15-9 Triple Integrals in Spherical Coordintes.sagews

var('p t')
spherical_plot3d(2, (t, 0, pi), (p, 0, 3*pi/4))    # The Sage default has rho(theta, phi):

# We can also use a "transformation"
var('rho theta phi')
spherical = (rho*sin(phi)*cos(theta), rho*sin(phi)*sin(theta), rho*cos(phi))
plot3d(2, (theta, 0, pi), (phi, 0, 3*pi/4), transformation = spherical)

(rho, theta, phi)

3D rendering not yet implemented

# rho = theta
spherical_plot3d(theta, (theta, 0, 4*pi), (phi, 0, pi), mesh = True, opacity = 0.5, plot_points = [100, 20])

3D rendering not yet implemented

# rho = phi
spherical_plot3d(phi, (theta, 0, 2*pi), (phi, 0, 4*pi), mesh = True, opacity = 0.1, plot_points = [50, 100])

3D rendering not yet implemented

#theta = phi
var('rho theta phi')
parametric_plot3d([rho*sin(theta)*cos(theta), rho*sin(theta)*sin(theta), rho*cos(theta)], (theta, 0, 2*pi), (rho, 0, 5), mesh = True, plot_points = [50, 5])

(rho, theta, phi)

3D rendering not yet implemented

spherical_plot3d(1 + 2*cos(2*phi), (theta, 0, 2*pi), (phi, 0, pi), mesh = True, opacity = 0.7)

3D rendering not yet implemented