Volume under an iso surface

I have an iso-surface of velocity V(a,b,c) as shown in the picture. I need to calculate the volume enclosed by this iso-surface and the X axis. I have the x,y,z co-ordinates corresponding to this iso-surface as three different 3D matrices. Any suggestions will be of great help! thank you!

[SNyk]

Answer 1

[Chad Greene]

This is a sum. Each grid cell has a volume which is its height x width x length. In your case height at a given row and column is V(row,col). If your grid cells are W*L in size, the volume under the surface of one grid cell is V(row,col)*W*L. For the entire surface, sum up all those volumes and multiply by grid size:

sum(V(:))*W*L

[Walter Roberson]

This applies if we assume a border of 0 around the values. If not then we have to subtract half of the boundary pixels (trapezoid rule.)