Marching Cubes Performance (2d)
I'm trying to implement a 2D version of the marching cubes algorithm (marching squares?), and one of the major roadblocks I've run into is the performance issues (using WebGL and three.js). I notice that there's a huge tradeoff between quality (voxel/square size) and performance, and I think that the culprit for this is the center (solid area) of the metaballs:
Obviously I don't care about the faces on the inside of the metaballs since that's a completely solid area anyways; but I'm not sure how to get around polyganizing the interior area without treating it the same as the rest of the surface. The problem becomes worse when I add more metaballs to the mix.
How can I get around this problem, to maintain a decent quality and be able to render many metaballs at a decent framerate?
If you are implementing the standard marching squares technique then the cases inside and outside the surface shouldn't be a problem. In fact they are the cheapest because you don't need to do any computation for them.
If you want to reduce the poly-count in areas where it is not needed (the central area of the circle), you need to look into using an adaptive sampling technique. In this case probably most adequate would be a quad-tree (2d octree).
The speed issue when decreasing the cell size would always be there because Marching Cubes is a O(n^3) algorithm (very slow), thus marching squares would be O(n^2) (still very slow). There is no way around that. (Using an adaptive sampling data-structure, as mentioned above, would speed things up.)
It seems to me you could improve on the quality at the lower resolution. The circle seems to be aliasing a lot (assuming this is not because it is actual low screen resolution). I would check again how you interpolate on the edges of the squares (i hope you don't just use the centres of the edges) - using a more appropriate interpolation will give you better approximation and you would get better results at lower resolution. See Paul Bourke's article on marching cubes and checkout the interpolation if you are not doing it.
Here are some references for 3d isosurface extraction techniques, (mostly based on MC) but you could benefit from them, in your 2d case:
(Kazdan et al, 2007)
(Manson and Shaefer, 2010)
(Wilhelms and Gleder, 1992)
PS: also check out their references for many more similar and maybe foundation papers!
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