How can I build the surface of a structure that is defined by vectors in python?

Question

I would like to build the surface of my data, which is defined by three-dimensional vectors in the Cartesian coordinates x, y, z. Data cannot be represented by a smooth function.

So, first we generate some dummy data using a function eq_points(N_count, r)that returns an array pointswith the x, y, z coordinates of each point on the surface of our object. Value omegais a solid angle, not now.

#credit to Markus Deserno from MPI
#https://www.cmu.edu/biolphys/deserno/pdf/sphere_equi.pdf
def eq_points(N_count, r):
    points = []
    a = 4*np.pi*r**2/N_count
    d = np.sqrt(a)
    M_theta = int(np.pi/d)
    d_theta = np.pi/M_theta
    d_phi = a/d_theta
    for m in range(M_theta):
        theta = np.pi*(m+0.5)/M_theta
        M_phi = int(2*np.pi*np.sin(theta)/d_phi)
        for n in range(M_phi):
            phi = 2*np.pi*n/M_phi

            points.append(np.array([r*np.sin(theta)*np.cos(phi),
                                    r*np.sin(theta)*np.sin(phi),
                                    r*np.cos(theta)]))

    omega = 4*np.pi/N_count

    return np.array(points), omega

#starting plotting sequence

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

points, omega = eq_points(400, 1.)

ax.scatter(points[:,0], points[:,1], points[:,2])
ax.scatter(0., 0., 0., c="r")
ax.set_xlabel(r'$x$ axis')
ax.set_ylabel(r'$y$ axis')
ax.set_zlabel(r'$Z$ axis')

plt.savefig("./sphere.png", format="png", dpi=300)
plt.clf()

The result is the scope shown in the following figure. Blue dots mark data from the array points, and a red dot is the beginning.

- . mplot3d . ax.scatter(), .

, , , . . , , . , . plot_surface() ? :

Answer 1

, . , , , , , , , . .

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from scipy.spatial import ConvexHull

def eq_points(N_count, r):
    points = []
    a = 4*np.pi*r**2/N_count
    d = np.sqrt(a)
    M_theta = int(np.pi/d)
    d_theta = np.pi/M_theta
    d_phi = a/d_theta
    for m in range(M_theta):
        theta = np.pi*(m+0.5)/M_theta
        M_phi = int(2*np.pi*np.sin(theta)/d_phi)
        for n in range(M_phi):
            phi = 2*np.pi*n/M_phi

            points.append(np.array([r*np.sin(theta)*np.cos(phi),
                                    r*np.sin(theta)*np.sin(phi),
                                    r*np.cos(theta)]))

    omega = 4*np.pi/N_count

    return np.array(points), omega

def eq_points_with_random_radius(N_count, r):
    points = []
    a = 4*np.pi*r**2/N_count
    d = np.sqrt(a)
    M_theta = int(np.pi/d)
    d_theta = np.pi/M_theta
    d_phi = a/d_theta
    for m in range(M_theta):
        theta = np.pi*(m+0.5)/M_theta
        M_phi = int(2*np.pi*np.sin(theta)/d_phi)
        for n in range(M_phi):
            phi = 2*np.pi*n/M_phi
            rr = r * np.random.rand()
            points.append(np.array([rr*np.sin(theta)*np.cos(phi),
                                    rr*np.sin(theta)*np.sin(phi),
                                    rr*np.cos(theta)]))

    omega = 4*np.pi/N_count

    return np.array(points), omega


N = 400
pts, _ = eq_points(N, 1.)
pts_rescaled, _ = eq_points_with_random_radius(N, 1.)
extremum = 2.

# plot points
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(pts_rescaled[:,0], pts_rescaled[:,1], pts_rescaled[:,2])
ax.set_xlim(-extremum, extremum)
ax.set_ylim(-extremum, extremum)
ax.set_zlim(-extremum, extremum)

# get indices of simplices making up the surface using points on unit sphere;
# index into rescaled points  
hull = ConvexHull(pts)
vertices = [pts_rescaled[s] for s in hull.simplices]

fig = plt.figure()
ax = Axes3D(fig)
triangles = Poly3DCollection(vertices, edgecolor='k')
ax.add_collection3d(triangles)
ax.set_xlim(-extremum, extremum)
ax.set_ylim(-extremum, extremum)
ax.set_zlim(-extremum, extremum)
plt.show()

Answer 2

, (.. , ). , x, y, z-.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from scipy.spatial import ConvexHull

N = 1000
pts = np.random.randn(N, 3)

# exclude outliers
# obviously, this is data dependent
cutoff = 3.
is_outlier = np.any(np.abs(pts) > cutoff, axis=1)
pts = pts[~is_outlier]

# plot points
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(pts[:,0], pts[:,1], pts[:,2])

ax.set_xlim(-(cutoff +1), cutoff+1)
ax.set_ylim(-(cutoff +1), cutoff+1)
ax.set_zlim(-(cutoff +1), cutoff+1)

# get and plot hull
hull = ConvexHull(pts)

fig = plt.figure()
ax = Axes3D(fig)
vertices = [pts[s] for s in hull.simplices]
triangles = Poly3DCollection(vertices, edgecolor='k')
ax.add_collection3d(triangles)

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