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After the release of Minecraft I saw more and more rip offs of the game but some actually began to change it up a bit making the game have a organic look instead of the iconic blocky one that Minecraft does.

If you'd like to look at the game that i'm referring to you can do so here. If you skip to around 50 seconds on the first video the steam page offers you can see the mining part that i'm wondering about.

I was wondering how this affect is achieved where they are able to remove part of the 3D object on collison with the players pick. I have heard about constructive solid geometry before and figured that could have been used but i'm not so sure.

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It could be Constructive Solid Geometry indeed. But they said in the store page it is a voxel-based world (unless they lied of course). Which is basically pixels in 3D (or i could say cubes in the case of minecraft, and others).

In this case, it seems to me they smooth out those voxels to achieve that organic looks. Something like Castle Story which you can clearly see some are smoothen out, well not everything is like in Rising World, but you get my point.

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