What is the projection of this land in North America?
English name: Map projection definition 1: A method of projecting points and lines on a reference ellipsoid onto a developable surface according to certain mathematical rules. Applied discipline: surveying and mapping (first-class discipline); Definition 2 of surveying and mapping (two disciplines): the method of transforming the latitude and longitude network on the earth's surface into the latitude and longitude network on the plane according to certain mathematical laws. Applied discipline: atmospheric science (first-class discipline); Definition 3 of dynamic meteorology (two disciplines): the method of projecting the longitude and latitude network of the earth ellipsoid onto the plane by using certain mathematical rules. That is, the method of transforming the earth coordinates of each point on the ellipsoid into the rectangular coordinates of the corresponding point on the plane. Applied discipline: geography (first-class discipline); Cartography (two disciplines) The above contents were examined and published by the National Committee for the Examination and Approval of Scientific and Technical Terminology.
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Map projection is a theory and method to transform the latitude and longitude of the earth's surface into a plane by using certain mathematical methods. Because the earth is an irregular pear-shaped sphere with a slightly wider equator and flat poles, and its surface is a curved surface that cannot be flattened, any mathematical method will produce errors and deformation. In order to reduce the error according to different needs, various projection methods have been produced.
catalogue
definition
principle
cause
phylogeny
classify
Shared species
Basic method geometric perspective method
Mathematical analysis method
Projection deformation
Map Projection Commonly Used in China Full Map
Application definition
principle
cause
phylogeny
classify
Shared species
Basic method geometric perspective method
Mathematical analysis method
Projection deformation
The definition of this paragraph is extended and edited by the map projection application commonly used in all China maps.
Map projection. The theory and method of transforming any point on the surface of the earth into a map plane by using certain mathematical rules. map projection
Written concept definition: map projection refers to the method of establishing a one-to-one correspondence between points on the earth's surface (or other planetary surfaces or celestial spheres) and points on the projection plane (that is, the map plane). That is, the mathematical conversion formula between the establishment. It will be used as a basic method to project an inflexible surface, that is, the earth's surface, onto a plane to ensure the connectivity and integrity of spatial information in the region. This projection process will produce projection deformation, and different projection methods have different projection deformation properties and sizes. Because the position of any point on the sphere is represented by geographical coordinates (λ, φ), and the position of the point on the plane is represented by rectangular coordinates (χ, у) or polar coordinates (r,), in order to transfer the point on the earth's surface to the plane, certain methods must be adopted to determine the relationship between geographical coordinates and plane rectangular coordinates or polar coordinates. This mathematical method of establishing the functional relationship between points on a sphere and a plane is the map projection method. The deformation of map projection is the inevitable result of the transformation of a sphere into a plane. Without deformation, there is no projection. For a map projection, if there is no such deformation, there must be one or two deformations. But it can be done in drawing: there is no angle and area deformation on some projection drawings; On some projections, there is no length distortion in a certain direction. The ellipsoid of the earth is a surface, and the map is usually a two-dimensional plane, so we should first consider transforming the surface into a plane when drawing. However, in a geometric sense, a sphere is an inflexible surface. If you want to spread it out into a plane, it is bound to crack and fold. This discontinuous and fractured plane is not suitable for making maps, and special methods must be adopted to realize the transformation from spherical surface to plane. The position of any point on the sphere depends on its latitude and longitude, so in the actual projection, first draw some intersections of latitude and longitude lines on the plane, connect the points with the same longitude to become longitude lines, and connect the points with the same latitude to become latitude lines to form a latitude and longitude network. Then the points on the sphere are plotted on the corresponding positions on the plane according to their latitudes and longitudes. It can be seen that map projection is to study the method and deformation of transferring the latitude and longitude network on the ellipsoid of the earth to the plane according to certain mathematical laws. Its mathematical formula is: the earth
χ=f 1(λ, φ)y=f2(λ, φ)(2- 1) According to the general formula of map projection, as long as the latitude and longitude (λ, φ) of ground points are known, the corresponding plane position (χ, Ф) can be found on the projection plane, thus meeting certain surveying and mapping needs. The latitude and longitude net is the "foundation" of making maps and the main mathematical element of maps.
Principles for editing this paragraph
Due to the deformation of projection, the geometric features (length, area, angle, shape) of land, island, ocean and other features on the map have also been deformed. Each map has different degrees of deformation; On the same picture, the deformation of different areas is also different. The larger the range represented on the map and the longer the distance from the projection standard latitude and longitude line or the projection center, the greater the deformation reflected by the map. Therefore, large-scale and small-scale maps can only be used to understand the distribution of surface phenomena, but not to accurately measure and calculate. map projection
The essence of map projection is to transform the geographical coordinates on the ellipsoid of the earth into plane rectangular coordinates. Using certain projection conditions, the geographical coordinate points on the projection sphere are projected into the plane coordinate system one by one, forming a certain map projection.
The reason for editing this paragraph
Because the earth is an irregular pear-shaped sphere with a slightly wider equator and flat poles, and its surface is a curved surface that cannot be flattened, any mathematical method will produce errors and deformation. In order to reduce the error according to different needs, various projection methods have been produced. According to the deformation properties, map projection can be divided into three categories: equidistant projection, equal area projection and arbitrary projection. Geometric perspective
Due to the deformation of projection, the geometric features (length, area, angle, shape) of land, island, ocean and other features on the map have also been deformed. Each map has different degrees of deformation; On the same picture, the deformation of different areas is also different. The larger the range represented on the map and the longer the distance from the projection standard latitude and longitude line or the projection center, the greater the deformation reflected by the map. Therefore, large-scale and small-scale maps can only be used to understand the distribution of surface phenomena, but not to accurately measure and calculate. The essence of map projection is to transform the geographical coordinates on the ellipsoid of the earth into plane rectangular coordinates. Using certain projection conditions, the geographical coordinate points on the projection sphere are projected into the plane coordinate system one by one, forming a certain map projection.
Edit the development history of this paragraph.
Eratosthenes, an ancient Greek geographer in the 3rd century BC, used projection method to draw maps for the first time. Before that, the map projection was used to compile the celestial map (but the projection of the celestial map was from the celestial sphere to the plane, not the earth; But the principle of the two is the same). When compiling the map of the known world with the Mediterranean as the center, erato painted clay applied isometric cylindrical projection with vertical latitude and longitude. 1569, the Belgian cartographer Mercator used isometric cylindrical projection for the first time to compile charts, which enabled navigators to sail in a great circle straight line without changing the direction of the compass. The projection designed by Cassini and his son for triangulation, the isometric projection theory put forward by Lambert and the designed isometric cone, isometric azimuth and isometric cylinder projection make the map projection of17-18th century have the characteristics of the times. 19th century, map projection mainly ensures the mathematical basis of large-scale maps to meet the needs of the development of military cartography and the expansion of topographic survey. /kloc-Gaussian projection also appeared in the 0/9th century, which is an elliptic cylinder projection with equal angle on the horizontal axis proposed by German Gaussian design. This projection method is supplemented by German Kr and becomes Gaussian -Kr projection. After the end of19th century, some Russian scholars have made in-depth research on projection, put forward new opinions on the determination of conic projection constant, and put forward new methods for calculating new projection according to known deformation distribution and calculating projection coordinates by numerical method. Since 1950s, China has put forward some new methods, such as double azimuth projection method and double standard longitude equiangular cylinder projection method. Since 1960s, American scholars have put forward spatial projection, variable scale map projection and multi-intersection map projection on the basis of the research results of map projection, which provide the needed projection for artificial earth satellites.
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Projection deformation
1. Isometric projection (1), also known as conformal projection, means that the angle between any two directions on the projection plane is equal to the corresponding angle on the ground. In a small range, the graphics on the map can remain similar to the field; Can't make its corresponding area keep a constant proportion; The local scale of any point on the map in all directions should be equal; The local scale of different places changes with the change of latitude and longitude. (2) Equal (surface) product projection is a projection method that any graphic area on the map is enlarged by main scale and keeps the same size as the corresponding graphic area on the ground. Equal-product projection, on the other hand, cannot keep equal angles at the same time by keeping equal products. (3) Arbitrary projection. Arbitrary projection is a projection with neither equal angle nor unequal product, and there is also an "isometric projection", which has no length deformation on the standard latitude and longitude lines and is mostly used for teaching drawing in primary and secondary schools. 2. A > is classified according to the shape of longitude and latitude lines projected on the positive axis; Geometric projection (using the perspective relationship, the latitude and longitude network of the earth's surface is projected onto a plane or a geometric surface such as a cylindrical surface or a conical surface that can stand on a plane. ) There are the following three types: (1) plane projection, also known as azimuth projection, which projects the latitude and longitude lines of the earth's surface onto the tangent or tangent plane of the sphere; Plane projection is mostly perspective projection, that is, taking a certain point as the viewpoint, the image on the spherical surface is directly projected onto the projection plane. (2) Cone projection, in which a cone surface is tangent or tangent to the latitude circle of the ground, and the axis of the cone coincides with the axis of the ground, and then the longitude and latitude lines on the ground are projected onto the cone surface from the viewpoint of the spherical center, and then cut into a plane along the cone mother line. Nature: On the map, the latitude is concentric arc, and the longitude is a straight line intersecting with the ends of the earth. (3) Cylindrical projection: a cylinder is sleeved on the earth, and the axis of the cylinder passes through the center of the sphere, so that the longitude and latitude lines on the ground are evenly projected onto the cylinder, and then flattened along the bus line of the cylinder to form a cylindrical projection network. (4) Multi-cone projection: In the projection, the weft is a coaxial arc, and the meridian is a curve with a symmetrical center diameter line. Projection classification of b> conditional projection (non-geometric projection)
(1) Pseudo-azimuth projection, in the case of positive axis, the latitude of pseudo-azimuth projection is still projected as concentric circles, except that the central meridian is projected as a straight line, other meridians are projected as curves symmetrical to the central meridian and intersect with the concentric circles of the latitude. (2) Pseudo-cylindrical projection, on the basis of cylindrical projection, it is stipulated that the latitude is still a concentric arc, and all other meridians are projected as curves symmetrical to the central meridian except that the central meridian is still a straight line. (3) Pseudo-conic projection, in which the latitude is a concentric arc and the longitude is a curve intersecting the center of the circle. 3. According to the relative position between the projection plane and the earth's surface (the relationship between the projection axis and the earth's axis) (1) Orthographic projection (coincidence): the center line of the projection plane is consistent with the earth's axis (2) Oblique axis projection (oblique): the center line of the projection plane is inclined with the earth's axis (3) Horizontal axis projection (vertical): the center line of the projection plane is perpendicular to the earth's axis (4) Geometric projection.
Edit common categories in this section.
At present, the commonly used projection methods include Mercator projection (isometric cylindrical projection of positive axis), Gauss -Kr projection, oblique isometric projection, double standard parallel isometric cone projection, equidifferential parallel multi-cone projection, positive axis azimuth projection and so on.
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Geometric perspective
Geometric perspective method is a projection method (with the help of geometric surface) that uses perspective relationship to project points on the projection surface. For example, suppose that the earth is scaled down to a transparent quasi-sphere, and a light source is placed at its center or on the spherical surface and outside the sphere, and the longitude and latitude lines on the spherical surface are projected onto the projection plane outside the sphere, that is, the longitude and latitude lines on the spherical surface are converted into longitude and latitude lines on the plane. Geometric perspective method is a primitive projection method, which has great limitations, difficult to correct projection deformation and low accuracy. Most map projections use mathematical analysis methods.
Mathematical analysis method
Mathematical analytic method is a projection method to establish the functional relationship between points on the spherical surface and the projection surface, and determine the intersection position of longitude and latitude lines by mathematical method. Most mathematical analysis methods are often based on perspective projection, which expands and establishes the functional relationship between points on the sphere and the projection plane, so the two projection methods are related to some extent. The establishment of map projection is based on the assumption that a projection plane (plane, developable cone or cylinder) is tangent, tangent or polyhedron to the original projection plane (earth ellipsoid), as shown in figure 1. Using certain projection conditions, the geographical coordinate points on the original plane are projected into the plane coordinate system one by one, which constitutes a certain map projection. Its essence is to transform the geographical coordinates (φ, λ) on the ellipsoid of the earth into plane rectangular coordinates (X, Y). The mathematical relationship between them is: x=f 1(φ, λ); Y=f2(φ, λ) where f 1 and f2 are functions.
Edit this projection deformation.
map projection
The map is a plane, and the ellipsoid of the earth is an unexpanded surface. When the latitude and longitude net on the undevelopable surface is depicted as a plane figure, various deformations will inevitably occur. This makes the scale of different points on the map not keep a constant value, but have main scale and local scale. Usually, the scale indicated on the map is main scale, which is the reduced scale of the earth, and the actual scale of different points is called local scale. The deformation of map projection includes angle deformation, area deformation and length deformation. However, not all projections have these three deformations. Isometric projection has no angular shape, and isometric projection has no area deformation. All other projections have these three deformations at the same time. Only by knowing the size and distribution law of a projection deformation can its practical application value be clear. The deformed ellipse can vividly illustrate the deformation of map projection. The deformed ellipse is a differential diagram with the radius of a point as the unit value on the ellipsoid of the earth, and the projection on the plane is generally a differential ellipse. It can be used to explain the characteristics and size of projection deformation.
Edit the commonly used map projection of this full map of China.
Projection parameters of tangent cone equal area projection (equal area cone projection): starting latitude: 0 or 10n central meridian: 105 E or10e standard latitude 1: 25 n standard latitude: 2: 45 n or 47. 2. China has a vast territory and a large latitude span (the latitude difference is 50), so it is necessary to control the deformation by cutting projection (double latitude). 3. In order to emphasize the area contrast between provinces and regions and between China and neighboring countries, equal area projection is adopted.
Edit this application.
The location, shape and scope of the surveying and mapping area, the scale, content and publishing method of the map affect the type of projection. For example, in polar regions, it should be a positive axis azimuth projection, and in mid-latitude regions, it should be a positive axis cone projection. Gauss-Kruger projection is usually used to make topographic maps, azimuth projection, conic projection and pseudo-conic projection are usually used to make regional maps, and multi-conic projection, cylindrical projection and pseudo-cylindrical projection are usually used to make world maps. But in general, we should choose according to the actual situation.