在NorthPolarStereo投影中用Cartopy绘制圆

Question

我想在NorthPolarStereo投影中的Cartopy中绘制圆，以lat，lon单位提供中心和半径。

底图here和正投影法here中的Cartopy都提供了类似且出色的问题和答案。但是，我想在Cartopy中使用NorthPolarStereo。尝试使用后一种方法，只需更改投影即可将圆固定在北极，而忽略您为其中心指定的坐标。

关于如何使用NorthPolarStereo投影在Cartopy中绘制圆，并提供其中心和半径为经度的任何想法？

import numpy as np
import cartopy.crs as ccrs
import cartopy.feature as cfeature
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches

# example: draw circle with 45 degree radius around the North pole
lat = 72 
lon = 100
r = 20

# Define the projection used to display the circle:
proj = ccrs.NorthPolarStereo(central_longitude=lon)


def compute_radius(ortho, radius_degrees):
    phi1 = lat + radius_degrees if lat <= 0 else lat - radius_degrees
    _, y1 = ortho.transform_point(lon, phi1, ccrs.PlateCarree())
    return abs(y1)

# Compute the required radius in projection native coordinates:
r_ortho = compute_radius(proj, r)

# We can now compute the correct plot extents to have padding in degrees:
pad_radius = compute_radius(proj, r + 5)

# define image properties
width = 800
height = 800
dpi = 96
resolution = '50m'

# create figure
fig = plt.figure(figsize=(width / dpi, height / dpi), dpi=dpi)
ax = fig.add_subplot(1, 1, 1, projection=proj)

ax.set_xlim([-pad_radius, pad_radius])
ax.set_ylim([-pad_radius, pad_radius])
ax.imshow(np.tile(np.array([[cfeature.COLORS['water'] * 255]], dtype=np.uint8), [2, 2, 1]), origin='upper', transform=ccrs.PlateCarree(), extent=[-180, 180, -180, 180])
ax.add_feature(cfeature.NaturalEarthFeature('physical', 'land', resolution, edgecolor='black', facecolor=cfeature.COLORS['land']))
ax.add_patch(mpatches.Circle(xy=[lon, lat], radius=r_ortho, color='red', alpha=0.3, transform=proj, zorder=30))

plt.show()

圆圈固定在北极，不会移动

Answer 1

圆的中心坐标必须是投影坐标。因此，需要进行坐标转换。

以下是相关代码：

# Note: lat = 72, lon = 100
# proj = ccrs.NorthPolarStereo(central_longitude=lon)

projx1, projy1 = proj.transform_point(lon, lat, ccrs.Geodetic()) #get proj coord of (lon,lat)
ax.add_patch(mpatches.Circle(xy=[projx1, projy1], radius=r_ortho, color='red', \
                            alpha=0.3, transform=proj, zorder=30))

输出图将是：

替代解决方案

由于使用的投影为conformal，因此天梭Indicatrix图在其上将始终是一个圆。这样，您所需的圆就可以用Indicatrix表示。这是您可以尝试的代码：

ax.tissot(rad_km=r_ortho/1000, lons=lon, lats=lat, n_samples=48, color='green', \
      alpha=0.3, zorder=31)

编辑1

用于替换错误功能的代码：

import pyproj

def compute_radius(val_degree):
    """
    Compute surface distance in meters for a given angular value in degrees
    """
    geod84 = pyproj.Geod(ellps='WGS84')
    lat0, lon0 = 0, 90
    _, _, dist_m = geod84.inv(lon0, lat0,  lon0+val_degree, lat0)
    return dist_m

compute_radius(1)  # get: 111319.49079327357 (meters)