Walk a line between two points in a 3D voxel space visiting all cells

Question

I have a line-of-sight problem I need to solve by visiting all possible cells in a 3D voxel space between two (non-grid-aligned) points.

I have considered using a 3D

Answer 1

I think 3d Bresenham is the way to go, just tweaked a bit. As a first pass at the problem, proceed as Bresenham, but be suspicious when you're about to take a step, or you've just taken a step, as these are the places where the line could pass through extra cells.

For simplicity, let's assume that z is dominant, meaning that z increments every step. The 3d Bresenham question is: "when do we increment/decrement in x or y?" The answer is when accumulated error in x reaches .5, or when the error in y does, or both.

For your case, I think you need to have a secondary threshold that uses slopeY = deltaY/deltaZto decide if the line is about to cross into a neighboring cell. If stepZ is the change in z along the line for each pixel, then a test like error > .5 - slopeY/stepZ should tell you to get cells on both sides of the line in y. A similar test tells you if you have to get the extra cell in x. If you have to get the extra cell in both x AND y, then you have to get the cell diagonal to the Bresenham cell as well.

If you've detected that you added a cell in y before the increment, you won't add a cell after. If you haven't added a y cell before, you will have to after, unless you happened to pass through a cell corner. How you handle that depends on your use-case.

These are my thoughts on the issue, I haven't tested anything, but something like it should work.