WO2007003721A1 - Procede et systeme de projection cartographique du globe terrestre et carte etablie selon le procede - Google Patents
Procede et systeme de projection cartographique du globe terrestre et carte etablie selon le procede Download PDFInfo
- Publication number
- WO2007003721A1 WO2007003721A1 PCT/FR2005/001695 FR2005001695W WO2007003721A1 WO 2007003721 A1 WO2007003721 A1 WO 2007003721A1 FR 2005001695 W FR2005001695 W FR 2005001695W WO 2007003721 A1 WO2007003721 A1 WO 2007003721A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- latitude
- projection
- globe
- projected
- cylinder
- Prior art date
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Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/05—Geographic models
Definitions
- the invention relates to a method for cartographic representation of the surface of the terrestrial globe.
- the problem at the origin of the invention is an interactive mapping problem on the Internet.
- Some Internet sites offer a card generation service, in which, following the entry of an address by a user, a server for implementing the service generates a map, of a determined portion of the surface of the globe located around this address, on a determined scale.
- the cards have been previously cut into "tiles" joined, which allows the user to either increase or decrease the scale, or move the map in a specific direction, simply by dragging it with the cursor; for these operations, the server only loads the missing tiles necessary for the desired display.
- Such services by their application to the Internet, require a generation of the map made with approximations, so that the calculations and therefore the data loading time are not too important.
- the globe is considered to be spherical and the projection is made on a cylinder, intersecting at the surface of the globe. along a line about the middle, in latitude, of the United States, that is, at a latitude of 39.5 °.
- the projected coordinates are directly proportional to the longitude and latitude angles, with a corrective ratio in cos (39.5) for latitudes, so that the longitude distances are maintained, the error being zero in latitude at the latitude of 39.5 ° and increasing when one moves away from it.
- the Universal Transverse Mercator (UTM) system is also known, in which the terrestrial globe is divided into spindles of amplitude 6 ° in longitude and in strips of amplitude 8 ° in latitude, projected on cylinders whose axis is contained in the plane of the equator.
- the function of projection that is to say the function which, at each point of the globe, associates a projected point, is more complex than in the preceding case, to take into account and to compensate for the crushing when one away from the intersecting curves between the projection cylinder and the terrestrial globe, as well as the elliptical shape of the terrestrial globe.
- the present invention aims at proposing a method of cartographic projection of at least a portion of the terrestrial globe, which meets the following requirements:
- the invention relates to a cartographic projection process of at least a portion of the earth, in which a projection cylinder, containing the globe or secant with it, is defined and the points of the globe are projected, of which the coordinates are defined by a longitude and a latitude, on this cylinder, associating with each longitude an abscissa, at each latitude an ordinate, in a referential of the developed cylinder, characterized by the fact that:
- n + 1 latitude angles ( ⁇ 0 , ..., ⁇ n ) is determined, defining n (n> 2) distinct ranges of latitudes,
- each north and / or south hemisphere of the globe is divided into n peripheral zones of latitudes corresponding to the n ranges of the sequence, each defined by two parallel limits of latitude,
- the parallels of limit latitude are projected on the projection cylinder and each point of one of the n zones of latitudes is projected at a point on the ordinate cylinder which is interpolated between those of the projected limit latitude parallels as a function of the relative latitude of the point between the two parallels.
- the assimilation of the globe to a sphere is not a necessary step in the implementation of the process and the plaintiff does not intend to limit the scope of its rights to this approximation. It is a preferred embodiment of the method, especially for an application to the generation of interactive maps on the Internet, with cutting of the map in tiles.
- the simplicity of implementation of the invention also allows its application to a projection process in which the earth is assimilated, for example, to an ellipsoid, the projection being adapted to such an approximation; such a method is also applicable to the interactive generation of cards on the Internet.
- the invention is particularly applicable to the generation of cards on the Internet, but the applicant does not intend to limit the scope of its rights to this application alone.
- the invention also relates to a cartographic projection system of at least a portion of the terrestrial globe, for the implementation of a projection method applied to interactive mapping on the Internet, comprising:
- a database comprising the coordinates of the points of the portion of the globe, defined by a longitude and a latitude, a database containing the latitude coordinates of a sequence of n + 1 limiting latitude angles,
- a module for generating an interactive map on the Internet from the calculated values of the projected coordinates a module for generating an interactive map on the Internet from the calculated values of the projected coordinates.
- the invention naturally also relates to the cards established according to the method of the invention and whatever their support.
- FIG. 1 represents a schematic view of the terrestrial globe whose northern hemisphere is divided into nine zones of latitudes
- FIG. 2 represents a schematic view illustrating the projection of a point contained in an area on the developed cylinder
- FIG. 3 is a flow chart showing a cartographic projection system for implementing the preferred embodiment of the method of the invention and the appendix comprises a computer program in C language which can be used for the implementation of implementation of the preferred embodiment of the method of the invention.
- the object of the method of the invention is to obtain a cartographic projection of a portion of the earth or even the entire globe.
- the terrestrial globe 1 is likened to a sphere.
- This approximation is used from widespread in cartographic projection processes and is not shocking to the user of the map that will be obtained through the mapping projection method, because the user is familiar with this approximation.
- Those skilled in the art may prefer an approximation of the shape of the globe to an ellipsoid, for example, if he wants a greater accuracy of the cartographic representation.
- each point A of the surface of the terrestrial globe 1 is defined by two of its coordinates: the longitude ⁇ and the latitude ⁇ , well known to those skilled in the art.
- the distance to the center C of the terrestrial globe 1 is not a necessary coordinate to determine the coordinates of a point A, because this distance is considered constant because of the approximation of the globe 1 to a sphere, the altitude of the points are not taken into account here.
- a projection cylinder on which are intended to be projected the points of the surface of the globe, to obtain, by developing the cylinder, a map with the projected points of the surface of the globe.
- a cylinder must either contain the terrestrial globe 1, or be intersecting with it, to obtain projections from each point of the globe to a point on the projection cylinder.
- the projected points are defined by their coordinates in a referential of the developed cylinder, namely, with reference to FIG. 2, where the developed cylinder 2 is shown schematically, an abscissa X and an ordinate Y. It will be understood that when the cylinder is not developed, the abscissa X is curvilinear on the cylinder.
- the cylinder is chosen by the skilled person according to the rendering of the card he wishes to obtain.
- the various parameters for defining the cylinder are its radius, the position and the angle of its axis with respect to the terrestrial globe 1.
- a cylinder tangent to the terrestrial globe along the equator will be chosen here.
- the axis of this cylinder is coincident with the north-south axis of the earth, 1 which is perpendicular to the plane of the equator 3, its radius being equal to that of the terrestrial globe 1, similar to a sphere.
- the northern hemisphere is divided into a first zone comprising all the points of the surface of the globe whose latitude is between 0 and 10 °, a second zone comprising all the points of the surface of the globe whose latitude is between 10 and 20 °, and so on until a last zone whose latitudes of points are between 80 and 90 °.
- the same operation is performed on the southern hemisphere, with negative latitudes.
- the remainder of the description will be made in relation only to the northern hemisphere, but it will be readily understood that the same operations may be carried out for the southern hemisphere.
- a projection function is defined which, at each point on the surface of the globe 1, associates a point projected on the projection cylinder. It is by this projection function that the parallel of limit latitude is projected onto the projection cylinder. This function therefore associates, at each coordinate point
- This function is a cylindrical projection function. Whatever this function, it will generate deformations in the projection; it is indeed impossible to project a sphere on a plane without deformations.
- a cylindrical projection function the projected meridians are parallel to each other and the projected parallels are parallel to each other.
- the function is chosen by those skilled in the art in relation to the deformations that he considers acceptable, according to his requirements and / or constraints.
- These projection functions verify various conditions and equations, which will not all be developed here.
- the method of the invention will be presented here in relation to a conformal cylindrical projection function.
- a compliant function must in particular verify the following relation:
- the function f as a projection function, the function f, called the Mercator function, which at each point of coordinates associates a projected point of coordinates (X, Y), with where f x and f y are respectively the component of the function f which at a longitude associates an abscissa with the component of the function f which at a latitude associates an ordinate.
- the function f is defined by the following relations: a proportionality factor chosen by those skilled in the art to make the abscissa X proportional to the longitude ⁇ )
- This function has in fact been chosen here because of its good behavior up to about 80 ° latitude, if one does not necessarily want to obtain a map for higher latitudes. If this were the case, one could either choose a different function f, or arbitrarily assign a value to f y (90); it is this last solution which is considered here.
- Each point of the surface of the terrestrial globe is then projected at a point in the ordinate cylinder that is interpolated between those of the projected parallel latitude of latitude, as a function of the relative latitude of the point between the two parallels.
- the interpolation is, in the preferred embodiment of the invention, a linear interpolation, but it goes without saying that any further interpolation can be implemented.
- the ordinate of the projected point is thus interpolated, between the ordinates of the projected two parallel of limit latitude defining the zone containing the point, according to the value of the latitude of the point with respect to these latitude latitudes on the surface of the globe.
- the ordinate of the projection of each point of the surface of the terrestrial globe on the projection cylinder is consequently calculated by linear interpolation between two of the values calculated above, these two values corresponding to the projected ordinates of the parallels whose latitudes define the area in which the point is located.
- a point A of the surface of the globe, of latitude ⁇ lies in one of the n zones, referenced 4, presented above, between two parallels 5, 6, that is to say that its latitude ⁇ is included in one of the n ranges that have been defined.
- the latitude ⁇ of this point lies in the range defined by the latitude angles ⁇ j and ⁇ i + 1 .
- the ordinate Y, of the projected point A 'of this point A of the globe of latitude ⁇ , is calculated by linear interpolation between the values of the projected ordinates of the latituts. ⁇ j + i, that is to say by linear interpolation between the value d and the one at
- the interpolation is carried out as follows: at a point A of the surface of the globe of latitude ⁇ , lying between two latitudes, the ordinate Y is assigned to the projection cylinder, which is defined by:
- n ranges are of constant amplitude, that is to say that is, for v 10 °.
- Point A ' projected from point A with coordinates ( ⁇ , ⁇ ), is therefore of coordinates (X, Y), in a reference of the developed projection cylinder 2:
- the error when we project a portion of the surface of the globe, which extends over several of the latitudes, the error, compared to the projection that would be made for all points with the projection function f, is limited to the error that is made on each of the zones of latitudes.
- These deformations are quite quantifiable for the skilled person, who can change the function or the number of areas in which the globe is cut, to obtain a greater or lesser accuracy depending on its requirements and / or constraints.
- some projection functions may be good on one part of the globe, but less good on others; for example, in this case, the behavior of the function is good up to about 80 ° latitude, but less good between 80 and 90 °.
- the method of the invention it is possible to assign, arbitrarily - but chosen by the skilled person according to what he wishes - a value to f y (90), in order to avoid its divergence towards + ⁇ .
- the value of f y (90) being thus fixed, the values taken by the projected ordinates of the points of latitude between 80 and 90 ° lie between f y (80) and f y (90) and do not diverge. It is thus possible, by assigning suitable values to some of the ordinates projections latitudes ⁇ o, ..., O n defining the ranges, to correct errors or to give a desired shape to the projection.
- the method of the invention has been presented in relation to a projection cylinder tangent to the equator, i.e. the scale is maintained at the equator. It goes without saying that a person skilled in the art can readily adapt the description that has been made in the case where the cylinder is for example secant or tangent along a parallel of latitude ⁇ o, by introducing correction constants dependent on O 0 . Note that, unlike the prior art where such O 0 implied errors when it deviates, the method of the invention would not be affected by such a factor.
- the approximation has been made here of the terrestrial globe assimilated to a sphere. But it goes without saying that another approximation can be made, for example that of the globe to an ellipsoid.
- the projection function f preferably cylindrical conform, is different, and more complex.
- the invention therefore also makes it possible to apply to interactive cartography on the Internet more complex and more precise approximations.
- mapping projection system 7 for the implementation of the method of the invention is now described, in the application to the generation of interactive maps on the Internet.
- This system 7 comprises a database 8 comprising cartographic information, from which one can extract the coordinates ( ⁇ , ⁇ ) of the points of the terrestrial globe, which are placed in a database 9.
- This database 9 thus comprises the coordinates points of the portion of the globe that we may wish to display.
- the coordinates ⁇ ; ie [0, n] of the limit latitude angles are also entered in a database 10.
- the system 7 comprises a calculation module 11, for the calculation of the projection of the limit latitude angles, that is to say the calculation of f y ( ⁇ i); this calculation module comprises for example a cylindrical projection program, comprising the function f y ; these calculated values f y ( ⁇ ;) are kept in a database 12.
- a user provides the system 7 with a request, by a request input module 13, typically a computer connected to the Internet.
- This request can be a request to generate a map around an address, on a portion of the globe, or with any other relevant parameter (scale, possibility of enlargement or reduction, ).
- This request makes it possible to select, in the database 9 comprising the coordinates ( ⁇ , ⁇ ) of the points of the globe, the coordinates of the points which must be displayed on the map, kept in a database 14 of selected data.
- These coordinates are entered in a comparison module, which compares each selected latitude with the latitudes of the database 10 having the coordinates of the latitudes ⁇ i5 ie [0, n].
- each point is assigned in an area of the globe between two points of limit latitude, its position between these two latitudes being determined; a calculation module 16 can calculate the value of the projected ordinate of this point, by interpolation between the projected values of the latitudes defining the zone in which it is, according to the position of the point in the zone.
- This calculation module 16 is for this purpose connected to the comparator 15 and the database 12 having the values of f y ( ⁇ j).
- the calculation module 16 also calculates the value of the projected abscissa of the longitude of each point. It thus makes it possible to obtain the projected coordinates (X, Y) of the points.
- the calculated values of the projected coordinates of the points of the portion of the terrestrial globe are entered in a module 17 for generating maps on the Internet, here comprising a function of cutting the map into tiles, as well as possibly overprint functions of layers and / or images.
- the resulting map is then displayed by means of a display module 18.
- the coordinates ⁇ ; ie [0, n] of the limit latitude angles are entered into the database 10 directly by those skilled in the art, prior to any generation of maps, the following of latitude limits thus being fixed for the future.
- the sequence of coordinates ⁇ , ie [0, n] of the angles of latitude limit is generated automatically by the system 7, depending on the request of the user. So, depending on the address or the portion of the earth that the user wishes to visualize, or the precision that he desires, this sequence of coordinates is generated, the number of limit latitudes or the pitch between them being able to be adapted case by case.
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Abstract
Description
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Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
AU2005333996A AU2005333996A1 (en) | 2005-06-29 | 2005-07-01 | Method and system for earth globe map projection and map obtained by said method |
BRPI0520409-7A BRPI0520409A2 (pt) | 2005-06-29 | 2005-07-01 | processo e sistema de projeção cartográfica de pelo menos uma porção do globo terrestre, e, mapa |
EP05786233A EP1908024A1 (fr) | 2005-06-29 | 2005-07-01 | Procede et systeme de projection cartographique du globe terrestre et carte etablie selon le procede |
CA002612966A CA2612966A1 (fr) | 2005-06-29 | 2005-07-01 | Procede et systeme de projection cartographique du globe terrestre et carte etablie selon le procede |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0551831A FR2888023B1 (fr) | 2005-06-29 | 2005-06-29 | Procede de projection cartographique du globe terrestre et carte etablie selon le procede |
FR0551831 | 2005-06-29 |
Publications (1)
Publication Number | Publication Date |
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WO2007003721A1 true WO2007003721A1 (fr) | 2007-01-11 |
Family
ID=35457433
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
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PCT/FR2005/001695 WO2007003721A1 (fr) | 2005-06-29 | 2005-07-01 | Procede et systeme de projection cartographique du globe terrestre et carte etablie selon le procede |
Country Status (7)
Country | Link |
---|---|
US (1) | US20070003911A1 (fr) |
EP (1) | EP1908024A1 (fr) |
AU (1) | AU2005333996A1 (fr) |
BR (1) | BRPI0520409A2 (fr) |
CA (1) | CA2612966A1 (fr) |
FR (1) | FR2888023B1 (fr) |
WO (1) | WO2007003721A1 (fr) |
Families Citing this family (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US8638327B2 (en) * | 2007-11-14 | 2014-01-28 | Microsoft Corporation | Tiled projections for planar processing of round earth data |
US20190076723A1 (en) * | 2017-09-14 | 2019-03-14 | Gregory Cromartie | Ball containment assembly |
CN109191935A (zh) * | 2018-10-17 | 2019-01-11 | 杭州师范大学 | 一种直观的多功能地图投影教学仪及其实现方法 |
CN109813255B (zh) * | 2019-01-16 | 2024-04-09 | 苏州科技大学 | 一种地球椭球面上大梯形图块的面积计算方法 |
CN112612916B (zh) * | 2020-12-29 | 2024-02-06 | 深圳航天宏图信息技术有限公司 | 一种海洋卫星数据的检验误差空间分布图生成方法及装置 |
CN115880973B (zh) * | 2023-02-02 | 2023-05-05 | 北京东方瑞丰航空技术有限公司 | 伪球面坐标系的飞行模拟机视景生成方法、装置和设备 |
Citations (3)
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US4899293A (en) * | 1988-10-24 | 1990-02-06 | Honeywell Inc. | Method of storage and retrieval of digital map data based upon a tessellated geoid system |
EP0509839A2 (fr) * | 1991-04-19 | 1992-10-21 | Hitachi, Ltd. | Système digital cartographique pour le traitement d'informations géographiques |
JPH11328157A (ja) * | 1998-05-13 | 1999-11-30 | Mitsubishi Electric Corp | データマッピング装置及びデータマッピング方法 |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
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US4414731A (en) * | 1980-03-31 | 1983-11-15 | Replogle Globes, Inc. | Method of manufacture of raised relief illuminated globe |
US4972319A (en) * | 1987-09-25 | 1990-11-20 | Delorme David M | Electronic global map generating system |
US5772441A (en) * | 1996-12-24 | 1998-06-30 | Wilson; Henry Allen | Visually reinforced learning and memorization methods |
US7171389B2 (en) * | 2001-06-01 | 2007-01-30 | Landnet Corporation | Identification, storage and display of land data on a website |
FR2826720B1 (fr) * | 2001-06-29 | 2003-09-05 | Thales Sa | Procede de synthese d'une image cartographique |
FR2826762B1 (fr) * | 2001-06-29 | 2004-02-06 | Thales Sa | Procede de synthese d'une image d'intervisibilite |
-
2005
- 2005-06-29 FR FR0551831A patent/FR2888023B1/fr not_active Expired - Fee Related
- 2005-07-01 AU AU2005333996A patent/AU2005333996A1/en not_active Abandoned
- 2005-07-01 EP EP05786233A patent/EP1908024A1/fr not_active Withdrawn
- 2005-07-01 WO PCT/FR2005/001695 patent/WO2007003721A1/fr active Application Filing
- 2005-07-01 CA CA002612966A patent/CA2612966A1/fr not_active Abandoned
- 2005-07-01 BR BRPI0520409-7A patent/BRPI0520409A2/pt not_active IP Right Cessation
- 2005-07-08 US US11/177,108 patent/US20070003911A1/en not_active Abandoned
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US4899293A (en) * | 1988-10-24 | 1990-02-06 | Honeywell Inc. | Method of storage and retrieval of digital map data based upon a tessellated geoid system |
EP0509839A2 (fr) * | 1991-04-19 | 1992-10-21 | Hitachi, Ltd. | Système digital cartographique pour le traitement d'informations géographiques |
JPH11328157A (ja) * | 1998-05-13 | 1999-11-30 | Mitsubishi Electric Corp | データマッピング装置及びデータマッピング方法 |
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EVENDEN G I: "THE MAPGEN CARTOGRAPHIC SYSTEM", PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON MARINE POSITIONING, REIDEL, DORDRECHT, NL, 14 October 1986 (1986-10-14), pages 285 - 294, XP009054493 * |
PATENT ABSTRACTS OF JAPAN vol. 2000, no. 02 29 February 2000 (2000-02-29) * |
RENKA R J: "Interpolation of data on the surface of a sphere", ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE USA, vol. 10, no. 4, December 1984 (1984-12-01), pages 417 - 436, XP002359955, ISSN: 0098-3500 * |
Also Published As
Publication number | Publication date |
---|---|
FR2888023A1 (fr) | 2007-01-05 |
BRPI0520409A2 (pt) | 2009-09-29 |
US20070003911A1 (en) | 2007-01-04 |
EP1908024A1 (fr) | 2008-04-09 |
AU2005333996A1 (en) | 2007-01-11 |
FR2888023B1 (fr) | 2008-02-29 |
CA2612966A1 (fr) | 2007-01-11 |
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