Methods of specifying global locations including indoor locations and database using the same

Abstract

A method is provided for integrally specifying a geographic location and an indoor location within a building. When the coordinates of one point on the Earth are given as a geodetic latitude φ, a longitude λ, and an ellipsoidal height h in a geodetic coordinate system based on the Earth ellipsoid, the location of the point is represented with a new coordinates including a Northing N, an Easting E, and selectively a floor representing integer F. The Northing N is given as a linear function of the distance measured along the prime meridian from the latitude-longitude origin to the waypoint, and the Easting is given as a linear function of the distance measured along the parallel of latitude from the waypoint to the ellipsoidal point.

Claims

1. A method of accurate integrally specifying geographic locations and indoor locations within buildings, the method comprising: a coordinate of any one point on an Earth is given as (X, Y, Z) in a three-dimensional Cartesian coordinate system which is fixed to the Earth and rotates with the Earth (Earth-Centered Earth-Fixed), having the Earth's center of mass as an origin, having the Earth's rotation axis as a Z-axis, and having a straight line from the origin to an intersection point of a prime meridian and an Equator as a X-axis, and given as a geodetic latitude φ, a longitude λ, and an ellipsoidal height h in a geodetic coordinate system based on an Earth ellipsoid, a location of the one point is represented by a new coordinate system including a Northing N, an Easting E, and selectively an integer F specifying a floor within a building, wherein, the Northing N has a unit of distance, and is given as a monotonically increasing function of the geodetic latitude φ, and the Easting E has a unit of distance, and is given as a monotonically increasing function of the latitude λ, wherein, the Northing N is given as a function of the geodetic latitude y as follows,
N=N.sub.o+R(ϕ−ϕ.sub.o) here N.sub.o is a default value of the Northing, R is an average radius of the Earth, φ.sub.o is the geodetic latitude of a reference point, the unit of angle is radian, the Easting E is given as a function of the geodetic latitude φ and the longitude λ, as follows,
E=E.sub.o+(λ−λ.sub.o)R cos ϕ here E.sub.o is a default value of the Easting, λ.sub.o is the longitude of the reference point, the geodetic latitude φ is given as a function of the Northing N as follows, $\varphi ={\varphi }_o+\frac{N-N_o}{R}$ and the longitude λ, is given as a function of the Northing N and the Easting E as follows, $\lambda ={\lambda }_o+\frac{E-E_o}{R\cos \left({\varphi }_o+\frac{N-N_o}{R}\right)}$ wherein, the Northing and the Easting are real numbers having positive (+) values.

2. A relational database stored in a device, wherein data is any one or more among digital contents, HTML pages, movable properties, real estates, and databases to which location attributes are assigned, wherein the location attribute includes a geodetic latitude φ, a longitude λ, and selectively a floor within a building, wherein the relational database includes a Northing corresponding integer I and an Easting corresponding integer J, which are non-nullable fields, and selectively an integer F representing a floor within a building, the Northing corresponding integer I is an integer obtained by rounding off the Northing N having a unit of distance, the Easting corresponding integer J is an integer obtained by rounding off the Easting E having a unit of distance, the Northing is given as a monotonically increasing function of the geodetic latitude φ, the Easting is given as a monotonically increasing function of the longitude λ, wherein, the Northing N is given as a function of the geodetic latitude φ as follows,
N=N.sub.o+R(ϕ−ϕ.sub.o) here N.sub.o is a default value of the Northing, R is an average radius of the Earth, λ.sub.o is the geodetic latitude of a reference point, the unit of angle is radian, the Easting E is given as a function of the geodetic latitude φ and the longitude λ, as follows,
N=N.sub.o+R(ϕ−ϕ.sub.o) here E.sub.o is a default value of the Easting, and λ.sub.o is the longitude of the reference point, wherein the Northing N and the Easting E functions determine and use accurate integrally specifying geographic locations and indoor locations within buildings.

3. The relational database stored in a device of claim 2, wherein, the geodetic latitude φ, the longitude λ, and the floor within a building included in the location attribute are the geodetic latitude φ, the longitude λ, and the floor within a building which the owner of the data subjectively recognizes as the location attribute of the data.

4. The relational database stored in a device of claim 2, wherein, the digital contents include photos, drawings, illustrations, cartoons, animations, videos, music files, audio files, poetries, novels, essays, historical or cultural commentaries, menu boards, catalogs, news articles, reviews, blueprints, and technical documents.

5. The relational database stored in a device of claim 2, wherein, the database is a relational or non-relational database for data in which the Northing corresponding integer I, the Easting corresponding integer J, and selectively the integer F representing a floor in a building are all the same.

6. A relational database stored in a device, having character strings to which location attributes are assigned as data, wherein, the location attribute includes a geodetic latitude φ, a longitude λ, and selectively a floor within a building, the relational database includes a Northing corresponding integer I and an Easting corresponding integer J which are non-nullable fields, and an integer F representing a floor within a building which is a nullable field, the Northing corresponding integer I is an integer obtained by rounding off the Northing N having a unit of distance, the Easting corresponding integer J is an integer obtained by rounding off the Easting E having a unit of distance, the Northing is given as a monotonically increasing function of the geodetic latitude φ, and the Easting is given as a monotonically increasing function of the longitude λ, wherein, the Northing N is given as a function of geodetic latitude φ as follows,
N=N.sub.o+R(ϕ−ϕ.sub.o) here N.sub.o is a default value of the Northing, R is an average radius of the Earth, φ.sub.o is the geodetic latitude of a reference point, the unit of angle is radian, the Easting E is given as a function of geodetic latitude φ and longitude λ, as follows,
E=E.sub.o+(λ−λ.sub.o)R cos ϕ here E.sub.o is a default value of the Easting, and λ.sub.o is the longitude of the reference point, wherein the Northing N and the Easting E functions determine and use accurate integrally specifying geographic locations and indoor locations within buildings.

7. The relational database stored in a device of claim 6, wherein, the geodetic latitude φ, the longitude λ, and the floor within a building included in the location attribute are the geodetic latitude φ, the longitude λ, and the floor within a building which the owner of the data subjectively recognizes as the location attribute of the data.

8. The relational database stored in a device of claim 6, wherein, the character strings to which location attributes are assigned include names, place names, trade names, nicknames, addresses, internet domains, email addresses, telephone numbers and Fax numbers.

9. The relational database stored in a device of claim 6, wherein, the character strings to which location attributes are assigned include a type of business as a common noun, a type of service, products, and services.

10. The relational database stored in a device of claim 6, wherein the device further comprising: a processor; and a memory including instructions that, when executed by the processor, cause the processor to: store, retrieve, modify, duplicate, and delete one or more records having non-nullable fields and nullable fields, wherein non-nullable fields include a Northing corresponding integer I and an Easting corresponding integer J, and nullable fields include an integer F corresponding to a floor in a building.

11. The relational database stored in a device of claim 2, wherein the device further comprising: a processor; and a memory including instructions that, when executed by the processor, cause the processor to: store, retrieve, modify, duplicate, and delete one or more records having non-nullable fields and nullable fields, wherein non-nullable fields include a Northing corresponding integer I and an Easting corresponding integer J, and nullable fields include an integer F corresponding to a floor in a building.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a conceptual diagram of latitude and longitude.

(2) FIG. 2 is a conceptual diagram of a geoid.

(3) FIG. 3 is a conceptual diagram of the Earth ellipsoid.

(4) FIG. 4 is a conceptual diagram showing the difference between geocentric latitude and geodetic latitude.

(5) FIG. 5 is a conceptual diagram illustrating the average radius of the Earth ellipsoid.

(6) FIG. 6 is an example of a map by the equirectangular projection method.

(7) FIG. 7 is a conceptual diagram illustrating various map projection methods.

(8) FIG. 8 is a conceptual diagram of the Mercator projection method.

(9) FIG. 9 is an example of a map created by the Mercator projection method.

(10) FIG. 10 is an example of a map by the web Mercator projection method.

(11) FIG. 11 is an example of a map by the sinusoidal projection method.

(12) FIG. 12 is an example of the world map drawn in the UTM coordinate system.

(13) FIG. 13 is a conceptual diagram of a UTM zone.

(14) FIG. 14 is an example of a table in a relational database.

(15) FIG. 15 is a customer information table implemented in PostgreSQL.

(16) FIG. 16 is the result of searching for a record with name Tom.

(17) FIG. 17 is the result of searching for a record with name Tom and city L.A.

(18) FIG. 18 is a drawing showing the concept of a centroid of a building and a minimum bounding box in a building floor plan.

(19) FIG. 19 is a conceptual diagram for understanding the world coordinate system according to the first embodiment of the present invention.

(20) FIG. 20 is a drawing showing the density of sample points in the longitude-first coordinate system.

(21) FIG. 21 is a drawing showing the density of sample points in the latitude-first coordinate system.

(22) FIG. 22 is a conceptual diagram of the Earth ellipsoid for calculating geodetic latitude and ellipsoidal height in the world coordinate system.

(23) FIG. 23 is an exaggerated shape of the geoid.

(24) FIG. 24 is a conceptual diagram showing the relationship between the ellipsoidal height and the altitude above sea level.

(25) FIG. 25 is a diagram showing the distribution of sample points in the first embodiment of the present invention.

(26) FIG. 26 is a diagram showing the distribution of sample points corresponding to uniform latitude and longitude intervals in the first embodiment of the present invention.

(27) FIG. 27 is a shape of a sphere expressed in the latitude-first coordinate system in the second embodiment of the present invention.

(28) FIG. 28 is a diagram illustrating a case where the ranges of the Northing and the Easting are moved to positive regions using default values of the Northing and the Easting in the third embodiment of the present invention.

(29) FIG. 29 is a diagram illustrating a case where the reference geocentric latitude and the reference longitude are changed from the origin of latitude-longitude origin to (38°, 127°) in the third embodiment of the present invention.

(30) FIG. 30 is a conceptual diagram illustrating the concept of floor information in the present invention.

(31) FIG. 31 is a conceptual diagram of a location identifier according to the present invention.

(32) FIG. 32 is a conceptual diagram of a minimum enclosing circle and a maximum included circle in the tenth embodiment of the present invention.

(33) FIG. 33 is an example of a simple database in the eleventh embodiment of the present invention.

(34) FIG. 34 is the result of searching with various keywords in the eleventh embodiment of the present invention.

DETAILED DESCRIPTION

(35) In traditional markets, we can see grandmothers selling things with stalls measuring only 1 m in width and length or smaller. In addition, street lights, traffic lights, telephone booths, fire hydrants, etc. occupy a smaller area. As such, there may be a need to accurately specify the location of a movable property or real estate with a small footprint. Or, if we want to meet friends by specifying the location in a place without any special geographical features while people are densely populated such as in the middle of the Gwanghwamun Plaza in Seoul, we need a method to specify and distinguish a section of about 1 m in width and length in a unique way.

(36) The surface area of a sphere with radius R is given by 4πR.sup.2. Using 6,371,008.8 m as the value of the average radius R of the spherical model Earth, the surface area is given as 5.1006588×10.sup.14 m.sup.2. In other words, if the surface of the Earth is divided into pieces of approximately 1 m in width and length, about 510 trillion pieces are obtained.

(37) The method of the sixth embodiment of the present invention may be used to divide the surface of the Earth into pieces of approximately 1 m in width: height, and to give each piece a location identifier given as a pair of two integers. That is, using the geodetic latitude and the longitude of the center position of the corresponding piece, the Northing N and the Easting E are calculated in meters. Most preferably, the Northing and the Easting given by Eqs. 99-100 are calculated.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 99]
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 100]

(38) By rounding off this Northing and Easting, they are converted into integers. In Eqs. 101-102, round( ) is a function that returns a rounded value of a real number. That is, round(9.4) is 9, and round(9.7) is 10.
I=round(N)  [Equation 101]
J=round(E)  [Equation 102]

(39) Any point on the Earth can be conveniently specified using the integers I, J thus obtained, and selectively an integer F representing the floor.

(40) FIG. 31 is a conceptual diagram of a three-dimensional location identifier. By using the method of the eighth embodiment in the present invention, the location can be specified using three integers (I, J, F) with an error range of less than 1 m.sup.2 regardless of the actual location on the surface of the Earth and the floor levels within all the buildings. We will refer these three integers as 3-dimensional geological location identifier or simply as location identifier.

(41) In FIG. 31, the location identifier of a place a on the Earth is (I, J, F), the location identifier of a point e about 1 m away from a in the north direction is (I+1, J, F), and the location identifier of a point d about 1 m away from a in the east direction is (I, J+1, F), and the location identifier of a point fat the same geodetic latitude and longitude but one floor above a is (I, J, F+1). In addition, by transmitting thus obtained location identifier (I, J) or (I, J, F) to a friend, we can easily inform our location even if we are in a wild plain or deep in the mountains. This set of integers not only consumes less data to transmit than the geodetic latitude and longitude, but also has the advantage that distances can be estimated because I and J have units of length. And the biggest advantage is that this location identifier indicates an area about 1 m in width and in height for any location on the Earth.

(42) In addition, when geodetic latitude and longitude are needed, they can be obtained using Eqs. 103-104.

(43) $\begin{array}{cc}{\varphi }_I={\varphi }_o+\frac{I-N_o}{R}& \left[\mathrm{Equation}103\right]\\ {\lambda }_{I,J}={\lambda }_o+\frac{J-E_o}{R\cos \left({\varphi }_o+\frac{I-N_o}{R}\right)}& \left[\mathrm{Equation}104\right]\end{array}$

(44) Hereinafter, embodiments of the present invention will be described in detail with reference to FIGS. 19-34.

First Embodiment

(45) In the first embodiment of the present invention, a sphere having a radius R is assumed as the shape of the Earth. FIG. 19 is a conceptual diagram of a World coordinate system or an Earth-Centered Earth-Fixed three-dimensional Cartesian coordinate system according to the first embodiment of the present invention. Hereinafter, it will be simply referred to as a three-dimensional Cartesian coordinate system. The origin C of this three-dimensional Cartesian coordinate system is located at the Earth's center of mass, the Z-axis coincides with the Earth's axis of rotation, the X-axis is a straight line from the origin through the intersection point of the Equator and the prime meridian, and the Y-axis direction is automatically determined by the principle of Right-Handed coordinate System (RHS).

(46) A point P with geocentric latitude ψ and longitude λ is located at geocentric altitude (geocentric height) A from the Earth's surface. A coordinate system using geocentric latitude and longitude and geocentric altitude will be referred to as a geocentric coordinate system.

(47) Assume that the Earth is a sphere with its center located at the origin, and this sphere will be referred to as a spherical model Earth. The radius of this spherical model Earth is R. As illustrated in FIG. 5, 6,371.0088 km may be used as the R value. The point P is separated by a distance (R+A) from the center of the Earth. Therefore, the coordinates of the point P can be written as (X, Y, Z) in the three-dimensional Cartesian coordinate system, and also can be written as (ψ, λ, A) in the geocentric coordinate system.

(48) Let's call the point where the line segment connecting the point P(X, Y, Z)=P(ψ, λ, A) and the center of the Earth C meets the Earth's surface, that is, the surface of the spherical model Earth, as an Earth point S(ψ, λ). The Earth point is also the intersection point of the meridian M(λ) with longitude λ and the parallel of latitude L(ψ) with geocentric latitude w.

(49) Among the parallels of latitude, the L.sub.O corresponding to latitude 0° is the Equator. Among the meridians, the prime meridian M.sub.O is the meridian which corresponds to 0° longitude. And the intersection point O of the Equator L.sub.O and the prime meridian M.sub.O is the latitude-longitude origin. Also, a point on the Earth's surface with 90° latitude is the North Pole (N.P.), and a point with −90° latitude is the South Pole (S.P.).

(50) The coordinates X, Y and Z of the three-dimensional Cartesian coordinate system are given by Eqs. 37-39 as functions of the coordinates of the geocentric coordinate system.
X=(R+A)cos ψ cos λ  [Equation 37]
Y=(R+A)cos ψ sin λ  [Equation 38]
Z=(R+A)sin ψ  [Equation 39]

(51) Conversely, the geocentric latitude ψ, the longitude λ, and the geocentric altitude A of the geocentric coordinate system are given by Eqs. 40-42 as functions of the coordinates of the three-dimensional Cartesian coordinate system.

(52) $\begin{array}{cc}\psi ={\tan }^{-1}\left(\frac{Z}{\sqrt{X^2+Y^2}}\right)& \left[\mathrm{Equation}40\right]\\ \lambda ={\tan }^{-1}\left(\frac{Y}{X}\right)& \left[\mathrm{Equation}41\right]\\ A=\sqrt{X^2+Y^2+Z^2}-R& \left[\mathrm{Equation}42\right]\end{array}$

(53) In the first embodiment of the present invention, extended concepts of Northing N, Easting E and geocentric altitude A are used in place of the geocentric latitude ψ, longitude λ and the geocentric altitude A. The Northing and the Easting were defined even in a plane rectangular coordinate system such as the UTM coordinate system. However, in the UTM coordinate system, the Northing and the Easting have the disadvantage that they are given as complex functions of the geodetic latitude φ and the longitude λ. In the first embodiment of the present invention, the Northing is defined as an arc length measured along a meridian, and the Easting is defined as an arc length measured along a parallel of latitude.

(54) Referring to FIG. 19, it can be seen that there are two methods of using Northing and Easting. A method through the waypoint U(λ) and a method through the waypoint W(ψ) are them. The waypoint U(λ) is the intersection point of the Equator L.sub.O and the meridian M(λ), and the waypoint W(ψ) is the intersection point of the prime meridian M.sub.O and the parallel of latitude L(ψ).

(55) In the method through the waypoint U(λ), the coordinates of the point P are expressed by the Easting Rλ measured along the Equator L.sub.O from the latitude-longitude origin O to the waypoint U(λ), the Northing Rψ measured from the waypoint U(λ) to the Earth point S(ψ, λ) along the meridian M(λ), and the elevation A from the Earth point S(ψ, λ) to the one point P(ψ, λ, A).
P.sub.U=(Rλ,Rψ,A)  [Equation 43]

(56) This method will be referred to as longitude-first coordinate system. A disadvantage of this longitude-first coordinate system can be seen in FIG. 20. In FIG. 20, the circumference of the Earth is set to 36 m, and each arrow corresponds to Easting 1 m or Northing 1 m. However, it can be seen that the lateral spacing between sampling points decreases as the latitude increases. That is, even if the effective digits of the Northing or the Easting are up to, for example, the first decimal place, the positional accuracy in the lateral direction changes with latitude.

(57) On the other hand, in the method through the waypoint W(ψ), the coordinates of the point P are expressed by the Northing Rψ measured along the prime meridian M.sub.O from the latitude-longitude origin O to the waypoint W(ψ), the Easting λR cos ψ measured from the waypoint W(ψ) to the Earth point S(ψ, k) along the parallel of latitude L(ψ), and the elevation A from the Earth point S(ψ, k) to the one point P(ψ, λ, A).
P.sub.W=(Rψ,λR cos ψ,A)  [Equation 44]

(58) That is, the Northing N and the Easting E satisfy the relations of Eqs. 45-48 with the radius R of the spherical model Earth, the geocentric latitude ψ and the longitude λ.

(59) $\begin{array}{cc}N=\mathrm{R\psi }& \left[\mathrm{Equation}45\right]\\ E=\lambda R\cos \psi & \left[\mathrm{Equation}46\right]\\ \psi =\frac{N}{R}& \left[\mathrm{Equation}47\right]\\ \lambda =\frac{E}{R\cos \psi }=\frac{E}{R\cos \left(\frac{N}{R}\right)}& \left[\mathrm{Equation}48\right]\end{array}$

(60) FIG. 21 shows the distribution of sample points in the latitude-first coordinate system. In FIG. 21, it can be seen that the intervals between the points are constant in the lateral direction or in the longitudinal direction. Thus, the latitude-first coordinate system is a far superior system.

(61) In the latitude-first coordinate system, sample points do not form a grid. As shown in FIG. 21, as the latitude increases, the number of sampling also decreases, so it is theoretically impossible to form a grid structure such as a go board. However, if we look at a local area on a global scale, for example, around Gwanghwamun Plaza in Seoul, the distribution of sample points may appear to form a grid structure. That is, while it surely looks like a Cartesian coordinate system locally, it has the characteristics of a spherical coordinate system on a global scale.

(62) In addition, since Northing N, Easting E, and geocentric height A all have units of length or distance, people can intuitively understand their meaning. It is best to use the meter as the unit of length, but other units such as km or mm can also be used. If we use meter as the unit of length, then anyone can figure out that the positional accuracy is 10 cm if the Northing is written down to the first decimal place. Therefore, by using such a latitude-first coordinate system, any location on the Earth can be designated, and it is very convenient because a unit of length rather than an angle is used.

(63) The mathematical formula of the latitude-first coordinate system is essentially the same as that of the sinusoidal projection. However, while the sinusoidal projection method has the purpose of drawing a map, the latitude-first coordinate system of the present embodiment has the purpose of designating the location of a point on the Earth in a useful and convenient way.

(64) One might wonder where to use this latitude-first coordinate system if it's not for drawing maps. One area where this coordinate system can be useful is to describe the trajectory of a flight vehicle such as a satellite, aircraft, or drone. When a satellite does not use its own power, the trajectory of a satellite becomes a circle centered on the Earth's center of mass. Therefore, it is an optimal coordinate system to describe the trajectory of an artificial satellite. It is also suitable for describing the trajectories of aircrafts, drones, and missiles.

(65) However, a map is essential in order to check our actual location, or find and go to a place. As described above, since the latitude-first coordinate system is not a coordinate system for drawing maps, not only a map drawn using other projection method such as the Mercator projection method is required, but also a method for matching the latitude-first coordinate system with an ordinary map is required.

(66) Most of the maps indicate geodetic latitude, longitude and elevation above sea level. And on most of the maps, distances doesn't mean much unless it's a large-scale map. This is because distances vary in a very strange way depending on the projection method, and even for 1 cm length on the same map, the actual distance can vary depending on the location within the map. This is because the distance scale varies depending on the projection method and on the location within the map. Also, the altitude is mainly altitude above sea level, and the altitude above sea level can only be obtained by knowing the exact shape of the geoid.

(67) FIG. 22 is a conceptual diagram of the Earth ellipsoid for calculating geodetic latitude and ellipsoidal height. The Earth ellipsoid (2201) uses the same three-dimensional Cartesian coordinate system as the spherical model Earth shown in FIG. 19. That is, the Earth ellipsoid is a flat rotational ellipsoid, i.e., an oblate spheroid, whose center is located at the origin of the three-dimensional Cartesian coordinate system. Also, the minor axis of the spheroid coincides with the Z-axis. That is, the Z-axis is the Earth's axis of rotation, and the X-Y plane is the Equatorial plane.

(68) The coordinates of a point P on the Earth are expressed as geodetic latitude φ, longitude λ, and ellipsoidal height h. A coordinate system using geodetic latitude φ, longitude λ and ellipsoidal height h is called a geodetic coordinate system. Here, the ellipsoidal height is not measured based on the line segment connecting the origin C and the point P on the three-dimensional Cartesian coordinate system. At point P, a normal (2202) is dropped to the Earth ellipsoid. The point (2203) where the normal (2202) meets the Earth ellipsoid (2201) will be referred to as an ellipsoidal point. If a tangent plane (2204) is drawn to the Earth ellipsoid (2201) at the ellipsoidal point (2203), then the normal (2202) passes vertically through the tangent plane (2204). The angle φ with which the normal (2202) meets the Equatorial plane is the geodetic latitude. Then, the distance from the point (2205) where the extended normal meets the Z-axis to the ellipsoidal point (2203) is the radius of curvature in the prime vertical RN [non-patent document 12].

(69) If the semimajor axis (radius of the semimajor axis), i.e., the long radius, is a, and the semiminor axis (radius of the semiminor axis), i.e., the short radius, is b, then the eccentricity e of the Earth ellipsoid is given by Eq. 49.

(70) 0$\begin{array}{cc}{e}^2=1-\frac{b^2}{a^2}& \left[\mathrm{Equation}49\right]\end{array}$

(71) And the radius of curvature in the prime vertical R.sub.N is given by Eq. 50 [non-patent document 15].

(72) $\begin{array}{cc}{R}_N=\frac{a}{\sqrt{1-{e^2\left(\sin \varphi \right)}^2}}& \left[\mathrm{Equation}50\right]\end{array}$

(73) That is, the radius of curvature in the prime vertical is not a constant but given as a function of the geodetic latitude φ. And, the Cartesian coordinates X, Y and Z are given as functions of geodetic coordinates, i.e., geodetic latitude φ, longitude λ and ellipsoidal height h as in Eqs. 51-53.
X=(R.sub.N+h)cos ϕ cos λ  [Equation 51]
Y=(R.sub.N+h)cos ϕ sin λ  [Equation 52]
Z={R.sub.N(1−e.sup.2)+h} sin ϕ  [Equation 53]

(74) Using these formulas, the geodetic latitude φ, longitude λ and ellipsoidal height h can be sequentially converted in (φ, λ, h).fwdarw.(X, Y, Z).fwdarw.(ψ, λ, A).fwdarw.(N, E, A) order, and the Northing N, the Easting E and the geocentric altitude A can be obtained. This can be summarized as follows.

(75) First, let's suppose that the semimajor axis (long radius) a and the flattening/of the Earth ellipsoid are given. Then the eccentricity of the Earth is given by Eq. 54.
e.sup.2=2f−f.sup.2  [Equation 54]

(76) Given the geodetic latitude φ, the longitude λ and the ellipsoidal height h of a point P on the Earth, the radius of curvature in the prime vertical is given by Eq. 55.

(77) $\begin{array}{cc}{R}_N=\frac{a}{\sqrt{1-{e^2\left(\sin \varphi \right)}^2}}& \left[\mathrm{Equation}55\right]\end{array}$

(78) In addition, the Cartesian coordinates X, Y and Z of the three-dimensional Cartesian coordinate system are given by Eqs. 56-58 as functions of the geodetic coordinates.
X=(R.sub.N+h)cos ϕ cos λ  [Equation 56]
Y=(R.sub.N+h)cos ϕ sin λ  [Equation 57]
Z={R.sub.N(1−e.sup.2)+h} sin ϕ  [Equation 58]

(79) On the other hand, X, Y and Z may also be written as functions of the geocentric coordinates as in Eqs. 59-61.
X=(R+A)cos ψ cos λ  [Equation 59]
Y=(R+A)cos ψ sin λ  [Equation 60]
Z=(R+A)sin ψ  [Equation 61]

(80) Therefore, from Eqs. 59-61, the geocentric latitude ψ, the longitude λ and the geocentric altitude A can be obtained as in Eqs. 62-64.

(81) $\begin{array}{cc}\psi ={\tan }^{-1}\left(\frac{Z}{\sqrt{X^2+Y^2}}\right)& \left[\mathrm{Equation}62\right]\end{array}$$\begin{array}{cc}\lambda ={\tan }^{-1}\left(\frac{Y}{X}\right)& \left[\mathrm{Equation}63\right]\end{array}$$\begin{array}{cc}A=\sqrt{X^2+Y^2+Z^2}-R& \left[\mathrm{Equation}64\right]\end{array}$

(82) In addition, the Northing N and the Easting E can be obtained as in Eqs. 65-66. [Equation 65]

(83) N=Rip

(84) [Equation 66] E=AR cos

(85) The Sejong Continuously Operating Reference Station (SEJN), one of the GNSS reference stations managed by the National Geographic Information Institute, has coordinates given by the geodetic latitude 36° 31′19.9682″, the longitude 127° 18′11.4836″ and the ellipsoidal height 181.196 m in the geodetic coordinate system based on the GRS80 ellipsoid. Converting the longitude and the latitude values into decimal system, in other words, express in decimal degrees, the geodetic latitude is 36.5222134° and the longitude is 127.3031899°. If we calculate the geocentric latitude and the longitude from this, the geocentric latitude is 36.3383398° and the longitude is 127.3031899°. That is, the difference between geodetic latitude and the geocentric latitude is 0.1838736°. Also, using R=6,371,008.8 m, the Northing and the Easting are calculated as N=4,040,644.61 m and E=11,402,698.22 m, respectively.

(86) In a geodetic coordinate system, the ellipsoidal height is not measured along the straight line passing through the center of the Earth. Therefore, even if the geodetic latitude is the same, the geocentric latitude is different if the ellipsoidal height is different. Assuming that the ellipsoidal height is 0, the geocentric latitude is given as 36.3383346°, and the Northing and the Easting are given as 4,040,644.03 m and 11,402,698.98 m, respectively.

(87) However, although GPS receivers sometimes display the ellipsoidal height, mostly display the elevation above sea level. And, not the ellipsoidal height but the elevation above sea level is marked on most of the maps. FIG. 23 shows an exaggerated shape of the geoid (https://commons.wikimedia.org/wiki/File:Geoid_undulation_10k_scale.jpg).

(88) As can be seen in FIG. 23, the shape of the geoid is very irregular. The Earth ellipsoid is a perfect spheroid which can be described by a simple mathematical equation, but the geoid depends on the topography and the density of underground minerals. Its theoretical concept is complicated, and it is very difficult to measure. Therefore, it is next to impossible to describe the shape of the geoid with a mathematical function such as a spheroid. Realistically, the Earth is divided into a grid structure and measured to create the geoid.

(89) Each country measures the geoid for its own territory and announces a standard model, that is, the Geoid datum. In Korea, there is a KNGEOID provided by the National Geographic Information Institute, and the accuracy is said to be about 3 cm. Considering that the horizontal distance has a millimeter-level accuracy, it can be said that the errors are considerable.

(90) FIG. 24 is a conceptual diagram for understanding the relationship between a geoid height and an ellipsoidal height. The altitude above sea level H at any point on the Earth is given as the ellipsoidal height h minus the geoid height N.
H=h−N  [Equation 67]

(91) Therefore, if a GPS or a map shows the elevation above sea level, the ellipsoidal height can be obtained by considering the geoid height. However, strictly speaking, H is not an elevation above sea level, but a value called orthometric height.

(92) In any case, we can obtain the geodetic latitude φ, the longitude λ and the elevation above sea level H from a GPS receiver, and from these by sequentially converting in (φ, λ, H).fwdarw.(φ, λ, h).fwdarw.(X, Y, Z).fwdarw.(ψ, λ, A).fwdarw.(N, E, A) order, we can obtain the Northing N, the Easting E and the geocentric altitude A.

(93) Conversely, the process of obtaining the geodetic latitude φ, the longitude λ, and the elevation above sea level H from the Northing N, the Easting E and the geocentric altitude A is far more difficult. Geodetic latitude φ, longitude λ and ellipsoidal height h as functions of coordinates X, Y and Z in three-dimensional Cartesian coordinate system are given by Eqs. 68-70 [non-patent document 16].

(94) $\begin{array}{cc}\varphi ={\tan }^{-1}\left[\frac{Z\left(R_N+h\right)}{\left\{R_N\left(1-e^2\right)+h\right\}\sqrt{X^2+Y^2}}\right]={\tan }^{-1}\left[\frac{Z+e^2{R}_N\sin \varphi }{\sqrt{X^2+Y^2}}\right]& \left[\mathrm{Equation}68\right]\end{array}$$\begin{array}{cc}\lambda ={\tan }^{-1}\left(\frac{Y}{X}\right)& \left[\mathrm{Equation}69\right]\end{array}$$\begin{array}{cc}h=\frac{\sqrt{X^2+Y^2}}{\cos \varphi }-R_N& \left[\mathrm{Equation}70\right]\end{array}$

(95) Taking Eq. 68 as an example, since the radius of curvature in the prime vertical R.sub.N is a function of the geodetic latitude φ, the geodetic latitude is present in the formula for calculating the geodetic latitude. Therefore, we cannot obtain this value by simply tapping on a calculator. To obtain this value, we can use a simplified formula by taking advantage of the fact that the difference between the geodetic latitude and the geocentric latitude is small. Or, we can recursively call this function until the value converges. These methods itself are still the subject of research, and new methods are being devised and published by researchers.

(96) Looking at Eq. 70, the geodetic latitude is required to obtain the ellipsoidal height. Therefore, finding the ellipsoidal height is not an easy problem, either. Only the formula for calculating longitude is simple, and it is the same regardless of whether the shape of the Earth is a sphere or an oblate spheroid.

(97) FIG. 25 shows the distribution of sample points set at Northing 1 m interval and Easting 1 m interval in the latitude-first coordinate system. It can be seen that the outline is the same as that of the map by the sinusoidal projection method shown in FIG. 11.

(98) FIG. 26 is a diagram showing how the Northing and the Easting of corresponding points are distributed when a latitude-longitude grid structure with 10° intervals in both directions is assumed. As expected, it can be seen that the same longitude interval does not correspond to the same Easting interval. Also, if latitude is the same, the Northing is the same, and if latitude interval is the same, the Northing interval is the same. And if we look at a very small area in FIG. 26, it can be seen that the distribution of sample points is close to a grid structure.

Second Embodiment

(99) As described above, the first embodiment of the present invention is a method not for creating a map, but for displaying the location of a point in a convenient and useful manner. However, rather than creating a map accompanying a map projection, the present invention can also be used to accurately express the shape of an object that is roughly spherical in shape. FIG. 27 shows a spherical surface expressed using the latitude-first coordinate system of the first embodiment of the present invention. That is, a spherical surface is modeled with a geocentric altitude A=0 and with the intervals of Northing N and the Easting E being both 1 m. As can be seen from FIG. 27, the spacing of the sampling points on the spherical surface is uniform regardless of the latitude.

(100) Such a latitude-first coordinate system may be used, for example, to express the shape of the geoid shown in FIG. 23. In the existing method, 1° latitude and 1° longitude intervals are divided into a grid structure like a go board, and then measures the geoid at each grid point. However, in this method, the sampling interval is wide near the Equator, and narrow at the Polar Regions. That is, in a geographic coordinate system using longitude and latitude, the sampling interval decreases as the latitude increases, and hence it is inefficient. In addition, the UTM coordinate system is not only complicated, but also it cannot express the Polar Regions at all. However, using a latitude-first coordinate system, any point on the Earth can be expressed while having uniform sampling density.

(101) In addition, the latitude-first coordinate system can be used to express the shape of the real Earth including mountain ranges, rivers, roads, overpass, high-rise buildings and the like in 3D. For example, a three-dimensional (3D) globe can be created by sampling every place on the Earth at 1 m lateral and longitudinal intervals.

Third Embodiment

(102) One drawback of the first embodiment is that the Northing and the Easting may have negative (−) values as well as positive (+) values. A data structure where values are symmetrically distributed in positive and negative directions with respect to the origin may appear very natural to people, but there are many inconveniences in processing them with computer. For computers, data that is expressed as a natural number which starts from 0 and increases in one direction only or that is expressed as a positive real number are convenient to deal with.

(103) Another drawback is that when we are interested in only a part of the Earth, the Northing or the Easting may have unnecessarily large values. In Korea, for example, a TM coordinate system having the west, the central, the east and the East Sea origin of Korea plane coordinate system is used. Since it is difficult to know the ellipsoidal heights of these origins, table 2 shows the Northing and the Easting for the Sejong Continuously Operating Reference Station and the four origins assuming that the ellipsoidal heights are 0.

(104) TABLE-US-00004 TABLE 2 classification geodetic latitude longitude Northing Easting Sejong Continuously 36.5222134° 127.3031899° 4040644.03 m 11402698.98 m Operating Reference Station west origin of Korea 38.0° 125.0° 4204668.95 m 10980669.51 m plane coordinate system central origin of Korea 38.0° 127.0° 4204668.95 m 11156360.22 m plane coordinate system east origin of Korea 38.0° 129.0° 4204668.95 m 11332050.93 m plane coordinate system East Sea origin of Korea 38.0° 131.0° 4204668.95 m 11507741.65 m plane coordinate system

(105) If we look at the Easting in table 2, the largest digit is all the same. If our interest are on purely domestic regions, it is unnecessary and inconvenient to display such a large number. In the third embodiment of the present invention, the Northing and the Easting are given by Eqs. 71-72.
N=N.sub.o+R(ψ−ψ.sub.o)  [Equation 71]
E=E.sub.o+(λ−λ.sub.o)R cos ψ  [Equation 72]

(106) Here, ψ.sub.o and λ.sub.o are the geocentric latitude and the longitude of the reference point. That is, not only the latitude-longitude origin, but also any point on the Earth can be used as a reference point. Also, N.sub.o and E.sub.o are the default values of the Northing and the Easting, respectively. When the reference geocentric latitude ψ.sub.o, the reference longitude λ.sub.o, the default Northing N.sub.o and the default Easting E.sub.o are all 0, it becomes the same as the first embodiment. In addition, by adjusting the reference geocentric latitude ψ.sub.o, the reference longitude λ.sub.o, the default Northing N.sub.o and the default Easting E.sub.o, the ranges of the Northing N and the Easting E can be adjusted.

(107) Geocentric latitude ψ and longitude λ are given as functions of the Northing N and the Easting E as in Eqs. 73-74.

(108) $\begin{array}{cc}\psi ={\psi }_o+\frac{N-N_o}{R}& \left[\mathrm{Equation}73\right]\end{array}$$\begin{array}{cc}\lambda ={\lambda }_o+\frac{E-E_o}{R\cos \left({\psi }_o+\frac{N-N_o}{R}\right)}& \left[\mathrm{Equation}74\right]\end{array}$

(109) FIG. 28 is a diagram illustrating a case where the ranges of the Northing and the Easting are moved to positive regions using the default values of the Northing and the Easting in the third embodiment of the present invention. Specifically, it is a case where assuming that the circumference of the spherical model Earth is 36 m, the default Northing is set at 10 m and the default Easting is set at 20 m. As can be seen in FIG. 28, the Northing N and the Easting E have positive (+) values over the entire region of the Earth's surface.

(110) FIG. 29 is a diagram showing a case where the reference geocentric latitude and the reference longitude are changed from the latitude-longitude origin to (38°, 127°) in the third embodiment of the present invention. It can be seen that the distribution of the sampling points have moved with respect to the origin, and the overall shape has also changed.

(111) As such, by changing the reference geocentric latitude and the reference longitude, or setting the default Northing and the default Easting appropriately, the latitude-first coordinate system can be optimized for any local area on the Earth.

(112) Table 3 shows the Northing and the Easting calculations for the Sejong Continuously Operating Reference Station and the four origins where the Sejong Continuously Operating Reference Station is set as the reference point and the ellipsoidal heights are assumed as 0.

(113) TABLE-US-00005 TABLE 3 classification geodetic latitude longitude Northing Easting Sejong Continuously 36.5222134° 127.3031899°    0.00 m    0.00 m Operating Reference Station west origin of Korea plane 38.0° 125.0° 164024.92 m −202324.54 m coordinate system central origin of Korea 38.0° 127.0° 164024.92 m  −26633.82 m plane coordinate system east origin of Korea 38.0° 129.0° 164024.92 m   149056.89 m plane coordinate system East Sea origin of 38.0° 131.0° 164024.92 m   324747.60 m Korea plane coordinate system

(114) As can be seen in table 3, the Northing and the Easting are given as small values by using this method.

Fourth Embodiment

(115) In the first and the third embodiments, the Northing and the Easting were calculated assuming a spherical model Earth. However, the Earth ellipsoid model is used to produce public maps at the national level or to conduct surveys related to large-scale civil engineering or construction works. Moreover, it would be desirable to use the Earth ellipsoid model to collect survey data compatible in the global scale. Therefore, the concepts of the Northing and the Easting should be also defined based on the Earth ellipsoid.

(116) Also in this case, as shown in FIG. 19, a three-dimensional Cartesian coordinate system is used where the coordinate system is fixed to the Earth and rotates with the Earth (Earth-Centered Earth-Fixed), the coordinate origin lies at the Earth's center of mass, and the Earth's rotational axis is set as the Z-axis. The X-axis is a straight line from the origin and passing through the point where the prime meridian meets the Equator. The Earth ellipsoid is an oblate spheroid whose center is located at the origin of the three-dimensional Cartesian coordinate system, and its minor axis coincides with the Z-axis.

(117) The rectangular coordinates (X, Y, Z) of a point P on the Earth have the geodetic latitude φ, the longitude λ and the ellipsoidal height h in the geodetic coordinate system based on the Earth ellipsoid. A normal (2202) is dropped from the one point to the Earth ellipsoid, and the point (2203) where the normal (2202) meets the Earth ellipsoid (2201) is called an ellipsoidal point. The normal (2202) is perpendicular to the tangent plane (2204) which is tangent to the Earth ellipsoid at the ellipsoidal point (2203). And the distance from the point where the extended normal (2202) meets the Z-axis, that is, the intersection point (2205) between the Z-axis and the normal (2202), to the ellipsoidal point is the radius of curvature in the prime vertical. The radius of curvature in the prime vertical RN is given by Eq. 75, where e is the eccentricity and a is the long radius of the Earth ellipsoid.

(118) $\begin{array}{cc}{R}_N=\frac{a}{\sqrt{1-{e^2\left(\sin \varphi \right)}^2}}& \left[\mathrm{Equation}75\right]\end{array}$

(119) Also, the rectangular coordinates X, Y and Z of the three-dimensional Cartesian coordinate system are given by Eqs. 76-78 as functions of the geodetic coordinates.
X=(R.sub.N+h)cos ϕ cos λ  [Equation 76]
Y=(R.sub.N+h)cos ϕ sin λ  [Equation 77]
Z={R.sub.N(1−e.sup.2)+h} sin ϕ  [Equation 78]

(120) Identical to the case of the spherical model Earth, meridians, prime meridian, parallels of latitude and Equator can be defined. That is, on the surface of the Earth ellipsoid, a meridian is a curve connecting points of the same longitude and is given as half an ellipse. The meridian corresponding to the longitude λ is denoted as M(λ). And the meridian M.sub.O≡M(0) corresponding to longitude λ=0 is the prime meridian. Also, parallels of latitude are curves connecting points having the same geodetic latitude on the surface of the Earth ellipsoid, and are always given as circles parallel to the Equator. The parallel of latitude corresponding to the geodetic latitude φ is L(φ), and among the parallels of latitude, the parallel of latitude L.sub.O≡L(0) corresponding to latitude 0° is the Equator. And the intersection point of the prime meridian and the Equator is the latitude-longitude origin O.

(121) In the fourth embodiment of the present invention, the location of a point having geodetic latitude φ, longitude λ and ellipsoidal height h is expressed as a Northing N, an Easting E and an ellipsoidal height h. Also, the intersection point of the prime meridian M.sub.O and the parallel of latitude L(φ) is called the waypoint W(φ). In this case, the Northing N is the distance from the latitude-longitude origin to the waypoint measured along the prime meridian M.sub.O. Although the derivation process of the equation is quite complicated, the result is simply given by Eq. 79 [non-patent document 16].

(122) $\begin{array}{cc}N=a\left(1-e^2\right){\int }_0^{\varphi }\frac{dt}{{\left(1-{e^2\left(\sin t\right)}^2\right)}^{\frac{3}{2}}}& \left[\mathrm{Equation}79\right]\end{array}$

(123) Similarly, the Easting E is the arc length from the waypoint to the ellipsoidal point, and is given by Eq. 80.
E=λR.sub.N cos ϕ  [Equation 80]

(124) The Northing N given by Eq. 79 can be given as Eqs. 81-86 by using the binomial theorem.

(125) $\begin{array}{cc}N\left(\varphi \right)=A_0\varphi +A_2\sin 2\varphi +A_4\sin 4\varphi +A_6\sin 6\varphi +A_8\sin 8\varphi +.Math.& \left[\mathrm{Equation}81\right]\end{array}$$\begin{array}{cc}{A}_0=a\left(1-\frac{e^2}{4}-\frac{3e^4}{64}-\frac{5e^6}{256}-\frac{175e^8}{16\times 1024}\right)& \left[\mathrm{Equation}82\right]\end{array}$$\begin{array}{cc}{A}_2=a\left(-\frac{3e^2}{8}-\frac{3e^4}{32}-\frac{5e^6}{1025}-\frac{420e^8}{16\times 1024}\right)& \left[\mathrm{Equation}83\right]\end{array}$$\begin{array}{cc}{A}_4=a\left(\frac{15e^4}{256}+\frac{45e^6}{1024}+\frac{525e^8}{16\times 1024}\right)& \left[\mathrm{Equation}84\right]\end{array}$$\begin{array}{cc}{A}_6=a\left(-\frac{35e^6}{3072}-\frac{175e^8}{12\times 1024}\right)& \left[\mathrm{Equation}85\right]\end{array}$$\begin{array}{cc}{A}_8=a\left(\frac{315e^8}{128\times 1024}\right)& \left[\mathrm{Equation}86\right]\end{array}$

(126) When this formula is applied, the error is said to be sub-millimeter.

(127) Using the spherical model Earth (R=6,371,008.8 m) to calculate the Northing of the North Pole (i.e. 1/4 of the circumference), we get 10,007,557.22 m. On the other hand, the Northing obtained by numerical integration of Eq. 79 using the Earth ellipsoid model is 10,001,965.7292 m. If the Northing is calculated using Eq. 81, it is also given as 10,001,965.7292 m. Therefore, it can be seen that Eq. 79 and Eq. 81 exactly match. On the other hand, if we draw a graph of the Northing as a function of the geodetic latitude, it is difficult with a naked eye to distinguish it from a straight line passing through the origin.

Fifth Embodiment

(128) When collecting data on the global scale, it would be desirable to use the latitude-longitude origin as the origin of the coordinate system. However, when using only in a local area, for example, when using only within the territory of the Republic of Korea, as with the case of using spherical model Earth, it would be desirable to use default Northing N.sub.o, default Easting E.sub.o and a reference point with geodetic latitude φ.sub.o and longitude λ.sub.o. Therefore, in general, the Northing N and the Easting E are given by Eqs. 87-88.

(129) $\begin{array}{cc}N=N_o+a\left(1-e^2\right){\int }_{{\varphi }_o}^{\varphi }\frac{dt}{{\left(1-{e^2\left(\sin t\right)}^2\right)}^{\frac{3}{2}}}& \left[\mathrm{Equation}87\right]\end{array}$$\begin{array}{cc}E=E_o+\left(\lambda -{\lambda }_o\right)R_N\cos \varphi & \left[\mathrm{Equation}88\right]\end{array}$

(130) Eq. 87 can be transformed as follows.

(131) 0$\begin{array}{cc}N\left(\varphi \right)=a\left(1-e^2\right){\int }_0^{\varphi }\frac{dt}{{\left(1-{e^2\left(\sin t\right)}^2\right)}^{\frac{3}{2}}}+\left\{N_o-a\left(1-e^2\right){\int }_0^{{\varphi }_o}\frac{dt}{{\left(1-{e^2\left(\sin t\right)}^2\right)}^{\frac{3}{2}}}\right\}& \left[\mathrm{Equation}89\right]\end{array}$

(132) When a function y has the form of Eq. 90, the function y is called a linear function with respect to the variable x. Here, a and b are constants, where a is called the slope and b is called the y-intercept.
y(x)=ax+b  [Equation 90]

(133) The first term in Eq. 89 is the Northing from the latitude-longitude origin to the geodetic latitude φ and it is identical to Eq. 79. And the second term has no dependency on geodetic latitude φ. That is, the second term is a constant. Then, Eq. 89 is a linear function of the Northing from the latitude-longitude origin to the geodetic latitude φ, where especially the slope is 1.

Sixth Embodiment

(134) The exact location on the Earth is uniquely determined when the rectangular coordinates (X, Y, Z) of the three-dimensional Cartesian coordinate system are given, but the rectangular coordinates (X, Y, Z) are recognized as empty numbers for people living on a roughly spherical surface of the Earth. The exact location can also be specified by the geocentric latitude ψ, the longitude λ, and the geocentric altitude A in the geocentric coordinate system. But maps, smartphones, or GPS receivers provide geodetic latitude, not geocentric latitude. Furthermore, geocentric altitude is not provided by them.

(135) Given the geodetic latitude φ, the longitude λ and the ellipsoidal height h in the geodetic coordinate system, it is possible to accurately specify a position on the Earth. However, most of the maps provide the geodetic latitude and the longitude but not the ellipsoidal height. If we use a smartphone or a GPS receiver, we can obtain the altitude above sea level. But if we don't know the geoid height, we can't find out the ellipsoidal height. If we don't know the ellipsoidal height, we don't know the exact location on the Earth, either.

(136) However, since most of the people live attached to the surface of the Earth or on sea level, only the geodetic latitude and the longitude are necessary to know to practically determine the location. That is, were it not for special cases, such as sending an Inter-Continental Ballistic Missile (ICBM) to surgically strike an enemy's military facilities, or specifying the exact location of an airplane, drone, or submarine, we only need to specify the geodetic latitude and the longitude. For example, when precise coordinates are needed to rescue a strayed traveler in a deep mountain or a boundless ocean, the altitude above sea level is not really necessary.

(137) Although it is possible to specify a location simply by geodetic latitude and longitude, as described above, it is difficult to guess how far away that location is from the current location or how vast positional error range the coordinates represents. Therefore, coordinates such as the Northing and the Easting according to the present invention are preferable. However, in the geodetic coordinate system based on the Earth ellipsoid, the formulas for calculating the Northing and the Easting from the geodetic latitude and the longitude are relatively complicated, and the inverse process of calculating the geodetic latitude and the longitude from the Northing and the Easting is even more complicated.

(138) However, even if the Northing and the Easting are perceived as more meaningful numbers by people, and in a format more suitable for transmission using transmission media such as the Internet, they should be converted back to the geodetic latitude and the longitude in order to find its location on a map. Therefore, for everyday purposes such as using maps and not surveying or scientific research, all we need are two numbers that have similar meanings to Northing and Easting and can be easily converted to and from a pair of geodetic latitude and longitude. We don't′ really need exact distances measured along meridians or parallel of latitude for a spherical model Earth or the Earth ellipsoid.

(139) Moreover, the distances measured along meridians or parallels of latitude on the Earth ellipsoid do not correspond to the actual distances we are moving when we travel. If the ellipsoidal height at my current location is not 0 m, or the ellipsoidal height is 0 m but the slope of the surface of the Earth is not 0°, then the two numbers do not match.

(140) Therefore, in the sixth embodiment of the present invention, the Northing has a unit of distance, and is given as a monotonically increasing function of geodetic latitude φ or a monotonically increasing function of geocentric latitude ψ, and the Easting is also given as a monotonically increasing function of longitude λ with units of distance.

(141) A monotonically increasing function means that when the variable value increases, the function value also increases, and therefore it refers to a special kind of function. For example, sin(x) is not a monotonically increasing function of x. This is because sin(x) repeats increasing and decreasing even though x continues to increase. Meanwhile, x.sup.3 is a monotonically increasing function, and exp(x) is also a monotonically increasing function. As x increases, x.sup.3 increases, and exp(x) also increases. However, the extents to which x.sup.3 increases and exp(x) increases are of course different. On the other hand, y(x)=−2x+3 is a monotonically decreasing function of x. This is because it is a linear function with a negative (−) slope. That is, a monotonically increasing function only cares if the function value increases when the variable value increases, and does not care how much it increases in value.

(142) In the fourth embodiment, the Northing and the Easting are given by Eqs. 91-92.

(143) $\begin{array}{cc}N\left(\varphi \right)=N_o+a\left(1-e^2\right){\int }_{{\varphi }_o}^{\varphi }\frac{dt}{{\left(1-{e^2\left(\sin t\right)}^2\right)}^{\frac{3}{2}}}& \left[\mathrm{Equation}91\right]\end{array}$$\begin{array}{cc}E\left(\lambda \right)=E_o+\left(\lambda -{\lambda }_o\right)R_N\cos \varphi & \left[\mathrm{Equation}92\right]\end{array}$

(144) First, since the default Northing N.sub.o and the long radius a of the Earth ellipsoid have units of distance, the Northing also has a unit of distance, for example, meter. Also, the Northing N(ϕ) is a monotonically increasing function of the geodetic latitude ϕ. Since the integrand is always greater than 0, the integral in Eq. 91 must always be a monotonically increasing function with respect to the geodetic latitude φ.

(145) The Easting E(λ) also has a unit of distance. This is because the default Easting E.sub.o and the radius of curvature in the prime vertical R.sub.N have units of distance. Moreover, the Easting is a monotonically increasing function with respect to the longitude λ. Since cos φ always has a positive value in the interval from −90° to +90°, Eq. 92 is a linear function of the longitude λ in which the slope R.sub.N cos φ has a positive value. Therefore, it is a monotonically increasing function.

(146) Similarly, in the case of the third and the fifth embodiments, the Northing is a monotonically increasing function of the geodetic latitude φ, and the Easting is a monotonically increasing function of the longitude λ.

(147) In the third embodiment, the Northing and the Easting are given by Eqs. 93-94.
N(ψ)=N.sub.o+R(ψ−ψ.sub.o)  [Equation 93]
E(λ)=E.sub.o+(λ−λ.sub.o)R cos ψ  [Equation 94]

(148) The Northing N(ψ) is a linear function with a positive slope R with respect to the geocentric latitude ψ, and the Easting E(λ) is a linear function with a positive slope R cos ψ with respect to the longitude λ. That is, both are monotonically increasing functions. In addition, the Northing and the Easting in the first embodiment are also monotonically increasing functions.

(149) Accordingly, the Northings used in embodiments 1, and 3 to 5 of the present invention are monotonically increasing functions of the geocentric latitude or the geodetic latitude, and the Easting is a monotonically increasing function of the longitude. And, all have units of distance. By the way, the Northing and the Easting in the third or the fifth embodiments are not preferable for the above-mentioned reasons. The most preferable forms of the Northing and the Easting are given by Eqs. 95-96.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 95]
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 96]

(150) That is, it is in the form of the equation in the third embodiment where the geocentric latitude is replaced by the geodetic latitude. In addition, formulas for obtaining geodetic latitude and longitude from the Northing and the Easting are given by Eqs. 97-98.

(151) $\begin{array}{cc}\varphi ={\varphi }_o+\frac{N-N_o}{R}& \left[\mathrm{Equation}97\right]\end{array}$$\begin{array}{cc}\lambda ={\lambda }_o+\frac{E-E_o}{R\cos \left({\varphi }_o+\frac{N-N_o}{R}\right)}& \left[\mathrm{Equation}98\right]\end{array}$

(152) That is, bidirectional calculations are given as simple formulas that can be calculated even by hand, and fast calculations are possible when processed by computers.

(153) Unlike in the third or fifth embodiment, the Northing and the Easting in the sixth embodiment of the present invention do not have clear geometrical meanings. Therefore, they should not be understood as actual distances. However, since the difference between the geocentric latitude and the geodetic latitude is not large, the Northing given by Eq. 95 and the Easting given by Eq. 96 allows us to roughly estimate the real distances. Also, if we want to know the exact corresponding location on the map, we can obtain the exact geodetic latitude and longitude using Eqs. 97-98. If we know the exact geodetic latitude and longitude, we can find its location directly on the map. If geocentric altitude or ellipsoidal height is added to this, the exact location on the Earth can be specified using the formula in the first embodiment.

Seventh Embodiment

(154) Most of the contemporary people live in cities. In cities, there are numerous buildings such as apartments and commercial buildings. For modern people living or working in indoor spaces, a method of comprehensively specifying the location including the indoor location is required along with the geographical location that can be specified by latitude and longitude.

(155) In the present invention, all the artificial structures will be called buildings without distinguishing between structures and buildings. Buildings and structures have different legal meanings, but not only they do not conform to the common senses, but also most of the people do not know the difference. Therefore, in the present invention, all the artificial structures such as apartments, commercial buildings, barns, school buildings, factories, churches or temples, underground shopping malls, baseball stadiums, and parking towers will be called buildings.

(156) When we are in multi-story buildings, such as apartment, underground shopping mall, building, or parking tower, floor information is more important than the altitude above sea level. For example, if we are to meet someone in a tall business building, information about which floor we are on is more important. Also, at one time or another, everyone has an experience of parking his/her car in an underground parking lot and get perplexed after finding out that he/she forgot the basement level he/she parked on. For these various reasons, floor information is more useful than the elevation above sea level.

(157) The concept of floors in commercial building or apartment is familiar to everyone. However, in general, the ground floor is called the first floor, and the way underground floors are called are like the first basement level and the second basement level. If the first basement level is considered as −1 floor and the second basement level is considered as −2 floor and the like, and if we substitute the floor levels by integers, the index becomes discontinuous because there is no zeroth floor. That is, it becomes like −3, −2, −1, 1, 2, 3, 4, 5, which is inconvenient to process with computers.

(158) FIG. 30 is a conceptual diagram for understanding the floor model used in the seventh embodiment of the present invention. In order to describe the entire Earth with a simple mathematical model and in a consistent concept, it is desirable to call the ground floor as the 0th floor. Of course, there is nothing wrong with calling the first floor as +1 floor as in the general concept, but the computer code will look a little messy.

(159) In any case, in the seventh embodiment of the present invention, the surface of the Earth, the surface of a lake, and the sea level in the middle of the ocean are all regarded as the 0th floor. The 0th floor in the seventh embodiment of the present invention refers to the surface of the Earth on which a person can walk around naturally with his feet and the floor of the building continuously connected to the surface of the Earth. Therefore, if John Doe goes jogging along the riverside road, or swim in the lake, or finds a favorite store and walks into the store from the sidewalk, he still remains on the 0th floor. Also, when he climb Mt. Baekdu or Mt. Everest and sing hurray at the top of the mountain, he is also on the 0th floor. That is, in the present invention, the 0th floor has nothing to do with the altitude above sea level.

(160) On the other hand, the floor we call the second floor is +1 floor, and the third floor is +2 floor. Also, the first basement level is −1 floor, and the second basement level is −2 floor. And if we are floating in the air on an airplane or on a hot air balloon, we are considered to be on +∞ floor regardless of the altitude. Also, if we are diving under a lake or in the sea, we are considered to be on −∞ level.

(161) In the present invention, the +∞ layer or −∞ layer does not actually mean an infinite number, but means the largest number or the smallest number. For example, assuming that floors from −612 to +611 are allowed in the embodiment of the present invention, the +611 floor is regarded as the +∞ floor, and the −612 floor is regarded as the −∞ floor.

(162) In the seventh embodiment of the present invention, the geocentric altitude, the ellipsoidal height, and the altitude above sea level are all ignored, and an integer F representing the floor is used instead. In addition, the location in the horizontal dimension uses the Northing N and the Easting E of the sixth embodiment. And an integer F representing the floor is selectively used. That is, if the location of one point is specified as (N, E, F), it means the F floor of a building with a Northing N and an Easting E. In reality, it represents a specific point on the F floor of a building where the geodetic latitude and the longitude of the point corresponds to the Northing N and the Easting E. On the other hand, if it is simply written as (N, E), it means (N, E, 0). That is, it may mean an outdoor place that does not require the concept of a floor, or it may mean the first floor of a multi-story building.

(163) This model can be used for a variety of purposes in large cities where most of the buildings are multi-story buildings, such as ordering food for delivery, delivering mail, making an appointment with other people, or visiting a restaurant found on the Internet.

Eighth Embodiment

(164) In traditional markets, we can see grandmothers selling things with stalls measuring only 1 m in width and length or smaller. In addition, street lights, traffic lights, telephone booths, fire hydrants, etc. occupy a smaller area. As such, there may be a need to accurately specify the location of a movable property or real estate with a small footprint. Or, if we want to meet friends by specifying the location in a place without any special geographical features and where people are densely populated such as in the middle of the Gwanghwamun Plaza in Seoul, we need a method to specify and distinguish a section of about 1 m in width and length in a unique way.

(165) The surface area of a sphere with radius R is given by 4πR.sup.2. Using 6,371,008.8 m as the value of the average radius R of the spherical model Earth, the surface area is given as 5.1006588×10.sup.14 m.sup.2. In other words, if the surface of the Earth is divided into pieces of approximately 1 m in width and length, about 510 trillion pieces are obtained.

(166) The method of the sixth embodiment of the present invention may be used to divide the surface of the Earth into pieces of approximately 1 m in width: height, and to give each piece a location identifier given as a pair of two integers. That is, using the geodetic latitude and the longitude of the center position of the corresponding piece, the Northing N and the Easting E are calculated in meters. Most preferably, the Northing and the Easting given by Eqs. 99-100 are calculated.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 99]
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 100]

(167) By rounding off this Northing and Easting, they are converted into integers. In Eqs. 101-102, round( ) is a function that returns a rounded value of a real number. That is, round(9.4) is 9, and round(9.7) is 10.
I=round(N)  [Equation 101]
J=round(E)  [Equation 102]

(168) Any point on the Earth can be conveniently specified using the integers I, J thus obtained, and selectively an integer F representing the floor.

(169) FIG. 31 is a conceptual diagram of a three-dimensional location identifier. By using the method of the eighth embodiment in the present invention, the location can be specified using three integers (I, J, F) with an error range of less than 1 m.sup.2 regardless of the actual location on the surface of the Earth and the floor within all the buildings. We will refer to these three integers as 3-dimensional geological location identifier or simply as location identifier.

(170) In FIG. 31, the location identifier of a place a on the Earth is (I, J, F), the location identifier of a point e about 1 m away from a in the north direction is (I+1, J, F), and the location identifier of a point d about 1 m away from a in the east direction is (I, J+1, F), and the location identifier of a point f at the same geodetic latitude and longitude but one floor above a is (I, J, F+1). In addition, by transmitting thus obtained location identifier (I, J) or (I, J, F) to a friend, we can easily inform our location even if we are in a wild plain or deep in the mountains. This set of integers not only consume less data to transmit than the geodetic latitude and longitude, but also have the advantage that distances can be estimated because I and J have units of length. And the biggest advantage is that this location identifier indicates an area about 1 m in width and height for any location on the Earth.

(171) In addition, when geodetic latitude and longitude are needed, they can be obtained using Eqs. 103-104.

(172) $\begin{array}{cc}{\varphi }_I={\varphi }_o+\frac{I-N_o}{R}& \left[\mathrm{Equation}103\right]\end{array}$$\begin{array}{cc}{\lambda }_{I,J}={\lambda }_o+\frac{J-E_o}{R\cos \left({\varphi }_o+\frac{I-N_o}{R}\right)}& \left[\mathrm{Equation}104\right]\end{array}$

Ninth Embodiment

(173) In building a photo database, many techniques as well as related techniques have been developed for adding location information of the places where pictures were taken to the database using built-in GPS receivers in smartphones. Location information is recorded in the form of latitude and longitude expressed as decimal numbers, or in the form of latitude, longitude and altitude. In addition, even if the photo is not uploaded to the database right away at the shooting site, location information can be recorded using additional information recorded in the photo, that is, metadata stored in EXIF (Exchangeable Image File Format).

(174) In the ninth embodiment of the present invention, all digital contents to which location properties are given, HyperText Mark-up Language (HTML) pages, movables, real estates, and databases are the targets for registration in a relational database. For this reason, digital contents, HTML pages, personal property, real estate and databases can be all called data.

(175) The fact that a location property is given means that for the location property of a certain data, for example, a photo taken at the summit of Seoraksan Mountain, the geodetic latitude φ and the longitude λ at the summit of Seoraksan Mountain are assigned as the location property of the photo. Also, in the case of a movable property, such as a street lamp, a traffic light, a fire hydrant, a statue erected in a plaza, a work of art displayed in a museum, a luxury bag displayed in a department store, or a photograph of an idol hanging in a girl's room, a location property can be assigned with the latitude and the longitude corresponding to the location of the movable property. In the case of a movable property located in a multi-story building, the location property includes the floor number within the building. For example, for a CCTV installed in an office in a high-rise building, a location properties (φ, λ, F) can be assigned by the latitude, the longitude and the floor number considering the floor of the office.

(176) An HTML page is a web document that is displayed through a web browser when we visit a web site using a web browser such as Internet Explorer or Google Chrome, and has an extension of htm or html.

(177) There are many small stores in department stores, shopping malls, and underground shopping malls, and most of them do not have their own homepages. In addition, in order to operate an independent website, first an Internet domain must be purchased and maintained. For example, Applicant's domain is www.S360VR.com. When we visit a website, an HTML page with the name index.html is usually displayed first in our web browser.

(178) There are many difficulties in all the small stores in the shopping mall purchasing Internet domains and running websites. Instead, create HTML pages all named index.html, and for each HTML page, add a set (φ, λ) of geodetic latitude φ and longitude λ of the store's representative location as the location attribute of the HTML page, or add (φ, λ, F) where the integer F represents the floor of the store. By generating location identifiers (I, J) or (I, J, F) from these location attributes (φ, λ) or (φ, λ, F), it is possible to maintain virtually individual homepages without each store having to purchase individual domain.

(179) In addition, for the case of real estate such as the house I live in or a cafe I frequently visit, the representative location of the real estate is selected, and location properties can be assigned for the real estate which include the geodetic latitude and the longitude of the representative location and selectively an integer specifying the floor in the building.

(180) However, the digital contents include not only photos that can specify the physical geodetic latitude and longitude of the place where the photos were taken, but also paintings, illustrations, cartoons, animations, moving pictures, music files, audio files, poetries, novels, essays, historical or cultural commentaries, menu boards, catalogs, news articles, reviews, blueprints, technical documents, and etc.

(181) A poem or a song may not have a special location attribute. However, in the present invention, the location property of a data is not objectively given, but is a property that the owner of the data subjectively recognizes. For example, even in the case of a photo taken at the top of the Seoraksan Mountain, the geodetic latitude and the longitude of the summit of Seoraksan Mountain can be used as the location attribute of the photograph. Alternatively, focusing not on the background in the photograph but on the main character in the photograph, the geodetic latitude and the longitude of the main character's home can be used as the location attribute. Or, both can be used as the location attributes.

(182) Even in the case of a painting or an illustration, if a special geographical feature appears in the painting or in the illustration, the location of the geographical feature can be used as the location attribute. Alternatively, the location of the atelier of the painter who draw that painting or the location of the author's workroom who draw that illustration can be used at the location attribute of the painting or the illustration.

(183) If we want to register the national anthem as data, we can use the latitude and the longitude of the Baekdusan Mountain appearing in the lyrics of the national anthem as the location attribute. Or, we can use the location of the birthplace of Mr. Ahn Eaktae who composed the national anthem as the location attribute, or the location of the Blue House, which is the symbol of Korea's ruling power, can be used as the location attribute. Or, all of them can be used as location attributes. If all of them are used as location attributes, they can be registered as multiple records in the same database, or they can be registered as a single record and multiple indexes can be created referencing that record.

(184) In addition, in the case of a newspaper article dealing with an assembly in Gwanghwamun Plaza, the location attribute of the article uses the location information the newspaper publishing company or the journalist subjectively recognizes as its attribute such as the central location of Gwanghwamun Plaza, the location of the statue of King Sejong which is the symbol of Gwanghwamun Plaza, the location of the office of the organization hosting the assembly, or the location of the newspaper publishing company the journalist is affiliated with.

(185) Data that can be added to the database of the present invention can be another database. For example, we can create a separate database by collecting only photos taken at the top of the Seoraksan Mountain. This is because we may want to compare and view only the photos taken at the top of the Seoraksan Mountain.

(186) Also, suppose that there is a nationally renowned bakery on the second floor of a commercial building, and proof shots or reviews of that bakery are constantly added. In this case, there are good reasons to create a separate database of all the photos, videos, and reviews with the same location identifier (I, J, F) corresponding to the geodetic latitude, longitude and floor (φ, λ, F) of the representative location of the bakery.

(187) In addition, a national museum can build a database of all the exhibits in the national museum, and the “Seoul Arts Center” or “Sejong Center for the Performing Arts” can build a separate database for all performance files performed at their respective institutions.

(188) Since the data registered in this database have the same location identifier (I, J, F), there is no need for fields (columns) corresponding to the Northing corresponding integer I, the Easting corresponding integer J, and the floor representing integer F. Therefore, there is no need to be a relational database, and a relational database or a non-relational database can be used as needed.

(189) On the other hand, since all data registered in the database according to the ninth embodiment of the present invention have location attributes, it is advantageous to use a relational database. A relational database may have non-nullable fields, that is columns, and nullable fields. More strictly speaking, the main table of a relational database may have non-nullable fields and nullable fields. This is because some databases may consist of only one table, but may also consist of one main table and multiple auxiliary tables. However, since there is no room for confusion, for the convenience of discussion, it will be phrased that a database can have non-nullable fields and nullable fields. A non-nullable field means that if the field (column) is not filled in, data is not registered as a record in the database and an error occurs.

(190) In the relational database according to the ninth embodiment of the present invention, there are a field for entering the Northing corresponding integer I, a field for entering the Easting corresponding integer J, and a field for entering the floor representing integer F. However, since there is still no room for confusion, hereinafter, for the convenience of discussion, the field names will be referred to as the Northing corresponding integer I, the Easting corresponding integer J, and the floor representing integer F. The Northing corresponding integer I and the Easting corresponding integer J are non-nullable (NOT NULL) fields, and the floor representing integer F is a nullable field.

(191) The Northing corresponding integer I is an integer obtained by rounding off the Northing N. The Northing N has a unit of distance and is a monotonically increasing function of the geodetic latitude φ. The Easting corresponding integer J is also an integer obtained by rounding off the Easting E. The Easting E has a unit of distance and is a monotonically increasing function of the longitude λ. For example, the Northing N and the Easting E may have a unit of meters. On the other hand, geodetic latitude and longitude have units of degrees or radians.

(192) Table 4 illustrates the structure of such a relational database.

(193) TABLE-US-00006 TABLE 4 number field_name description datatype constraints 1 id identification number integer serial primary key 2 I integer corresponding to the Northing of integer not null the data 3 J integer corresponding to the Easting of the integer not null data 4 F floor number integer 5 data_name name of the data string 6 data_category data category such as photographs, music, string HTML page, immovable, database and etc. 7 owner owner who registered the data string 8 time the date and time when the data was string registered 9 file_path the full path to the data including string not null directories and file name 10 . . . 11 . . . 12 . . . 13 . . . 14 . . .

(194) In table 4, id is an integer that is automatically generated (serial) as a primary key. That is, whenever data is added as a record, id is assigned sequentially starting from 1.

(195) Field I is the Northing corresponding integer and cannot be omitted (not null). The field J is the Easting corresponding integer and cannot be omitted. Field F is an integer corresponding to the floor number and can be omitted. For the fields I, J and F, if the owner who registers the data subjectively determines the geodetic latitude and the longitude for the data and, if necessary, the floor number, from there, the Northing corresponding integer I and the Easting corresponding integer J are calculated, and registered in the database along with the floor number F.

(196) The data_name is the name of the data. The data_name can be entered by the user, but if the user does not explicitly enter it, the server can create it for the user and enter it. For example, if the user take a picture with a smartphone, a file name is automatically created by combining the date and the time.

(197) The data_category is a character string entered by the user or the server in order to distinguish whether the data is a photo, a music file, an HTML, page, a real estate, or another database.

(198) The owner is the name or user id of the user who entered the data, and is a character string. The time is the date and the time the server automatically entered as a character string when registering the data.

(199) The file_path is a full file path including a folder name and a file name in which the data is registered. For example, it can be in the form of “D:\DB2019(Personal)\Photos2019(DSLR)\20191023A\4O4A0403.JPG”

(200) Since data can be a picture, a video, a poetry, or NoSQL, the data types registered in the relational database of this embodiment are diverse. Therefore, in this case, the data itself cannot be entered. Instead, the path name must be stored.

(201) The Northing N and the Easting E can be implemented in various ways from the pair (ϕ, λ) of geodetic latitude φ and longitude λ, but the most preferred form of the Northing N is given by Eq. 105 as a function of the geodetic latitude ϕ.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 105]

(202) Here, N.sub.o is the default value of the Northing, R is the average radius of the Earth, φ.sub.o is the geodetic latitude of the reference point, and the unit of angle is radian.

(203) Also, the Easting E is given by Eq. 106.
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 106]

(204) Here, E.sub.o is the default value of the Easting, and λ.sub.o is the longitude of the reference point.

(205) In this case, the Northing corresponding integer I is obtained by rounding off the Northing N as in Eq. 107.
I=round(N)  [Equation 107]

(206) Further, the Easting corresponding integer J is obtained by rounding off the Easting E as in Eq. 108.
J=round(E)  [Equation 108]

(207) Instead of the latitude and the longitude, which is difficult to estimate the corresponding distance or error range, the reason for using the Northing and the Easting has already been explained enough. However, the reason for converting these numbers again from real numbers to integers and storing them is as follows. First of all, the latitude and the longitude expressed as decimal numbers or the Northing and the Easting in the form of real numbers can be used as fields. However, due to the nature of computers, the task of examining real numbers is much slower than that of examining integers.

(208) More importantly, if we use latitude⋅longitude or Northing⋅Easting where the location attributes are given as real numbers, for example, to determine if a certain photograph was taken at the top of the Seoraksan Mountain, we have to do proximity test by comparing the location attribute of the top of the Seoraksan Mountain and the location attribute of the photograph. Therefore, if it is found to be within the pre-determined criterion, it is judged to be the same place, and if it is found to exceed the criterion, it is judged to be taken in a different place. However, such proximity test not only takes a lot of time, but also has a possibility of error.

(209) On the other hand, if we let it have all the same Northing corresponding integer I and the same Easting corresponding integer J when it is within an area of about 1 m in width and length, after checking whether the Northing corresponding integer I and the Easting corresponding integer J of the top of the Seoraksan Mountain match those of the photograph, it is judged to be the same place if both integers match, and not the same place if at least one integer does not match. Therefore, not only is the search fast, but also there is no possibility of error.

(210) In addition, when there is a need to specify a location with maximum precision, such as the location of a cadastral control point, meter-level numbers are assigned to integers I and J, and numbers (distances) less than a meter can be stored in separate fields in a relational database. So there is no problem in using it even when precise positioning is required.

Tenth Embodiment

(211) It can be useful in various fields if the outdoor map and the indoor map are displayed together by superimposing floor plans of buildings on the outdoor map. For this purpose, it is desirable to construct a database of floor plans for each floor of buildings. Among them, a relational database will be the most preferable.

(212) In order to overlappingly display the map and the floor plan for each floor, it is desirable to create the floor plan for each floor in GeoJSON format, or convert to GeoJSON format from CAD data format such as AutoCAD or map data format such as shapefile.

(213) Since a building occupies a considerable area, it is necessary to select a representative point of the building. The representative point can be selected in a variety of ways, but one method that can be automated is to use the centroid of the floor plan of the ground floor of the building as a representative point. When a representative point is selected, the Northing corresponding integer I and the Easting corresponding integer J are generated from the geodetic latitude and the longitude of the representative point.

(214) The Northing corresponding integer I is an integer obtained by rounding off the Northing N. The Northing N has a unit of distance and is a monotonically increasing function of the geodetic latitude φ. The Easting corresponding integer J is also an integer obtained by rounding off the Easting E. The Easting E has a unit of distance and is a monotonically increasing function of the longitude λ.

(215) The Northing N and the Easting E can be implemented in various ways from the pair (ϕ, λ) of the geodetic latitude φ and the longitude λ, but in the most preferred form, the Northing N is given by Eq. 109 as a function of the geodetic latitude ϕ.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 109]

(216) Here, N.sub.o is the default value of the Northing, R is the average radius of the Earth, φ.sub.o is the geodetic latitude of the reference point, and the unit of angle is radian.

(217) Also, the Easting E is given by Eq. 110.
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 110]

(218) Here, E.sub.o is the default value of the Easting, and λ.sub.o is the longitude of the reference point.

(219) The Northing corresponding integer I is obtained by rounding off the Northing N as in Eq. 111.
I=round(N)  [Equation 111]

(220) In addition, the Easting corresponding integer J is obtained by rounding off the Easting E as in Eq. 112.
J=round(E)  [Equation 112]

(221) And, needless to say, there is a field for entering a floor plan in GeoJSON format, or a full file path including the file name and the folder wherein the floor plan is stored. Using PostGIS extension allows us to directly save GeoJSON files in PostgreSQL, so directly saving GeoJSON files may be preferable.

(222) In a relational database according to the tenth embodiment of the present invention, there are Northing corresponding integer I and Easting corresponding integer J, which are non-nullable fields, and floor representing integer F, which is a nullable field. If the building is a single-story building, the field for the floor can be left unfilled, or 0 can be entered. In the case of a floor plan of the second floor, an integer 1 is entered in the floor field, and in the case of a floor plan of the third floor, 2 is entered in the floor field. Furthermore, in the case of the first basement floor, −1 is entered in the floor field, and in the case of the second basement floor, −2 is entered in the floor field.

(223) In order to overlap floor plan per level on a map, or to quickly search for buildings located within the map area, we can use the method of including the coordinates of the boundary points of the minimum bounding box enclosing the floor plan of a building in the database. It would be preferable to use the upper-left corner point and the lower-right corner point of the minimum bounding box as the boundary points. In this case, the fields of the relational database will contain the coordinates of the boundary points of the minimum bounding box enclosing the floor plan of a building either as two pairs of Northing and Easting or as two pairs of geodetic latitude and longitude. Table 5 exemplifies the structure of such a relational database, and shows a case in which the Northing and the Easting of the upper left corner and the Northing and the Easting of the lower right corner are added as fields.

(224) TABLE-US-00007 TABLE 5 number field_name description datatype constraints 1 id identification number integer serial primary key 2 I integer corresponding to the Northing of integer not null the centroid 3 J integer corresponding to the Easting of integer not null the centroid 4 F floor number integer 5 Northing_upper Northing of the upper left corner of the real bounding box 6 Easting_left Easting of the upper left corner of the real bounding box 7 Northing_bottom Northing of the lower right corner of the real bounding box 8 Easting_right Easting of the lower right corner of the real bounding box 9 floor_map floor map in F floor GeoJSO not null N 10 . . . 11 . . . 12 . . . 13 . . . 14 . . .

(225) In Table 5, id is the primary key, which is an automatically generated (serial) integer. That is, whenever a data is added as a record, id is assigned sequentially starting from 1. Field I is the Northing corresponding integer, and is a non-nullable field (not null). The field J is the Easting corresponding integer, and is a non-nullable field. Field F is the floor representing integer and is a nullable field.

(226) When a representative point is selected in the floor plan of the ground floor of a building, the Northing corresponding integer I and the Easting corresponding integer J are automatically generated from the geodetic latitude and the longitude of the representative point. If the building is a multi-story building, the floor plan of each floor is entered as individual data (record), where the Northing corresponding integer I and the Easting corresponding integer J are the same, and F is entered differently according to the floor.

(227) floor_map is the floor plan for each floor written in GeoJSON format.

(228) In table 5, it is assumed that the positions of the upper-left and the lower-right corners of the minimum bounding box are stored as Northing and Easting, but it may be better to directly enter the geodetic latitude and the longitude in these columns. This is because these fields are not used for sorting and searching, but are only used when displaying on a map.

(229) However, the method of using a minimum bounding box has many inconveniences. First, when viewing a map using a smartphone, the direction of the map changes to match the direction the smartphone is facing. In that case, the orientation of the floor plan superimposed on the map must also be changed, and therefore the minimum bounding box must also be rotated. Instead of such a minimum bounding box, a minimum enclosing circle may be used. The minimum enclosing circle is a circle with the smallest radius among the circles enclosing all of the floor plan of the building.

(230) The above-mentioned centroid may be used as the center of the minimum enclosing circle, or the center and the radius of the optimal circle having the minimum radius may be searched irrespective of the centroid. In FIG. 32, a centroid is indicated by assuming that the boundary of the school campus is a floor plan, and a minimum enclosing circle having the centroid as its center is also indicated.

(231) The most convenient way to specify a circle is to specify the location of the center and the radius. In order to specify the center of the minimum enclosing circle containing the floor plan of a building therein, the field of the relational database includes the coordinates of the center position either as a pair of Northing and Easting or as a pair of geodetic latitude and longitude. Also, since radius must have a unit of length, the database contains a field storing the radius of the minimum enclosing circle in the same unit as the Northing.

(232) Another circle is indicated in FIG. 32, which will be referred to as a maximum included circle. The maximum included circle is a circle with the largest radius among the circles that are completely contained within the floor plan. The maximum included circle may also have the centroid as its center, or the center and the radius of the circle having the largest radius may be determined regardless of the centroid. In FIG. 32, the maximum included circle was obtained irrespective of the centroid, and as shown in FIG. 32, the center of the circle is at a different position from the centroid. In fact, since the centroid is just a point at which the physical moments are balanced, the center of the maximum included circle does not needs to coincide with the centroid.

(233) In this case also, the fields of the relational database contain the center coordinates of the maximum included circle contained in the floor plan for each floor of the building either as a pair of Northing and Easting or as a pair of geodetic latitude and longitude. The fields also contain the radius of the maximum included circle in the same unit as the Northing.

(234) Finally, instead of the maximum included circle, we can use a maximum included box. The maximum included box is a rectangle with the largest area among the rectangles that are completely contained within the floor plan. The center of the maximum included box may also be the centroid, or the upper left corner and the lower right corner of a box having the largest area may be determined irrespective of the centroid.

(235) In this case, the fields of the relational database include the coordinates of the boundary points of the maximum included box contained within the floor plan per level of the building either as two pairs of Northing and Easting or as two pairs of geodetic latitude and longitude.

(236) Apart from the concept of a maximum included circle or a maximum included box and how to specify them, one might wonder why a maximum included circle or a maximum included box is needed. The use of a maximum included circle or a maximum included box is the same. The purpose of the maximum included circle is to check whether the center of the map screen indicating the user's position on the map or the position of the mouse cursor is clearly located within the building. That is, it is used to determine for 100% sure whether a smartphone user or the mouse cursor of a user searching the map on a PC is located within a certain building.

(237) In fact, if it is outside the maximum included circle and still within the floor plan, the test will fail despite the fact that it is within the floor plan for sure. But this is not important. If the user move the mouse further and the cursor enters within the maximum included circle, we know with 100% certainty that the user is inside the building, and this is the information we really need. In addition, the search algorithm is simple, and it does not matter even if the screen is rotated.

(238) In this way, when it is confirmed that the user is inside a building, a menu for selecting a floor in a multi-story building appears and allows the user to select the desired floor. When the desired floor is selected, the floor plan of that floor is superimposed on the map and shown to the user.

Eleventh Embodiment

(239) When using an internet map service such as Google map, we can search the map by entering a latitude and a longitude, but we can also search by entering an address. This is because, in this case, the map server finds the latitude and the longitude corresponding to the address. This technique of finding the latitude and the longitude from a name of a place or an address is called geocoding. Conversely, the technique of finding the address from a latitude and a longitude is called reverse geocoding.

(240) In the eleventh embodiment of the present invention, the concept of this geocoding technique is extended to give a location attribute to any proper noun, common noun, or more general arbitrary character string, and a relational database is built for the character string. In such a relational database according to the eleventh embodiment of the present invention, data is a character string to which a location attribute is assigned. Location attribute include a geodetic latitude φ and a longitude λ and selectively a floor number within the building.

(241) As in the ninth embodiment of the present invention, the location attribute in the eleventh embodiment of the present invention is the location attribute of the data (i.e., character string) the owner of the data, in other words, a database user who registers the character string in a relational database, subjectively recognizes as its attribute. From the location attribute of the character string, a Northing corresponding integer I and an Easting corresponding integer J are generated, and these two integers (I, J) are entered into the database. If not on the ground floor, in other words, 0.sup.th floor, an integer F specifying the floor in a building is also entered into the database.

(242) In a relational database according to the eleventh embodiment of the present invention, a Northing corresponding integer I and an Easting corresponding integer J are non-nullable fields (NOT NULL), and a floor representing integer F is a nullable field. The Northing corresponding integer I is an integer obtained by rounding off the Northing N. The Northing N has a unit of distance and is a monotonically increasing function of the geodetic latitude φ. The Easting corresponding integer J is also an integer obtained by rounding off the Easting E. The Easting E has a unit of distance and is a monotonically increasing function of the longitude λ.

(243) The Northing N and the Easting E can be implemented in various ways from the pair (ϕ, λ) of the geodetic latitude φ and the longitude λ, but in the most preferred form, the Northing N is given by Eq. 113 as a function of the geodetic latitude φ.
N=N.sub.o+R(ϕ−ϕ.sub.o)  [Equation 113]

(244) Here, N.sub.o is the default value of the Northing, R is the average radius of the Earth, φ.sub.o is the geodetic latitude of the reference point, and the unit of angle is radian.

(245) Also, the Easting E is given by Eq. 114.
E=E.sub.o+(λ−λ.sub.o)R cos ϕ  [Equation 114]

(246) Here, E.sub.o is the default value of the Easting, and λ.sub.o is the longitude of the reference point.

(247) The Northing corresponding integer I is obtained by rounding off the Northing N as in Eq. 115.
I=round(N)  [Equation 115]

(248) In addition, the Easting corresponding integer J is obtained by rounding off the Easting E as in Eq. 116.
J=round(E)  [Equation 116]

(249) If an objective location attribute is related to a specific character string, preferentially a location identifier (I, J) or (I, J, F) will be generated from the location attribute. For example, for a character string “Namdaemun”, a Northing corresponding integer I and an Easting corresponding integer J can be assigned corresponding to the geodetic latitude and the longitude of the Namdaemun. Also, for “Sungnyemun”, the official name of the Namdaemun, the same Northing corresponding integer I and the Easting corresponding integer J are assigned. In addition, the same Northing corresponding integer I and the Easting corresponding integer J are assigned to the string “40 Sejong-daero, Jung-gu, Seoul”, which is the address of the Namdaemun. And since Namdaemun is Korea's National Treasure No. 1, the same Northing corresponding integer and the Easting corresponding integer are assigned to the string “National Treasure No. 1”. In addition, a corresponding location identifier can also be assigned to a place name such as “Seoraksan Mountain rocking stone”.

(250) The company name of the present applicant is “S360VR CO., LTD.”. Then, with the geodetic latitude and the longitude and the floor number of the applicant's office location, a Northing corresponding integer I, an Easting corresponding integer J, and a floor representing integer F are assigned to the character string “S360VR”. In addition to this, the same location identifier (I, J, F) is assigned to the representative's name, “Kweon Gyeongil”. In addition, the same location identifier is assigned to the applicant's representative phone number, fax number, e-mail address, and internet domain. In addition, the same location identifier is assigned to the applicant's main product, “scanning stereoscopic panoramic camera,” and to the main service area, “software development.”

(251) “S360VR” and “software development” are obviously character strings, but we might think that the representative phone number is not a character string but a number. For example, the usual way to write the applicant's office phone number including the country code is +82-42-226-8664. Here, 82 is the country code of the Republic of Korea, 42 is the area code of Daej eon, 226 is the telephone exchange number, and 8664 is the rest of the number.

(252) However, the dash (−) is not part of the phone number, but is inserted for convenience so that people can easily distinguish the phone number from the country code and the area code. It's also clear from the fact that we don't press the dash (−) button when making a call. So, the phone number in the purest form would be 82422268664. In other words, it can be thought of as a very large integer. Therefore, even if a location attribute is assigned to a phone number, we might wonder it cannot be registered as data because it is not a character string.

(253) However, most of the software allows converting an integer or a real number into a character string, or storing as a character string. In addition, functions are provided to convert numeric data stored in character string format back to the original numeric format. In PostgreSQL, we can convert numbers to character strings just by enclosing them in quotation marks. That is, if it is saved as ‘82-42-226-8664’ or as ‘82422268664’, it can be inserted into a field whose datatype is a character string.

(254) As such, all names, place names, trade names, nicknames, addresses, internet domains, email addresses, telephone numbers, fax numbers, and etc. whereon location attributes are assigned can be entered as data. The above location attribute includes not only an objective location attribute, in other words, (geodetic) latitude and longitude, but also a subjective location attribute the owner of the data considers as its location attribute.

(255) In addition, the character strings to which location attributes are assigned include a type of business as a common noun, a type of service, services, and products. For example, if an electrician living in a certain neighborhood registers a character string such as “electrical repairs”, the location attribute of the character string may specify the location attribute of the electrician's shop, or the location attribute of his or her house.

(256) Similarly, ‘starbucks’, ‘coffee house’, ‘cafe’, ‘Americano’ and ‘coffee’ can all be registered as data by assigning the location attribute corresponding to the same address. Then, whether the user searches by ‘cafe’, or ‘Americano’, searches will be successful for all cases.

(257) Since ‘cafe’ and ‘coffee’ are both common nouns, data with the same keywords, i.e., ‘cafe’ or ‘coffee’, can be entered by many cafes. Therefore, when a user using the relational database of the embodiment of the present invention searches for ‘coffee’ using a smart phone, numerous data will be retrieved. Then, after the database software finds out the user's current location from the smartphone, the search results can be displayed by listing them in the order closest to the user's current location. Therefore, it can be used for various purposes, such as ordering food for delivery or finding a movie theater or a gas station.

(258) The relational database according to the eleventh embodiment of the present invention may have a structure as shown in table 6. Table 6 illustrates the main table of a relational database whose data is a character string with a location attribute assigned in a very simple format.

(259) TABLE-US-00008 TABLE 6 number field_name description datatype constraints 1 id identification number integer serial primary key 2 keyword keyword string not null 3 category category string 4 I integer corresponding to the integer not null Northing of the data 5 J integer corresponding to the integer not null Easting of the data 6 F floor number integer 7 owner owner who registered the data string

(260) In table 6, keyword is a character string to which a location attribute is assigned. In other words, it is a data. And, category is an additional information entered in order to improve efficiency in data management and searching.

(261) As such, “keywords”, a database for character strings with location attributes, can be created in PostgreSQL with the following SQL command.

(262) TABLE-US-00009   CREATE TABLE keywords ( id BIGSERIAL NOT NULL PRIMARY KEY, keyword VARCHAR(100) NOT NULL, category VARCHAR(50), I BIGINT NOT NULL, J BIGINT NOT NULL, F SMALLINT, owner VARCHAR(50));

(263) Here, the datatype of id is listed as BIGSERIAL, which is an integer type that is automatically generated like SERIAL, but starts from 1 and the maximum integer value is possible up to 9223372036854775807. Both BIGINT and SMALLINT are integer types with different ranges.

(264) FIG. 33 shows a database using PostgreSQL having one table “keywords”, and FIG. 34 shows search results with various keywords.

INDUSTRIAL APPLICABILITY

(265) It can be used in various industrial fields such as wayfinding by integrally specifying a geographic location and an indoor location within a building by two or three integers.