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Sorry I might have missed this in lecture but could you elaborate more on why implicit representation is easier to handle changes in topology and what do you mean by saying changes in topology?


I think changes in topology means the calculation of the boundary between two substances (like air and a fluid). In earlier slides there's some discussion of implicit descriptions of fluids like level sets. It's easier to handle the change from fluid to air because it's easy to detect whether a point is in or outside our fluid boundary.


@harveybia I mean that in a fluid, you can have things like a splash of fluid breaking up into many droplets, or many droplets merging together to form a larger volume of water. You can also have a thin sheet of fluid develop many small "holes". Etc. This is easy to handle with a level set representation, as we saw with (for instance) "blobby" surfaces. Much harder to do with meshes, because you have to explicitly determine how the connectivity of the edges, faces, etc., changes during these merge/split events. However, it has been done; see for instance this super cool paper by Chris Wojtan on Deforming Meshes that Split and Merge.