Volume of 3-Space Object using 3-Space co-ordinates

Question

I am rather new to Python and I think I'm trying to attempt something quite complicated? I have repeatedly tried to search for this and think I'm missing some base knowledge as I truly don't understand what I've read.

Effectively I have 3 arrays, which contain x points, y points, and z points. They create an approximately hemispherical shape. I have these points from taking a contour of a 2D axisymmetrical semicircular shape, extracting the x points and y points from it into separate arrays, and creating a "z points" array of zeros of the same length as the previous two arrays.

From this, I then rotate the y points into the z-domain using angles to create a 3D approximation of the 2D contour.

This 3D shape is completely bounded (in that it creates both the bottom and the top), as linked below:

3d Approximation

I've butchered the following code from my much longer program, it's the only part that is pertinent to my question however:

c, contours, _ = cv2.findContours(WB, mode = cv2.RETR_EXTERNAL, method = cv2.CHAIN_APPROX_NONE) # Find new contours in recently bisected mask
contours = sorted (contours, key = cv2.contourArea, reverse = True) #                           # Sort contours (there is only 2 contours left, plinth/background, and droplet)
contour = contours[1] # Second longest contour is the desired contour           

xpointsList = [xpoints[0][0] for xpoints in contour] # Create new array of all x co-ordinates
ypointsList = [ypoints[0][1] for ypoints in contour] # Create new array of all y co-ordinates
zpointsList = np.zeros(len(xpointsList)) #           # Create an array of 0 values to represent the z domain. True contour sits at 0 on all points in the z-domain

angles = np.arange(0,180,5, dtype = int) #  # Creating an array of angles between to form a full drop in degrees of 5

i = 0
b = 0
d = 0

qx = np.zeros(len(xpointsList)*len(angles)) # Setting variable to equal the length of x points times the length of iterative angle calculations
qy = np.zeros(len(ypointsList)*len(angles)) # Setting variable to equal the length of x points times the length of iterative angle calculations
qz = np.zeros(len(zpointsList)*len(angles)) # Setting variable to equal the length of x points times the length of iterative angle calculations

ax = plt.axes(projection='3d')

for b in range(0,len(angles)):
    angle = angles[b]
    for i in range(0,len(ypointsList)):
        qx[i+d] = xpointsList[i]-origin[0] # Setting the x-axis to equal it's current values around the origin
        qz[i+d] = origin[0] + math.cos(math.radians(angle)) * (zpointsList[i]) - math.sin(math.radians(angle)) * (ypointsList[i] - origin[1]) # creating a z value based on 10 degree rotations of the y values around the x axis
        qy[i+d] = origin[1] + math.sin(math.radians(angle)) * (zpointsList[i]) + math.cos(math.radians(angle)) * (ypointsList[i] - origin[1]) # adapting the y value based on the creation of the z values.
        i = i + 1
    b = b + 1
    d = d + len (xpointsList)
ax.plot3D (qy, qz, qx, color = 'blue', linewidth = 0.1)

Effectively my question is, how do I use this structure to somehow find the volume using the co-ordinate arrays? I think I need to use some kind of scipy.spatial ConvexHull to fill in the areas between my rotations so that it has a surface and work from there?

Answer 1

I don't understand your approach (I'm not that good in Python) so can't help you fix it, but there was a similar question with much simpler solution here:

https://stackoverflow.com/a/48114604/1479630

Your situation is even easier because what you basically have is a distorted sphere, and you have a regular grid on its surface. You can iterate over all surface triangles and for each, compute volume of tetrahedron made of this triangle and center of object. If you sum up those volumes you'll get volume of entire object.