為什么六邊形網格在極坐標立體投影中失真

Question

我試圖了解為什么在北極或南極立體投影中的六邊形圖顯示的是六角形，即使網格的面積為正方形且投影的面積大致相等。

我已經使用底圖嘗試了南北極立體投影。

import numpy as np
from numpy.random import uniform
import matplotlib.pyplot as plt 
from mpl_toolkits.basemap import Basemap

fig = plt.figure(figsize=(12,10)) # width, height in inches
ax =fig.add_axes([-0.02,0.1,0.74,0.74]) 

m = Basemap(epsg='3413',lon_0=0.,resolution='l',width=6000000,height=6000000)

m.drawcoastlines()

m.drawmapscale(0.,90.,0.,90.,1000)

npts=2000
lats = uniform(60.,80.,size=npts)
lons = uniform(0.,360.,size=npts)
data = uniform(0.,4800.,size=npts)

x,y=m(lons, lats)

thiscmap=plt.cm.get_cmap('viridis')

p=m.hexbin(x,y,C=data,gridsize=[10,10],cmap=thiscmap)

plt.show()

Answer 1

我不知道為什么你會squashed hexagons 。 但是您可以通過設置適當的gridsize值來調整六邊形形狀。 在這里，我修改您的代碼並獲得更好的繪圖。

import numpy as np
from numpy.random import uniform
import matplotlib.pyplot as plt 
from mpl_toolkits.basemap import Basemap

fig = plt.figure(figsize=(12,10)) # width, height in inches
ax =fig.add_axes([-0.02, 0.1, 0.74, 0.74]) 

# North polar stereographic projection epsg='3413'; ***large areal distortion***
#m = Basemap(epsg='3413', lon_0=0., resolution='c', width=6000000, height=6000000)

# 'laea':  Lambert Azimuthal Equal Area
# Thematic mapping with ground surface data should be plotted on 'equal-area' projection
m = Basemap(projection='laea', lon_0=0., lat_0=90, resolution='l', width=6000000, height=6000000)

m.drawcoastlines(linewidth=0.5)

m.drawmapscale(0.,90.,0.,90.,1000)  # 1000 km?

npts = 2000
lats = uniform(60.,80.,size=npts)  # not cover N pole
lons = uniform(0.,360.,size=npts)  # around W to E
data = uniform(0.,4800.,size=npts)

x,y = m(lons, lats)

thiscmap = plt.cm.get_cmap('viridis')

# To get 'rounded' hexagons, gridsize should be specified appropriately
# need some trial and error to get them right
#p=m.hexbin(x, y, C=data, gridsize=[10,10], cmap=thiscmap)  # original code
m.hexbin(x, y, C=data, gridsize=[16,11], cmap=thiscmap)     # better

plt.colorbar()  # useful on thematic map

plt.show()

您使用的投影（epsg：3413）是具有較大面失真的立體投影。 在這種情況下，更適合主題映射的投影是Lambert Azimuthal Equal Area 。

結果圖：