Can someone explain the different parameters in matplotlib.patches.arc? - python-3.x

Question

I just want to understand the basic parameters and what they do specifically - width, height, angle, theta1, theta 2. I followed the official documentation and I understood what the centre is, but I don't get what the theta 1 or 2 does, or the angle does or what the length of the horizontal or vertical axis means.
I tried experimenting with the parameters using different numbers but failed to hit upon an accurate result.
I'm trying to create the arc of the 3-point area in the basketball court

Answer 1

The Arc type is a subclass of Ellipse, extended to add two values theta1 and theta2. The behaviour of angle is the same for both Ellipse and Arc and determines the angle at which the ellipse is drawn.
from matplotlib import pyplot as plt
from matplotlib.patches import Ellipse
fig = plt.figure(figsize=(2,5))
ax = fig.add_subplot(1,1,1)
ax.set_ylim(0, 50)
ax.set_xlim(0, 20)
ax.axis('off')
a = Ellipse((10, 45), 10, 3, 0, color='red', lw=1)
ax.add_patch(a)
a = Ellipse((10, 40), 10, 3, 10, color='red', lw=1)
ax.add_patch(a)
a = Ellipse((10, 35), 10, 3, 20, color='red', lw=1)
ax.add_patch(a)
a = Ellipse((10, 30), 10, 3, 30, color='red', lw=1)
ax.add_patch(a)
for a in range(0, 360, 40):
a = Ellipse((10, 20), 10, 3, a, color='red', lw=1, fc='none')
ax.add_patch(a)
This produces —
Note that for a perfect circle (an ellipse of equal height and width) this makes no difference (as a circle is rotationally symmetrical).
from matplotlib import pyplot as plt
from matplotlib.patches import Ellipse
fig = plt.figure(figsize=(2,4))
ax = fig.add_subplot(1,1,1)
ax.set_ylim(0, 40)
ax.set_xlim(0, 20)
ax.axis('off')
a = Ellipse((10, 25), 10, 10, 0, color='red', lw=1)
ax.add_patch(a)
a = Ellipse((10, 10), 10, 10, 45, color='red', lw=1)
ax.add_patch(a)
Both circles are the same.
The Arc documentation for the matplotlib.patches.Arc explains that theta 1 & 2 are —
theta1, theta2 : float, optional
Starting and ending angles of the arc in degrees. These values are relative to angle, .e.g. if angle = 45 and theta1 = 90 the absolute starting angle is 135. Default theta1 = 0, theta2 = 360, i.e. a complete ellipse.
The key statement there is "Default theta1 = 0, theta2 = 360, i.e. a complete ellipse." — these parameters are used to draw partial ellipses, to create an arc. theta1 is the angle (or position on) the ellipse at which to start drawing, and theta2 is when to stop. Note that the calculation of the ellipse is unaffected.
The following code draws a series of arcs which should make the logic apparent —
from matplotlib import pyplot as plt
from matplotlib.patches import Arc
fig = plt.figure(figsize=(2,5))
ax = fig.add_subplot(1,1,1)
ax.set_ylim(0, 50)
ax.set_xlim(0, 20)
ax.axis('off')
# A complete ellipse, using theta1=0, theta2=360.
a = Arc((10, 45), 10, 3, 0, 0, 360, color='red', lw=1)
ax.add_patch(a)
# Reduce theta2 to 350, last 10 deg of ellipse not drawn.
a = Arc((10, 40), 10, 3, 0, 0, 350, color='red', lw=1)
ax.add_patch(a)
# Rotate the ellipse (angle=90), theta1 & theta2 are relative to start angle & rotate too.
a = Arc((10, 30), 10, 3, 90, 0, 350, color='red', lw=1)
ax.add_patch(a)
# Rotate the ellipse (angle=180), as above.
a = Arc((10, 20), 10, 3, 180, 0, 350, color='red', lw=1)
ax.add_patch(a)
# Draw the top half of the ellipse (theta 0-180 deg).
a = Arc((10, 10), 10, 3, 0, 0, 180, color='red', lw=1)
ax.add_patch(a)
# Draw the bottom half of the ellipse (theta 180-360 deg).
a = Arc((10, 5), 10, 3, 0, 180, 360, color='red', lw=1)
ax.add_patch(a)
This produces the following image, with arcs drawn above going from top to bottom. Compare with the comments in the code for explanation.