真球上に投影された２つの地点間を結ぶ直線を回転軸として回転する処理と、
    　回転された平面と前記真球の表面との交線を補間経路として設定する処理と、をコンピュータに実行させる、
    　地理情報処理プログラムが格納された非一時的なコンピュータ可読媒体。     A process of reading information of two points on the spheroid from the storage device;
    A process of projecting two points on the read spheroid onto a sphere defined by a reference latitude;
    A process of rotating a plane to which a great circle connecting two points projected on the true sphere belongs, with a straight line connecting the two points projected on the true sphere as a rotation axis;
    Causing the computer to execute a process of setting an intersection line between the rotated plane and the surface of the true sphere as an interpolation path;
    A non-transitory computer readable medium storing a geographic information processing program.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116214542A (en) * 2023-03-23 2023-06-06 广东省特种设备检测研究院东莞检测院 Digital twin system of spherical tank inner wall climbing robot

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0684100A (en) * 1992-09-03 1994-03-25 Mitsubishi Electric Corp Flight path retreival device
JP2002351307A (en) * 2001-05-30 2002-12-06 Denso Corp Method and device for map display
JP2006064892A (en) * 2004-08-26 2006-03-09 Hasegawa Shoji:Kk Position calculating device, position calculating method, position calculating program, and storage medium for position calculating program
JP2012085139A (en) * 2010-10-13 2012-04-26 Kansai Electric Power Co Inc:The Program for making computer function as calculation device of separation distance
US20140108464A1 (en) * 2012-06-05 2014-04-17 Google Inc. System and Method for Storing and Retrieving Geospatial Data
WO2014108957A1 (en) * 2013-01-08 2014-07-17 日本電気株式会社 Coordinate conversion device, non-transitory computer readable medium in which coordinate conversion program is stored, and coordinate conversion method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0684100A (en) * 1992-09-03 1994-03-25 Mitsubishi Electric Corp Flight path retreival device
JP2002351307A (en) * 2001-05-30 2002-12-06 Denso Corp Method and device for map display
JP2006064892A (en) * 2004-08-26 2006-03-09 Hasegawa Shoji:Kk Position calculating device, position calculating method, position calculating program, and storage medium for position calculating program
JP2012085139A (en) * 2010-10-13 2012-04-26 Kansai Electric Power Co Inc:The Program for making computer function as calculation device of separation distance
US20140108464A1 (en) * 2012-06-05 2014-04-17 Google Inc. System and Method for Storing and Retrieving Geospatial Data
WO2014108957A1 (en) * 2013-01-08 2014-07-17 日本電気株式会社 Coordinate conversion device, non-transitory computer readable medium in which coordinate conversion program is stored, and coordinate conversion method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
YUSUKE OKUNO ET AL., FOURTH EDITION, GIS AND GEO-SPATIAL INFORMATION, KOKON SHOIN, 27 March 2016 (2016-03-27), pages 6 - 12 , 181 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116214542A (en) * 2023-03-23 2023-06-06 广东省特种设备检测研究院东莞检测院 Digital twin system of spherical tank inner wall climbing robot
CN116214542B (en) * 2023-03-23 2023-11-10 广东省特种设备检测研究院东莞检测院 Digital twin system of spherical tank inner wall climbing robot

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