Level set vs Color field

For the mesh extraction part of particle based fluid simulation, you have to create a surface field before actually execute the mesh extraction function(e.g. marching cube). And generally there're two ways of doing this: level set and color field.

For level set, the idea is to splat each particle to the region it belongs to, and in terms of different values assigned to a certain sample point, min operator could be employed to get the exact data. 

However, this could be slow. The level set field for a certain particle is continuous, that is, no matter how far the sample point is, there's always a value for that. So you have to decide a radius that the particle have to splat to. Theoretically, the larger the splatting radius is, the closer the final result is to the "ideal" field. 

Another huge problem is, this could only be useful for spherical particles. I'm using anisotropic particles(elliptic), and calculating the distance from an arbitrary point to an ellipsoid is not trivial task. With my current configuration, a single frame would cost more that 10 mins to create the level set field only. The problem lies in the solving part. By using ellipsoids, the distance solving part relies on iterative method, and that is the bottleneck for performance.

So in order to calculate a field faster, I turned to the "color field". Level set is defined as "signed distance field", while the color field is defined as "1 for the particle center, and 0 for outside region", and for the position within the radius of the particle, the value is decided by the smoothing kernel(e.g. B-cubic kernel).

The only problem for color field is, it does not satisfy the Eikonal Equation. And this would lead to a improper value for the normal. For the past few days, I've been thinking about methods that could eliminate or improve this part. 

One of my idea is extend the kernel. Right now the kernel is limited to the (-r, r) range, and other from that, all the values are 0. Let's imagine the level set method works in a similar way as kernel: the kernel for level set has no boundary. And that's what I've mentioned about: no matter how far the sample point is, there's always a value. 

If we could design a kernel without boundary, and also could return a value that somehow reflect the definition of color field, the problem would be improved. (Not totally solved cause the Eikonal Equation still remains a problem). 

If anyone has good ideas about this, don't hesitate to contact me. This could be huge.