投影造成的面积变形
麦卡托投影法(Mercator projection)不能保持面积. 该方法并不是等面积投影.
In[1]:=
![Click for copyable input](assets.zh/area-distortion-by-a-projection/In_28.png)
GeoProjectionData["Mercator", "EqualArea"]
Out[1]=
![](assets.zh/area-distortion-by-a-projection/O_19.png)
非洲的面积比格陵兰面积的大 14 倍以上.
In[2]:=
![Click for copyable input](assets.zh/area-distortion-by-a-projection/In_29.png)
GeoArea[Entity["GeographicRegion", "Africa"]]/
GeoArea[Entity["Country", "Greenland"]]
Out[2]=
![](assets.zh/area-distortion-by-a-projection/O_20.png)
但在麦卡托地图中,非洲和格陵兰的面积却近乎相同.
In[3]:=
![Click for copyable input](assets.zh/area-distortion-by-a-projection/In_30.png)
GeoGraphics[{GeoStyling[Green],
Polygon[Entity["Country", "Greenland"]], GeoStyling[Red],
Polygon[Entity["GeographicRegion", "Africa"]]},
GeoProjection -> "Mercator", GeoRange -> "World",
GeoBackground -> "Satellite"]
Out[3]=
![](assets.zh/area-distortion-by-a-projection/O_21.png)
使用等面积投影法,比如摩尔魏特(Mollweide),来表示更合适的和相对大小.
In[4]:=
![Click for copyable input](assets.zh/area-distortion-by-a-projection/In_31.png)
GeoProjectionData["Mollweide", "EqualArea"]
Out[4]=
![](assets.zh/area-distortion-by-a-projection/O_22.png)
In[5]:=
![Click for copyable input](assets.zh/area-distortion-by-a-projection/In_32.png)
GeoGraphics[{GeoStyling[Green],
Polygon[Entity["Country", "Greenland"]], GeoStyling[Red],
Polygon[Entity["GeographicRegion", "Africa"]]},
GeoProjection -> "Mollweide", GeoRange -> "World",
GeoBackground -> "Satellite"]
Out[5]=
![](assets.zh/area-distortion-by-a-projection/O_23.png)