如何通过两点（直径端）画圆？

Question

立体投影上有两个点如图：

这些点应该位于圆直径的端点上。通过这两点怎么画圆？

上图代码：

import matplotlib.pylab as plt
from mpl_toolkits.basemap import Basemap
import numpy as np
from scipy.interpolate import splev, splrep

# create instance of basemap, note we want a south polar projection to 90 = E
myMap = Basemap(projection='spstere',boundinglat=0,lon_0=180,resolution='l',round=True,suppress_ticks=True)
# set the grid up
gridX, gridY = 10.0, 15.0
parallelGrid = np.arange(-90.0,90.0,gridX)
meridianGrid = np.arange(-180.0,180.0,gridY)

# draw parallel and meridian grid, not labels are off. We have to manually create these.
myMap.drawparallels(parallelGrid,labels=[False,False,False,False])
myMap.drawmeridians(meridianGrid,labels=[False,False,False,False],labelstyle='+/-',fmt='%i')


# plot azimuth labels, with a North label.
ax = plt.gca()
ax.text(0.5,1.025,'N',transform=ax.transAxes,horizontalalignment='center',verticalalignment='bottom',size=25)
for para in np.arange(gridY,360,gridY):
    x= (1.1*0.5*np.sin(np.deg2rad(para)))+0.5
    y= (1.1*0.5*np.cos(np.deg2rad(para)))+0.5
    ax.text(x,y,u'%i\N{DEGREE SIGN}'%para,transform=ax.transAxes,horizontalalignment='center',verticalalignment='center')

summerAzi = np.array([0, 360])
summerAlt = np.array([40, 4])
summerX, summerY = myMap(summerAzi, -summerAlt)


summerX_new = np.linspace(summerX.min(), summerX.max(),30)
summerY_smooth = splev(summerX_new, splrep(summerX, summerY, k=1))

myMap.plot(summerX_new, summerY_smooth, 'g')

myMap.plot(summerX, summerY, 'go')   
plt.show()

Answer 1

此极坐标表示中的圆看起来不像矩形网格上的圆（即 "round"）。除此之外，您可以像在笛卡尔平面上一样绘制圆，从极坐标开始，转换为笛卡尔坐标，偏移中心并使用绘图功能。

summerAzi = np.array([0, 360])
summerAlt = -np.array([40, 4])
summerX, summerY = myMap(summerAzi, summerAlt)

phi = np.linspace(0,2.*np.pi)
r = np.abs(np.diff(summerAlt))/2.
x = r*np.cos(phi)
y = -r*np.sin(phi)+summerAlt.mean()
X,Y= myMap(x,y)

myMap.plot(X,Y, color="crimson")
myMap.plot(summerX, summerY, color="gold", marker="o")

Answer 2

内置的 tissot() 函数足以在共形投影上绘制圆圈（如本例所示）。在非等角投影上，它绘制椭圆。这里天梭指标的中点是 (0, -22) 度数。它的半径 = (40-4)/2 = 18 度。点数=36即可。

如何通过两点（直径端）画圆？

How to draw a circle through two points (at diameter end)?

python

plot

matplotlib

matplotlib-basemap