The regular grid algorithm advances between cells similar to Bresenham's line algorithm. It considers the evenly-spaced, infinite planes that separates cells. You can think of a ray like a particle traveling at constant rate away from the observer. The components of the particle’s velocity vector are independent of each other. Meaning, the time required for the particle to traverse the space between two neighboring, parallel planes is always constant. There is a constant time for each axial direction.
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