Cases 5 and 10 in the article are actually ambiguous. In each case there are two ways to draw lines to separate the high and low points and a naïve algorithm wi

Cases 5 and 10 in the article are actually ambiguous. In each case there are two ways to draw lines to separate the high and low points and a naïve algorithm will just hardcode one of each like it's done in the article. This isn't a serious problem in the two dimensional marching squares algorithm but the same problem can lead to holes in the surface generated by the three dimensional marching cubes algorithm. During a visit to Washington University I had the opportunity to work with this flaw in the algorithm and I ended up publishing a scientific paper about the subject. I then went on to write my thesis (in Danish) where I worked more rigorously on how to deal with this. It's so long ago that I almost forgot so reading about marching squares again was a nice trip down memory lane. https://martinliversage.blob.core.windows.net/publications/1992%20Automedica.pdf https://martinliversage.blob.core.windows.net/publications/1... https://martinliversage.blob.core.windows.net/publications/1994-09%20Visualisering%20af%20tredimensionale%20medicinske%20data.pdf https://martinliversage.blob.core.windows.net/publications/1...