How to draw general shapes

4.1 Introduction

This how-to will demonstrate how to draw curves and polygons of any shape in Python.
As an example, consider a half-circle. The points on a circle of radius can be parametrized in terms of an angle, :
where fulfills . In order to plot a half-circle, it suffices to draw a large number of small linear segments between points on the half-circle. To do so, we need to generate a range of angles, which is conveniently done with the linspace function in NumPy. linspace takes three arguments, a starting value, an ending value, and the number of evenly distributed values from the starting to the ending value. Here we ask for 10 values from 0 to : 
theta = np.linspace(0,np.pi,10)
theta

array([0.        , 0.34906585, 0.6981317 , 1.04719755, 1.3962634 ,
       1.74532925, 2.0943951 , 2.44346095, 2.7925268 , 3.14159265])
A half-circle with may now be plotted with this piece of code: 
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

plt.rc('font', size=18)
fig, ax = plt.subplots()

theta = np.linspace(0,np.pi,10)
r = 2
x = r * np.cos(theta)
y = r * np.sin(theta)
ax.plot(x,y,linewidth=3,color='c')

ax.grid()
ax.set_aspect('equal')
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
but it looks a bit raggy:

Figure 1

Introducing more values for remedies this, as seen here for the half-circle with radius : 
theta = np.linspace(0,np.pi,100)

r = 1
x = r * np.cos(theta)
y = r * np.sin(theta)
ax.plot(x,y,linewidth=3,color='k')

ax.legend(['$r=1$','$r=2$'])
fig

Figure 2

4.2 Reversing a NumPy array

With two half-circles drawn, a neat application would be to color the region between them. This can be done with Matplotlibs fill function, where we provide the -points as one runs around the perimeter of the desired polygon. One problem with this is that if we provide points on the outer half-circle in anti-clockwise order, then we have to provide the points on the inner half-circle in clockwise order. Thus the -values must be supplied in opposite order. That can be done in several ways. A cryptic one: 
theta[::-1]

array([3.14159265, 2.7925268 , 2.44346095, 2.0943951 , 1.74532925,
       1.3962634 , 1.04719755, 0.6981317 , 0.34906585, 0.        ])
and a more intuitive one, where the first two arguments of linspace are interchanged: 
theta = np.linspace(np.pi,0,10)
theta

array([3.14159265, 2.7925268 , 2.44346095, 2.0943951 , 1.74532925,
       1.3962634 , 1.04719755, 0.6981317 , 0.34906585, 0.        ])
As you become more and more fluent in Python, you will probably prefer the former way (since it does not involve recalculating the values in the list), but while you are learning Python, the latter way is certainly fine.

4.3 Glue together NumPy arrays

Another thing we need to be able to do is to "glue" together the of - and -coordinates from the two half-circles. Consider two simple NumPy arrays: 
a1 = np.linspace(0,2,3)
a2 = np.linspace(10,12,3)

a1,a2

(array([0., 1., 2.]), array([10., 11., 12.]))
If you try to glue together the NumPy arrays with the +-operator you get the elementwise sum: 
a3 = a1 + a2
a3

array([10., 12., 14.])
which is very useful in many contexts. But to get a NumPy array of all elements within the two original NumPy arrays, you have to resort to the NumPy concatenate function: 
a4 = np.concatenate((a1,a2))
a4
(don't miss the double set of parentheses), which gives: 
array([ 0.,  1.,  2., 10., 11., 12.])

4.4 Coloring between half-circles

We now have all Python skills required to form a polygon that fills the space between two half-circles: 
fig, ax = plt.subplots()

r = 2
theta = np.linspace(0,np.pi,100)
x1 = r * np.cos(theta)
y1 = r * np.sin(theta)

r = 1
theta = np.linspace(np.pi,0,100)
x2 = r * np.cos(theta)
y2 = r * np.sin(theta)

x = np.concatenate((x1,x2))
y = np.concatenate((y1,y2))

ax.fill(x,y,linewidth=3,facecolor='pink',edgecolor='k')

ax.grid()
ax.set_aspect('equal')
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')

Figure 3