Some say that Marching Squares have Ambiguous Cases, but they limit what has Ambiguous Cases. Here is a list of the regular cases:

Case 0: empty.

Case 1: lower left corner.

Case 2: lower right corner.

Case 3: lower half.

Case 4: upper right corner.

Case 5: backslash.

Case 6: right half.

Case 7: no upper left.

Case 8: upper left.

Case 9: left half.

Case 10: fore-slash.

Case 11: not upper right.

Case 12: upper half.

Case 13: not lower right.

Case 14: not lower left.

Case 15: full.

Here is a list of alternative cases. Basically, everything is not connected together. Case 5 and 10 are well known:

Case 3 Alternative

Case 5 Alternative

Case 6 Alternative

Case 7 Alternative

Case 9 Alternative

Case 10 Alternative

Case 11 Alternative

Case 12 Alternative

Case 13 Alternative

Case 14 Alternative

Case 15 Alternative

Here's another set of alternatives. Alternative 2 are connected vertically. Alternative 3 are connected horizontally. A and B distinguish for Case 15 Alternative 2 and Alternative 3:

Case 7 Alternative 2

Case 11 Alternative 2

Case 13 Alternative 2

Case 14 Alternative 2

Case 15 Alternative 2A

Case 15 Alternative 2B

Case 7 Alternative 3

Case 11 Alternative 3

Case 13 Alternative 3

Case 14 Alternative 3

Case 15 Alternative 3A

Case 15 Alternative 3B

Why talk about these additional alternative cases? Well, Marching Cubes indirectly mention these alternative cases. If we look at a Marching Cube, then there are six faces that are marching squares, and 6 diagonal surfaces of rectangle 1:SQ-RT(2) proportion that also follow marching squares (adjusted for the length increased). Marching Cubes only have ambiguous cases when at least one of the twelve Marching Squares has ambiguous cases.

## No comments:

Post a Comment