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)