Implementing Marching Squares (opens in new tab)

>> Cases 5 and 10 in the article are actually ambiguous.

They are. He does mention using interpolation to make better boundaries. For example if you're using a threshold value and flag points as above/below that value, you can position the end-point of a line based on that threshold. When the lines don't exactly split a squares edge then cases 5 and 10 can be made less ambiguous by selecting the lines that minimize total line-length within a square. Or some similar heuristic.

>> For instance, if you are plotting the line where the field crosses zero, and one point is at 9 and its neighbour at -1, you should place the intersection point at 90% of the distance from the first to the second.

He does mention interpolation but doesn't go into it. That can also be used to resolve the ambiguity in cases 5 and 10.

you can also use the original field to produce normals that look a lot better (for cubes)

It is deterministic, though I am not sure if it gives one unique solution. In the example shown, there are many squares with white dots on one diagonal and black dots on the other; in these cases, it always seems to separate the white dots. (These are the cases liversage points out are ambiguous.) I guess that if you reversed the coloring, or used the alternatives for cases 5 and 10, the resulting partitioning would join the previously-white dots together.

Now I am wondering if you could use the alternative for case 5 or 10, but not both.