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Marching Cubes

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Hi there I'm trying to implement Marching Cubes algorithm... Algorithm authors says that: "blabla... Two different symmetries of the cube reduce the problem from 256 cases to 14 patterns" Here patterns: marching cubes patterns But patterns 11 and 14 is identical!!! 11==flip_horizontal(14) If 11 and 14 is not identical, why pattern 6 has no "double"? (flipped/mirrored pattern) I'm confused... o_O Original article: http://www.cs.virginia.edu/~gfx/Courses/2002/BigData/papers/Volume%20Rendering/Marching%20Cubes%20-%20A%20High%20Resolution%20Surface%20Reconstruction%20Algorithm.pdf#search=%22Marching%20cubes%3A%20A%20high%20resolution%203D%20surface%20construction%20algorithm%20pdf%22 ps: Forgive for mistakes, I badly know English.

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I think you're right - 14 is a duplicate of 11. As you say, mirroring must be allowed in order to get your pattern from 6. There are also other patterns which can only be reached by mirroring.

As well as this, note that the text consistently refers to there being 14 patterns after symmetries have been taken into account, but the diagram shows 15.

Conclusion - the diagram is incorrect.

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The "empty" case isn't counted in the 14... Why it's in the diagram is anyone's guess (to make it look nice?). But the cases 11 and 14 are indeed mirror images. That's odd.

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The empty case is certainly one of the 14, as it is one of the 256 which are reduced by symmetry to 14. It should therefore be in the diagram. It is no. 14 which should not be in the diagram.

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