
from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt


def simple_3d():
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    zline = np.linspace(0, 15, 1000)
    xline = np.sin(zline)
    yline = np.cos(zline)
    ax.plot3D(xline, yline, zline, 'gray')

    # Data for three-dimensional scattered points
    zdata = 15 * np.random.random(100)
    xdata = np.sin(zdata) + 0.1 * np.random.randn(100)
    ydata = np.cos(zdata) + 0.1 * np.random.randn(100)
    ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens');

    plt.show()


def f(x, y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))


def color_3d():
    x = np.linspace(-6, 6, 30)
    y = np.linspace(-6, 6, 30)
    X, Y = np.meshgrid(x, y)
    Z = f(X, Y)
    fig = plt.figure()

    ax = plt.axes(projection='3d')
    ax.contour3D(X, Y, Z, 50, cmap='binary')
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('z')
    ax.view_init(60, 35)
    plt.show()


def wireframes():
    x = np.linspace(-6, 6, 30)
    y = np.linspace(-6, 6, 30)
    X, Y = np.meshgrid(x, y)
    Z = f(X, Y)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot_wireframe(X, Y, Z, color='black')
    ax.set_title('wireframe');

    ax = plt.axes(projection='3d')
    ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
    ax.set_title('surface');
    r = np.linspace(0, 6, 20)
    theta = np.linspace(-0.9 * np.pi, 0.8 * np.pi, 40)
    r, theta = np.meshgrid(r, theta)

    X = r * np.sin(theta)
    Y = r * np.cos(theta)
    Z = f(X, Y)

    ax = plt.axes(projection='3d')
    ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
    plt.show()


def surface_triangulations():
    theta = 2 * np.pi * np.random.random(1000)
    r = 6 * np.random.random(1000)
    x = np.ravel(r * np.sin(theta))
    y = np.ravel(r * np.cos(theta))
    z = f(x, y)
    ax = plt.axes(projection='3d')
    ax.scatter(x, y, z, c=z, cmap='viridis', linewidth=0.5)
    ax = plt.axes(projection='3d')
    ax.plot_trisurf(x, y, z, cmap='viridis', edgecolor='none')
    plt.show()


def visualize_mobius_strip():
    theta = np.linspace(0, 2 * np.pi, 30)
    w = np.linspace(-0.25, 0.25, 8)
    w, theta = np.meshgrid(w, theta)
    phi = 0.5 * theta
    # radius in x-y plane
    r = 1 + w * np.cos(phi)

    x = np.ravel(r * np.cos(theta))
    y = np.ravel(r * np.sin(theta))
    z = np.ravel(w * np.sin(phi))

    # triangulate in the underlying parametrization
    from matplotlib.tri import Triangulation
    tri = Triangulation(np.ravel(w), np.ravel(theta))

    ax = plt.axes(projection='3d')
    ax.plot_trisurf(x, y, z, triangles=tri.triangles, cmap='viridis', linewidths=0.2);

    ax.set_xlim(-1, 1); ax.set_ylim(-1, 1); ax.set_zlim(-1, 1)
    plt.show()


if __name__ == '__main__':
    print('Numpy Version:', np.__version__)
    # simple_3d()
    # color_3d()
    # wireframes()
    # surface_triangulations()
    visualize_mobius_strip()




from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt


def simple_3d():
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    zline = np.linspace(0, 15, 1000)
    xline = np.sin(zline)
    yline = np.cos(zline)
    ax.plot3D(xline, yline, zline, 'gray')

    # Data for three-dimensional scattered points
    zdata = 15 * np.random.random(100)
    xdata = np.sin(zdata) + 0.1 * np.random.randn(100)
    ydata = np.cos(zdata) + 0.1 * np.random.randn(100)
    ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens');

    plt.show()


def f(x, y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))


def color_3d():
    x = np.linspace(-6, 6, 30)
    y = np.linspace(-6, 6, 30)
    X, Y = np.meshgrid(x, y)
    Z = f(X, Y)
    fig = plt.figure()

    ax = plt.axes(projection='3d')
    ax.contour3D(X, Y, Z, 50, cmap='binary')
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('z')
    ax.view_init(60, 35)
    plt.show()


def wireframes():
    x = np.linspace(-6, 6, 30)
    y = np.linspace(-6, 6, 30)
    X, Y = np.meshgrid(x, y)
    Z = f(X, Y)
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot_wireframe(X, Y, Z, color='black')
    ax.set_title('wireframe');

    ax = plt.axes(projection='3d')
    ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
    ax.set_title('surface');
    r = np.linspace(0, 6, 20)
    theta = np.linspace(-0.9 * np.pi, 0.8 * np.pi, 40)
    r, theta = np.meshgrid(r, theta)

    X = r * np.sin(theta)
    Y = r * np.cos(theta)
    Z = f(X, Y)

    ax = plt.axes(projection='3d')
    ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
                    cmap='viridis', edgecolor='none')
    plt.show()


def surface_triangulations():
    theta = 2 * np.pi * np.random.random(1000)
    r = 6 * np.random.random(1000)
    x = np.ravel(r * np.sin(theta))
    y = np.ravel(r * np.cos(theta))
    z = f(x, y)
    ax = plt.axes(projection='3d')
    ax.scatter(x, y, z, c=z, cmap='viridis', linewidth=0.5)
    ax = plt.axes(projection='3d')
    ax.plot_trisurf(x, y, z, cmap='viridis', edgecolor='none')
    plt.show()


def visualize_mobius_strip():
    theta = np.linspace(0, 2 * np.pi, 30)
    w = np.linspace(-0.25, 0.25, 8)
    w, theta = np.meshgrid(w, theta)
    phi = 0.5 * theta
    # radius in x-y plane
    r = 1 + w * np.cos(phi)

    x = np.ravel(r * np.cos(theta))
    y = np.ravel(r * np.sin(theta))
    z = np.ravel(w * np.sin(phi))

    # triangulate in the underlying parametrization
    from matplotlib.tri import Triangulation
    tri = Triangulation(np.ravel(w), np.ravel(theta))

    ax = plt.axes(projection='3d')
    ax.plot_trisurf(x, y, z, triangles=tri.triangles, cmap='viridis', linewidths=0.2);

    ax.set_xlim(-1, 1); ax.set_ylim(-1, 1); ax.set_zlim(-1, 1)
    plt.show()


if __name__ == '__main__':
    print('Numpy Version:', np.__version__)
    # simple_3d()
    # color_3d()
    # wireframes()
    # surface_triangulations()
    visualize_mobius_strip()



# Data for three-dimensional scattered points # radius in x-y plane # triangulate in the underlying parametrization # simple_3d() # color_3d() # wireframes() # surface_triangulations()