Find corner points of a cube that has a random point in a 3D grid

Question

I have coordinates (x,y,z) for a evenly spaced 3D grid. Given a random 3D point (x,y,z) somewhere on the grid, how to find which cube has the point. I need to know the 8 corners of the cube.
I have the grid point data in a list of vectors in c++.

Thanks.

Answer 1

Assuming equal length for the grid cubes in all dimentions, you can get the coordinate closest to ohe origo by calculating

gx = x - x%l;
gy = y - y%l;
gz = z - z%l;

Where gx, gy, gz are the grid cube coordinates closest to the origo (I'm assuming x,y,z>=0 here), % is the modulus operator and l is the length of the grid cubes.

Note: You can perform the calculations this way as well: gx = static_cast<int>(x)/l*l; (static_cast<> to account for non-integer x)

Then the 8 corners of the grid cube (x, y, z) falls into are:

(gx, gy, gz)
(gx+l, gy, gz)
(gx, gy+l, gz)
(gx, gy, gz+l)
(gx+l, gy+l, gz)
(gx+l, gy, gz+l)
(gx, gy+l, gz+l)
(gx+l, gy+l, gz+l)

Answer 2

Assuming the origin of the grid is at (0,0,0), you should divide (x,y,z) by the grid's size. Then you should round the result and multiply it by the grid's size, that is:

(nx, ny, nz) = [(x,y,z) / grid_size] * grid_size

where [x] is the greatest integer n, so that n<=x (in practice, you should just cast the result of floating-point operation to an int). The points you're searching for are:

(nx, ny, nz)
(nx+grid_size, ny, nz)
(nx, ny+grid_size, nz)
(nx, ny, nz+grid_size)
(nx+grid_size, ny+grid_size, nz)
(nx+grid_size, ny, nz+grid_size)
(nx, ny+grid_size, nz+grid_size)
(nx+grid_size, ny+grid_size, nz+grid_size)