# plot_who5.py3 parabaloid rotated
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from math import sin, cos, pi
import matplotlib.cm as cm

print("plot_who5.py3 running")
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

#creating grid
y = np.linspace(-1,1,200)
x = np.linspace(-1,1,200)
x,y = np.meshgrid(x,y)

#set z values
z0 = x**2+y**2
print("before rotated")
print("x[0][0]=",x[0][0])
print("y[0][0]=",y[0][0])
print("z0[0][0]=",z0[0][0])

# rotate the samples by pi / 4 radians around y
a = pi / 4
t = np.transpose(np.array([x,y,z0]), (1,2,0))
m = [[cos(a), 0, sin(a)],[0,1,0],[-sin(a), 0, cos(a)]]
x,y,z = np.transpose(np.dot(t, m), (2,0,1))
# or `np.dot(t, m)` instead `t @ m`
print("rotated")
print("x[0][0]=",x[0][0])
print("y[0][0]=",y[0][0])
print("z[0][0]=",z[0][0])

#label axes
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_title('plot_who5.py3 rotated')
#plot figure
ax.plot_surface(x,y,z,linewidth=0, antialiased=False, shade = True, alpha = 0.5, facecolors=cm.viridis(z0))
plt.show()
print("plot_who5.py3 finished")