One question: does level set require evaluation of f(x) on a grid of points, as shown in the example? If not, does it require prior knowledge of the function shape?

Does the trilinear filtering of level set works in the similar ways to the texture mapping (e.g. the further away from camera, the greater the mip level)?

I have the same question as @goku2021.

What's the difference in storage space between storing this grid and storing a spaced out point cloud near the surface and interpolating between those points? Is the latter not doable?

What's the needed computation power for this method? It seems like pre-calculating the approximation function and doing filtering would be computationally expensive. Or would the approximation function/level set be given, like we were given texture maps?

@liangcyn I think the two methods are quite similar but storing a point cloud should be more memory efficient. After all, a point cloud is a collection of points, but a level set is a grid of numbers that tell us more about the curve and at the same time require more storage.