How to plot an angle in python using matplotlib ?

An example step by step of how to plot an angle in python using matplotlib and basic mathematics:

Table of contents

Define two lines
Find the intersection point between the two lines:
Plot a circle with the line intersection point as origin:
Find the intersections between the circle and the lines
Calculate the angles for each intersection
Plot an angle
Source Code
References

Define two lines

How to plot an angle in python using matplotlib ?

import matplotlib.pyplot as plt
import numpy as np

m1, b1 = 0.1, 2.0 # slope & intercept (line 1)
m2, b2 = 2.0, -3.0 # slope & intercept (line 2)

x = np.linspace(-10,10,500)

plt.plot(x,x*m1+b1)
plt.plot(x,x*m2+b2)

plt.xlim(-2,8)
plt.ylim(-2,8)

plt.title('How to plot an angle with matplotlib ?', fontsize=8)

#plt.savefig("plot_an_angle_matplotlib_01.png", bbox_inches='tight')

Find the intersection point between the two lines:

x0 = (b2-b1) / (m1-m2)
y0 = m1 * x0 + b1

#plt.scatter(x0,y0, color='black' )

#plt.savefig("plot_an_angle_matplotlib_02.png", bbox_inches='tight')

Plot a circle with the line intersection point as origin:

theta = np.linspace(0, 2*np.pi, 100)

r = np.sqrt(4.0) # circle radius

x1 = r * np.cos(theta) + x0
x2 = r * np.sin(theta) + y0

#plt.plot(x1, x2, color='gray')

#plt.savefig("plot_an_angle_matplotlib_03.png", bbox_inches='tight')

Find the intersections between the circle and the lines

x_list = []
y_list = []

def line_and_circle_intersection_points(m,b,x0,y0,r):

    c1 = 1 + m ** 2
    c2 = - 2.0 * x0 + 2 * m * ( b - y0 )
    c3 = x0 ** 2 + ( b - y0 ) ** 2 - r ** 2

    # solve the quadratic equation:

    delta = c2 ** 2 - 4.0 * c1 * c3

    x1 = ( - c2 + np.sqrt(delta) ) / ( 2.0 * c1 )
    x2 = ( - c2 - np.sqrt(delta) ) / ( 2.0 * c1 )

    x_list.append(x1)
    x_list.append(x2)

    y1 = m * x1 + b
    y2 = m * x2 + b

    y_list.append(y1)
    y_list.append(y2)

    return None

line_and_circle_intersection_points(m1,b1,x0,y0,r)

#plt.scatter( x_list[0], y_list[0], color='black' )
#plt.scatter( x_list[1], y_list[1], color='black' )

#plt.text( x_list[0], y_list[0], 'P1', color='black' )
#plt.text( x_list[1], y_list[1], 'P2', color='black' )

line_and_circle_intersection_points(m2,b2,x0,y0,r)

#plt.scatter( x_list[2], y_list[2], color='black' )
#plt.scatter( x_list[3], y_list[3], color='black' )

#plt.text( x_list[2], y_list[2], 'P3', color='black' )
#plt.text( x_list[3], y_list[3], 'P4', color='black' )

#plt.savefig("plot_an_angle_matplotlib_04.png", bbox_inches='tight')

Calculate the angles for each intersection

def get_point_angle(x,y,x0,y0):

    num = x - x0
    den = np.sqrt( ( x - x0 )**2 + ( y - y0 )**2 )

    theta = np.arccos( num / den )

    if not y - y0 >= 0: theta = 2 * np.pi - theta

    #print(theta, np.rad2deg(theta), y - y0 )

    return theta

theta_list = []

for i in range(len(x_list)):

    x = x_list[i]
    y = y_list[i]

    theta_list.append( get_point_angle(x,y,x0,y0) )

Plot an angle

theta_1 = theta_list[0]
theta_2 = theta_list[3]

theta = np.linspace(theta_1, theta_2, 100)

x1 = r * np.cos(theta) + x0
x2 = r * np.sin(theta) + y0

plt.plot(x1, x2, color='gray')

mid_angle = ( theta_1 + theta_2 ) / 2.0

mid_angle_x = (r+0.45) * np.cos(mid_angle) + x0
mid_angle_y = (r+0.45) * np.sin(mid_angle) + y0

angle_value = round( np.rad2deg(abs(theta_1-theta_2)), 2)

plt.text(mid_angle_x, mid_angle_y, angle_value, fontsize=8)

plt.savefig("plot_an_angle_matplotlib_08.png", bbox_inches='tight')

Source Code

import matplotlib.pyplot as plt
import numpy as np

m1, b1 = 0.1, 2.0 # slope & intercept (line 1)
m2, b2 = 2.0, -3.0 # slope & intercept (line 2)

#----------------------------------------------------------------------------------------#
# Step 1: plot the lines

x = np.linspace(-10,10,500)

plt.plot(x,x*m1+b1)
plt.plot(x,x*m2+b2)

plt.xlim(-2,8)
plt.ylim(-2,8)

plt.title('How to plot an angle with matplotlib ?', fontsize=8)

#plt.savefig("plot_an_angle_matplotlib_01.png", bbox_inches='tight')

#----------------------------------------------------------------------------------------#
# Step 2: calculate the point of intersection between the two lines

x0 = (b2-b1) / (m1-m2)
y0 = m1 * x0 + b1

#plt.scatter(x0,y0, color='black' )

#plt.savefig("plot_an_angle_matplotlib_02.png", bbox_inches='tight')

#----------------------------------------------------------------------------------------#
# Step 3: plot the circle

theta = np.linspace(0, 2*np.pi, 100)

r = np.sqrt(4.0) # circle radius

x1 = r * np.cos(theta) + x0
x2 = r * np.sin(theta) + y0

#plt.plot(x1, x2, color='gray')

#plt.savefig("plot_an_angle_matplotlib_03.png", bbox_inches='tight')

#----------------------------------------------------------------------------------------#
# Step 4: calculate the points of intersection between a line and the circle

x_list = []
y_list = []

def line_and_circle_intersection_points(m,b,x0,y0,r):

    c1 = 1 + m ** 2
    c2 = - 2.0 * x0 + 2 * m * ( b - y0 )
    c3 = x0 ** 2 + ( b - y0 ) ** 2 - r ** 2

    # solve the quadratic equation:

    delta = c2 ** 2 - 4.0 * c1 * c3

    x1 = ( - c2 + np.sqrt(delta) ) / ( 2.0 * c1 )
    x2 = ( - c2 - np.sqrt(delta) ) / ( 2.0 * c1 )

    x_list.append(x1)
    x_list.append(x2)

    y1 = m * x1 + b
    y2 = m * x2 + b

    y_list.append(y1)
    y_list.append(y2)

    return None

line_and_circle_intersection_points(m1,b1,x0,y0,r)

#plt.scatter( x_list[0], y_list[0], color='black' )
#plt.scatter( x_list[1], y_list[1], color='black' )

#plt.text( x_list[0], y_list[0], 'P1', color='black' )
#plt.text( x_list[1], y_list[1], 'P2', color='black' )

line_and_circle_intersection_points(m2,b2,x0,y0,r)

#plt.scatter( x_list[2], y_list[2], color='black' )
#plt.scatter( x_list[3], y_list[3], color='black' )

#plt.text( x_list[2], y_list[2], 'P3', color='black' )
#plt.text( x_list[3], y_list[3], 'P4', color='black' )

#plt.savefig("plot_an_angle_matplotlib_04.png", bbox_inches='tight')

#----------------------------------------------------------------------------------------#
# Step 5: calculate the angle for each intersection points

def get_point_angle(x,y,x0,y0):

    num = x - x0
    den = np.sqrt( ( x - x0 )**2 + ( y - y0 )**2 )

    theta = np.arccos( num / den )

    if not y - y0 >= 0: theta = 2 * np.pi - theta

    #print(theta, np.rad2deg(theta), y - y0 )

    return theta

theta_list = []

for i in range(len(x_list)):

    x = x_list[i]
    y = y_list[i]

    theta_list.append( get_point_angle(x,y,x0,y0) )

#----------------------------------------------------------------------------------------#
# Step 6: plot the angle

theta_1 = theta_list[0]
theta_2 = theta_list[3]

theta = np.linspace(theta_1, theta_2, 100)

x1 = r * np.cos(theta) + x0
x2 = r * np.sin(theta) + y0

plt.plot(x1, x2, color='gray')

#----------------------------------------------------------------------------------------#
# Step 7: add label

mid_angle = ( theta_1 + theta_2 ) / 2.0

mid_angle_x = (r+0.45) * np.cos(mid_angle) + x0
mid_angle_y = (r+0.45) * np.sin(mid_angle) + y0

angle_value = round( np.rad2deg(abs(theta_1-theta_2)), 2)

plt.text(mid_angle_x, mid_angle_y, angle_value, fontsize=8)

plt.savefig("plot_an_angle_matplotlib_08.png", bbox_inches='tight')

References

Links	Site
Best way to plot an angle between two lines in Matplotlib	stackoverflow
Intersection d'une droite et d'un cercle	ilemaths.net
Equation du second degré	mathematiquesfaciles.com
SECOND DEGRE	maths-et-tiques.fr
Finding the Angle Between Two Vectors	wikihow
numpy.arccos	docs.scipy.org

Developer in my spare time, I’m interested in Earth observation and satellite-based fire detection. Passionate about Python, machine learning, and open science.