This article is published by NetEase Cloud
Author: Liu Yang (This article is only for internal sharing in Zhihu. If you need to reprint, please obtain the author's consent and authorization.)
Everyone is familiar with the map, but it is estimated that many people do not know that there are many doorways in the maps we usually see. Today I will come to them one by one.
Let's first take a look at what our most common world map looks like.
It is easy to think that such a figure cannot be flatly attached to the surface of a sphere. The map that really needs to be posted on the surface of the sphere is like the picture below, and even so, it is only approximately flat.
Since the earth is an approximate sphere, the surface of the earth is an unexpandable surface, so there will inevitably be tears and folds after the surface of the earth is unfolded. The process of mapping the three-dimensional surface of the earth to a two-dimensional plane is the projection of the map. Due to the reduction of the spatial dimension, the distortion and deformation of the map cannot be avoided during the projection process. Therefore, when drawing the world map, the area, direction and distance cannot be fully taken into account.
Take the world map just now as an example: the projection method used in the world map above is called equidifference parallel polyconic projection. The equator of the projection is a coaxial circular arc symmetrical to the equator, and the center of the circle is located on the central meridian. The central meridian is a straight line, and the other meridians are curves symmetrical to the central meridian, and the distance from the central meridian decreases proportionally; The shape of the net has a spherical feel. Our country is placed near the center of the map, keeping the Pacific Ocean intact. Since the nature of the projection is an arbitrary projection close to the same area, the area deformation of most areas in my country is small. The world's climate type and ocean current map, the world political map and the distribution map of natural zones in the world map used in secondary schools are all using this projection map.
The above figure shows the degree of deformation of the equidifference parallel polyconic projection. The 1.0 line in the figure indicates that the area is deformed to 0. If it is greater than 1.0, the area on the map is enlarged compared to the actual area. If it is less than 1.0, the area on the map is smaller than the actual area. . Part of the reason why this projection method is widely used in our country is that most of our country's land area is in a map with a low degree of deformation.
In addition, the problem with using this projection is that even directions that are actually perpendicular to each other appear to be non-perpendicular on the map . For example, the warp and weft in the image below.
In order to truly represent the direction in the map, the famous Mercator Projection must be mentioned . The world map projected by it is shown in the figure below. The meridians and latitudes are perpendicular to each other and the direction is correct. Mercator projection is widely used in map scenarios such as Google Maps, NetEase Youshu (here is hard and wide: NetEase Youshu can draw various types of charts such as filled maps, map scatter plots, etc., and provides visualization data for provinces and cities across the country. Analysis function, quickly click NetEase to have a number - NetEase Big Data|Professional Privatized Big Data Platform Trial)
The Mercator projection is a type of cylindrical projection, invented by the geographer Mercator in the 16th century. Like all other cylindrical projections, in the world map of the Mercator projection, the Earth's latitude lines are parallel to the left and right, with the same length, covering the entire map frame; while the meridian lines are parallel to the top and bottom and perpendicular to the latitude. However, in the real world, this is obviously wrong: if you take a globe and look closely, you can find that although the latitude lines of the earth are parallel, the lengths are different: the equator is the longest, and the shorter the two directions. While the meridians are all the same length, they are not parallel, but meet at the north and south poles.
The drawing method of the Mercator projection is to roll a piece of paper into a cylinder to wrap the earth, the paper surface touches the earth's equator, simulates the earth's spherical center as a light source, and illuminates the outline of the earth's surface onto the cylinder to form a map. At the equator, the projected area and direction are also completely real because the Earth is in contact with the paper surface. However, leaving the equator to the north-south direction, it can be clearly found that the projected pattern area is deformed. Since the light source is at the center of the sphere, the north and south poles will not appear in the projection, and even the polar circles of the two levels will not be projected in the map.
Let R be the equatorial radius and r be the radius of the latitude 60 degrees north. r/R=sin(90-60)=0.5, perimeter=2*pi*radius, so the radius of the equator is 2 times the latitude of 60 degrees north. However, in the Mercator projection of the world map, sixty degrees north latitude is the same length as the equator. Therefore, in order to maintain the shape of the continent, at 60 degrees north latitude, the north-south direction of the map is also stretched by 2 times. Therefore, in the Mercator projection map, the high latitude areas will be greatly enlarged.
How exaggerated this enlargement is, here are a few moving pictures for you to feel it.
The link is here, play it yourself: Compare Countries With This Simple Tool
However, even if the Mercator projection has such a problem, it is still difficult to prevent its wide application. In addition, the maps drawn can have different characteristics by selecting different baselines.
Finally, I want to emphasize a misunderstanding in the Mercator projection or most projections:
the distance between two points on the map is not necessarily the shortest distance in practice.
For example, the airline route from London, UK to Seattle, USA is as follows:
Here are a few more common projection methods for comparison:
- Isometric projection
Tangent azimuthal projection , mainly used for maps of polar regions. Taking the pole as the projection center, it is also called spherical polar projection. The latitude line is a concentric circle with the center of the pole, the longitude line is a straight line radiating from the pole to the surrounding, and the weft distance expands from the center to the outside. The length and area of the central part of the projection are deformed little and gradually increase outward.
- Equal area projection
The Moorweed projection is a pseudocylindrical projection, similar to the cylindrical projection, but optimized mathematically. This projection method maintains the accuracy of the area and also controls the amount of deformation of the shape to a large extent. It selects a meridian as the benchmark, and then draws a circle on the map of the two meridians that form a great circle with the meridian facing east and west at 90 degrees. The effect is as shown in the figure:
- Equidistant projection
Equidistant Cylindrical Projection. It is recognized as the simplest mathematical transformation of all map projections. The Mercator projection stretches the distance between parallels to keep the shape accurate at high latitudes; the distance between all adjacent meridians and parallels is the same for the equidistant conic projection. Therefore, in the north-south direction, the distance between any two points on the map is kept accurate. This kind of map has many disadvantages, neither maintaining the accuracy of the shape nor the accuracy of the area. However, because it is simple to make, it is often used as a projection for index maps (such as lists of countries in the world) or schematic maps (such as maps of time zones, currency distribution, membership distribution of international organizations, etc.).
- The most compromised solution for area, angle and distance
Robinson Projection. It has been discussed before that in the process of converting a 3-dimensional earth into a 2-dimensional map, the accuracy of such aspects cannot be preserved. As a result, cartographers began to look for compromises to minimize distortion in these areas as much as possible. The Robinson projection is one result of these attempts. It works like this:
In the Robinson projection, the shape, area and angle are not precise, but they are compromised with each other. Compared with the Mercator map, the shape of its land outline is acceptably distorted, and the area changes at high latitudes, although still present, are much smaller. After this projection method was invented, it was soon used to draw various world maps.
So, is there a map of equal area, equal distance and equal angle? Of course there is
Learn about NetEase Cloud :
NetEase Cloud official website: https://www.163yun.com/
New user gift package: https://www.163yun.com/gift
NetEase Cloud Community: https://sq.163yun.com/