Unexpected behavior from Cartopy

I'm trying to draw a 'straight' line on the surface of the Earth (a great circle), which should appear curved on an orthographic projection that isn't looking straight down on the curve. However, when I try to connect two points with a geodetic line in cartopy I get a line with a kink in it. Where is this kink coming from? And how can I get a correctly rendered great circle segment?

import matplotlib.pyplot as plt
import cartopy.crs as ccrs

lats = [0, 36]
lons = [15, 76]
ax = plt.axes(projection = ccrs.Orthographic(central_longitude=0, central_latitude=45))
ax.plot(lons, lats, transform=ccrs.Geodetic())
ax.set_global()
ax.gridlines()

From the option transform=ccrs.Geodetic(), the implication is that you need great-circle arc as a result of your ax.plot() statement.

Without proper setting of projection._threshold you will get the kinked line as you experienced.

Here is the modified code and the expected result.

import matplotlib.pyplot as plt
import cartopy.crs as ccrs

lats = [0, 36]
lons = [15, 76]

myProj = ccrs.Orthographic(central_longitude=0, central_latitude=45)
myProj._threshold = myProj._threshold/20. 

ax = plt.axes(projection = myProj)
ax.plot(lons, lats, transform=ccrs.Geodetic())
ax.set_global()
ax.gridlines()

Smaller values of the threshold will cause the plotted lines to have denser vertices along the lines. Additional vertices are not obtained by simple interpolation when great-circle arcs are required in this case.