from numpy import *
import matplotlib.pyplot as plt

# 3D plott av en ellipsoide
x=linspace(-5,3,20)
y=linspace(-5,3,20)
X,Y=meshgrid(x,y)
ax = plt.axes(projection ='3d') 
ax.plot_surface( X, Y, (X+1)**2/1.5**2 + (Y+1)**2/3**2 )
plt.show()

# 2D Contour plott av ellipsoiden
plt.contour(X,Y,(X+1)**2/1.5**2 + (Y+1)**2/3**2)
plt.axis('equal')
plt.show()

# 3D contour plott av ellipsoiden
ax = plt.axes(projection ='3d') 
ax.contour3D(X,Y,(X+1)**2/1.5**2 + (Y+1)**2/3**2)
plt.show()

# 3D plott av en paraboloide
theta = linspace(0,2*pi,50)
r = linspace(0,2,50)
rv,thetav = meshgrid(r,theta)
ax = plt.axes(projection ='3d') 
ax.plot_surface(rv*cos(thetav),rv*sin(thetav), rv**2)
plt.show()

# Halvkule med radius 2
phi = linspace(0,pi/2,50)
theta = linspace(0,2*pi,50)
phiv,thetav = meshgrid(phi,theta)
ax = plt.axes(projection ='3d') 
ax.plot_surface(2*cos(thetav)*sin(phiv),2*sin(thetav)*sin(phiv), 2*cos(phiv))
plt.show()

# 2D vektorfelt plott
x=linspace(-1,1,10)
y=x
X,Y=meshgrid(x,y)
plt.quiver(X,Y,-X/(X**2+Y**2)**(3/2), -Y/(X**2+Y**2)**(3/2))
plt.show()

# 3D vektorfelt plott
x=linspace(-1,1,10)
y=x; z= x;
X,Y,Z=meshgrid(x,y,z)
ax = plt.axes(projection ='3d') 
ax.quiver(X,Y,Z,-X/(X**2+Y**2+Z**2)**(3/2), -Y/(X**2+Y**2+Z**2)**(3/2), -Z/(X**2+Y**2+Z**2)**(3/2))
plt.show()

# 2D str?mlinjeplott
x=linspace(-1,1,10)
y=x
X,Y=meshgrid(x,y)
plt.streamplot(X,Y,-X/(X**2+Y**2)**(3/2), -Y/(X**2+Y**2)**(3/2))
plt.show()

# 3D plott av en torus
theta=linspace(0,2*pi,100)
phi=linspace(0,2*pi,100)
thetav,phiv=meshgrid(theta,phi)
ax = plt.axes(projection ='3d') 
ax.plot_surface( (3+cos(phiv))*cos(thetav), (3+cos(phiv))*sin(thetav), sin(phiv))
plt.show()