How can you iterate linearly through a 3D grid?

Question

Assume we have a 3D grid that spans some 3D space. This grid is made out of cubes, the cubes need not have integer length, they can have any possible floating point length.<

Answer 1

Well if you are working with floats, you can make the equation for the line in direction specifiedd. Which is parameterized by t. Because in between any two floats there is a finite number of points, you can simply check each of these points which cube they are in easily cause you have point (x,y,z) whose components should be in, a respective interval defining a cube.

The issue gets a little bit harder if you consider intervals that are, dense.

The key here is even with floats this is a discrete problem of searching. The fact that the equation of a line between any two points is a discrete set of points means you merely need to check them all to the cube intervals. What's better is there is a symmetry (a line) allowing you to enumerate each point easily with arithmetic expression, one after another for checking.

Also perhaps consider integer case first as it is same but slightly simpler in determining the discrete points as it is a line in Z_2^8?