How to generate random and lattice points inside of an irregular object?

I have an irregular 3d object and want to know the surface of this object. The object can be both convex or non convex type. I can get the surface of this object applying any method like marching cube, surface contour, or isosurface.

All this methods give me triangulated mesh which is basically contains edges and vertex.

My task is to generate random and lattice points inside the object.

How should i check whether my point is inside or outside?

Any suggestion? Thanks a lot.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

from skimage import measure, io
from skimage.draw import ellipsoid
import skimage as sk 
import random 

I=np.zeros((50,50,50),dtype=np.float)

for i in range(50):
  for j in range(50):
    for k in range(50):
        dist=np.linalg.norm([i,j,k]-O)
        if dist<8:
            I[i,j,k]=0.8#random.random()  
        dist=np.linalg.norm([i,j,k]-O2)
        if dist<16:
            I[i,j,k]=1#random.random()  

verts, faces, normals, values = measure.marching_cubes_lewiner(I,0.7)

fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
mesh = Poly3DCollection(verts[faces])
mesh.set_edgecolor('k')
ax.add_collection3d(mesh)
plt.show()

%now forget the above code and suppose i have only verts and
%faces information. Now how to generate random points inside this Data

Data=verts[faces]
???????