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Conics with matplotlib.py
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Conics with matplotlib.py
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#!/usr/bin/env python
# coding: utf-8
# In[1]:
# Importing all the required Libraries
#Importing matplotlib
import matplotlib.pyplot as mpl
#Impoting numpy
import numpy as np
#Defining values for x and y
x = np.linspace(-50, 51, 200)
y = np.linspace(-50, 51, 200)
#meshgrid makes an array, this is useful in defining functions
x, y = np.meshgrid(x, y)
#Axes() as a function, this will highlight our origin
def axes():
mpl.grid()
mpl.axhline(0, alpha= .2, linewidth= 2, color='k' )
#Printing Horizontal line, X axis
mpl.axvline(0, alpha= .2, linewidth= 2, color='k' )
#Printing Vertical line, Y axis
#mpl.axis('equal')
#For taking valid inputs as values, defining a f(n)
def options(prompt):
while True:
try:
#Ensuring the input to be integer
number = int(input(prompt))
break
except ValueError :
#Printing Output for correction, Giving user another chance to enter value
print('Please enter a Valid input ')
pass
return number
def delta(a,b,c,f,g,h):
if a*(b)*c +2*f*g*h -a*f^2 -b*g^2 -c*h^2 != 0:
return True
else :
return False
while True :
print('Conic section Graphs')
print('Menu \n 1. Parabola \n 2. Ellipse and circles \n 3. Hyperbolas \n 4.EXIT')
opts = options(' Please enter any one of the options ')
if opts == 1:
while True:
print('PARABOLA')
print("MENU \n 1. Parabola in standard equation \n 2. Parabola in Expanded equation \n 3.Return to Menu")
ch = int(input('Choose an option'))
if ch == 1:
print('1. Parabola in standard equation')
a = float(input('Please enter the value of \'a\' ' ))
parabola = (y**2 - 4*a*x)
print(' Parabolas in standard eqn are of the form \n y^2 = 4ax ')
print('Do you Want to see directrix and focus as well ? ')
duff = input (' y for YES and n for NO ')
if duff == 'y':
axes()
# Printing Focus as a DOT.
mpl.plot(a, 0, '.')
# Printing Directrix, using a vertical line axvline.
mpl.axvline(-a)
mpl.contour(x, y, parabola, [0], colors='r' )
mpl.show()
else :
axes()
mpl.contour(x, y, parabola, [0], colors='k')
mpl.show()
elif ch == 2:
while True:
print('2. Parabola in Expanded equation')
print('Parabolas in non-standard eqn are of the form :')
print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \n where H^2−4AB=0')
a = options(' Please enter the Value of A ')
b = options(' Please enter the Value of B ')
c = options(' Please enter the Value of C ')
f = options(' Please enter the Value of 2F ')
g = options(' Please enter the Value of 2G ')
h = options(' Please enter the Value of 2H ')
if delta(a,b,c,f,g,h) and (h)**2 - 4*a*b == 0 :
print('Your Equation is : ')
print('\t',a,'^2x + ',h,'xy + ',b,'y^2 + ',g,'x + ',f,'y + ',c,' = 0 ' )
axes()
mpl.contour(x, y,(a*x**2 + h*x*y + b*y**2 + g*x + f*y + c), [0], colors='k')
mpl.show()
else:
print('Condition : h**2 - 4*a*b = 0 \t NOT SATISFIED \n Try again :( ')
continue
elif ch == 3 :
break
else:
continue
elif opts == 2:
while True:
print('ELLIPSE AND CIRCLES')
print("MENU \n 1. Circle \n 2. Ellipse in Standard equation \n 3. Ellipse in Expanded equation \n 4.Return to Menu")
ch = int(input('Choose an option'))
if ch ==1 :
print('1. Circle')
r= int(input('Please enter radius of circle '))
h = int(input('Please enter x coordinate of centre '))
k = int(input('Please enter y coordinate of centre '))
print('Radius of circle ',r, 'with centre ','(',h,',',k,')')
t = np.linspace(0,2*np.pi, 1000)
x = r*np.cos(t) + h
y = r*np.sin(t) + k
mpl.axis('equal')
mpl.grid()
mpl.plot(x,y)
mpl.show()
if ch==2:
print('2. Ellipse in Standard equation')
print('x^2/A^2 + y^2/B^2 = 1')
a = options(' Please enter the Value of A ')
b = options(' Please enter the Value of B ')
print('Do you Want to see directrix and focus as well ? ')
duff = input (' y for YES and n for NO ')
while True:
if duff == 'y':
axes()
h = int(input('Please enter x coordinate of centre '))
k = int(input('Please enter y coordinate of centre '))
t = np.linspace(0,2*np.pi, 1000)
p = h + a*np.cos(t)
q = k + b*np.sin(t)
mpl.axis('equal')
mpl.plot(p,q)
# Defining Eccentricity.
e = np.sqrt(1 - b**2/a**2)
# Printing Foci as DOTs.
mpl.plot(a*e, 0, '.', -a*e, 0, '.')
# Printing Directrix, using a vertical lines axvline
mpl.axvline(a/e)
mpl.axvline(-a/e)
mpl.show()
break
elif duff == 'n' :
axes()
h = int(input('Please enter x coordinate of centre '))
k = int(input('Please enter y coordinate of centre '))
t = np.linspace(0,2*np.pi, 1000)
p = h + a*np.cos(t)
q = k + b*np.sin(t)
mpl.axis('equal')
mpl.grid()
mpl.plot(p,q)
mpl.show()
break
else :
continue
if ch ==3:
while True:
print('3. Ellipse in Expanded equation')
print('For ellipses, the eccentricity,e is 0<e<1 \n It is defined as e**2 = 1 - B**2/A**2 ')
print('To define a ellipse in a non-standard position is has to follow the form :')
print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \n where H^2−4AB<0')
a = options(' Please enter the Value of A ')
b = options(' Please enter the Value of B ')
c = options(' Please enter the Value of C ')
f = options(' Please enter the Value of 2F ')
g = options(' Please enter the Value of 2G ')
h = options(' Please enter the Value of 2H ')
if delta(a,b,c,f,g,h) and (h)**2 - 4*a*b < 0:
print('Your Equation is : ')
print('\t',a,'^2x + ',h,'xy + ',b,'y^2 + ',g,'x + ',f,'y + ',c,' = 0 ' )
axes()
mpl.contour(x, y,(a*x**2 + h*x*y + b*y**2 + g*x + f*y + c), [0], colors='k')
mpl.axis('equal')
mpl.show()
break
else :
print('Condition : 2h**2 - 4*a*b < 0 \t NOT SATISFIED \n Try again :( ')
continue
elif ch==4:
break
else:
continue
elif opts == 3:
q = np.linspace(-100, 101, 200)
w = np.linspace(-100, 101, 200)
q, w = np.meshgrid(q, w)
while True:
print('HYPERBOLA')
print('*** PRO TIP : Users are requested to use values less than 50, for best results :) ***')
print("MENU \n 1. Hyperbola in standard equation \n 2. Hyperbola in Expanded equation \n 3.Return to Menu")
ch = int(input('Choose an option'))
if ch == 1:
print('1. Hyperbolas in standard equation are of the form')
print('x^2/A^2 - y^2/B^2 = 1 ')
a = options(' Please enter the Value of A ')
b = options(' Please enter the Value of B ')
hyperbola = (q**2/a**2 - w**2/b**2)
print('Do you Want to see directrix and focus as well ? ')
duff = input (' y for YES and n for NO ')
while True:
if duff == 'y':
axes()
mpl.contour(q, w,hyperbola, [1], colors='k')
# Defining Eccentricity.
e = np.sqrt(1 + b**2/a**2)
# Printing Foci as DOTs.
mpl.plot(a*e, 0, '.', -a*e, 0, '.')
# Printing Directrix, using a vertical line axvline
mpl.axvline(a/e)
mpl.axvline(-a/e)
mpl.show()
break
elif duff =='n' :
axes()
mpl.contour(q, w,hyperbola, [1], colors='k')
mpl.show()
break
else:
continue
elif ch == 2:
while True:
print('2. Hperbola in Expanded equation')
print('Hyperbolas in non-standard eqn are of the form ::')
print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \n where H^2−4AB=0')
a = options(' Please enter the Value of A ')
b = options(' Please enter the Value of B ')
c = options(' Please enter the Value of C ')
f = options(' Please enter the Value of 2F ')
g = options(' Please enter the Value of 2G ')
h = options(' Please enter the Value of 2H ')
hyperx = (a*x**2 + h*x*y + b*y**2 + g*x + f*y + c)
if delta(a,b,c,f,g,h) and h**2 - 4*a*b > 0 :
print('Your Equation is : ')
print('\t',a,'^2x + ',h,'xy + ',b,'y^2 + ',g,'x + ',f,'y + ',c,' = 0 ' )
axes()
mpl.contour(x, y,hyperx, [0], colors='k')
mpl.show()
break
else:
print('Condition : h**2 - 4*a*b > 0 \t NOT SATISFIED \n Try again :( ')
continue
elif ch == 3 :
break
else:
continue
if opts == 4:
break
print('EOP')
# In[ ]: