Ploting solid of revolution in Python 3 (matplotlib maybe)

Question

Greetings the problem:

R is a region in the xy plane bounded by the parabola y=x^2+1 and line y=x+3. A solid of revolution is formed by rotating R around the x axi

Answer 1

Piggybacking on above, you can make these dynamic with widgets or gifs.

Make a gif: Use the gif package:

import gif

@gif.frame
def plot_volume(angle):
    fig = plt.figure(figsize = (20, 15))

    ax2 = fig.add_subplot(1, 1, 1, projection = '3d')
    angles = np.linspace(0, 360, 20)
    x = np.linspace(-1, 2, 60)
    v = np.linspace(0, 2*angle, 60)

    U, V = np.meshgrid(x, v)
    Y1 = (U**2 + 1)*np.cos(V)
    Z1 = (U**2 + 1)*np.sin(V)
    Y2 = (U + 3)*np.cos(V)
    Z2 = (U + 3)*np.sin(V)
    X = U
    ax2.plot_surface(X, Y1, Z1, alpha = 0.2, color = 'blue', rstride = 6, cstride = 6)
    ax2.plot_surface(X, Y2, Z2, alpha = 0.2, color = 'red', rstride = 6, cstride = 6)
    ax2.set_xlim(-3,3)
    ax2.set_ylim(-5,5)
    ax2.set_zlim(-5,5)
    ax2.view_init(elev = 50, azim = 30*angle)
    ax2.plot_wireframe(X, Y2, Z2)
    ax2.plot_wireframe(X, Y1, Z1, color = 'black')
    ax2._axis3don = False

frames = []
for i in np.linspace(0, 2*np.pi, 20):
    frame = plot_volume(i)
    frames.append(frame)

gif.save(frames, 'images/vol1.gif', duration = 500)

from IPython.display import Image

Image('images/vol1.gif')

Make Interactive: Use ipywidgets.

def three_d_plotter(angle, rotate, turn):
    fig = plt.figure(figsize = (13, 6))
    ax = fig.add_subplot(1, 1, 1, projection='3d')

    u = np.linspace(-1, 2, 60)
    v = np.linspace(0, angle, 60)
    U, V = np.meshgrid(u, v)

    X = U
    Y1 = (U**2 + 1)*np.cos(V)
    Z1 = (U**2 + 1)*np.sin(V)

    Y2 = (U + 3)*np.cos(V)
    Z2 = (U + 3)*np.sin(V)

    ax.plot_surface(X, Y1, Z1, alpha=0.3, color='red', rstride=6, cstride=12)
    ax.plot_surface(X, Y2, Z2, alpha=0.3, color='blue', rstride=6, cstride=12)
    ax.plot_wireframe(X, Y2, Z2, alpha=0.3, color='blue', rstride=6, cstride=12)
    ax._axis3don = False
    ax.view_init(elev = rotate, azim = turn)

    plt.show()

from ipywidgets import interact
import ipywidgets as widgets

interact(three_d_plotter, angle = widgets.FloatSlider(0, min = 0, max = 2*np.pi, step = np.pi/10),
        rotate = widgets.FloatSlider(0, min = 0, max = 360, step = 5),
         turn = widgets.FloatSlider(0, min = 0, max = 500, step = 5))