Cube sample

The most important thing today is I finished the cube sampling part.

Usually a cube is consist of 6 discontinuous surfaces, which is hard for constructing level set field. Actually I've done several experiments to create level set from discrete meshes like a triangle mesh, but the I failed all the time because I don't know how to deal with the discontinuity.

This time I'm using a trick to avoid the discontinuity. By using spherical surface on the corner and cylindrical surface on the edge, I could create correct level set data for a "soft" cube.

This is important because in most cases, the scene is just a box, and I need this cube sample to do construct all the solid particles.

Now everything new has pretty much be finished. The only thing left is to assemble all the parts together. Yet SigGraph is approaching, so I might not have enough time to finish this project. Anyway I'll try my best.

Here's a image of cube sample. The test scene for me would be a large spherical water drop falling in a cube. Or maybe a water cube falling in a sphere. I'm so excited it's almost done!

Solid particle sample finished

A good news is I totally understood the process of sampling today. 

I've been reading this paper for around 10 times to finally figure out the main process of sampling. I really wish the authors could explain more on the basic process instead of focusing on their contribution.

Solid particles are sampled only once at the beginning of the simulation. And later the solid particles would not move, or move only with the solid object. The paper mentioned there is a velocity for solid particle. That is its ghost velocity and would only be used in calculating the viscosity force for fluid particles that is near the solid surface. In integration, there is no real velocity for solid particles(as long as solid object does not move).

Because the relaxation process is really really slow for fluid volume samples, and based on the fact that all the fluid sample and solid sample has only to be done once during the simulation, I decided to write a file exporter/importer. I can run the simulator with a relatively higher relaxation iteration number and thus getting a better distribution of all the particles, and export particles to a certain file. This has to be done only once, and later when I will be testing other parts, I can just import initial state of particle from the generated file instead of sampling again.

Now the biggest problem to be is related to projection. In the sample process, a random sample is supposed to be projected to the surface which is described by a level set. Yet when I tried to use level set grid to do the projection work, I ended up with a crappy result. I think that is my fault in implementation. Hopefully I will fix that tomorrow, cause I don't want to use implicit surface only.

I'll post a picture of all kinds of particles when I fixed the existing problems.

Ghost SPH Sample Finished

Finished the sampling part of ghost SPH.

The sampling process take a few steps as follows. The input is a level set field which describe the shape of the fluid.

1. Sample the surface, namely those voxels where level set change sign.

2. Relaxing surface particles. This would yield better distribution of surface particles(blue noise).

3. Sample the interior part of fluid. Using the surface particles as initial seed.

4. Apply volume relaxation. This is a extremely slow process, multiple iterations, and within each iteration, neighbor search has to be applied to each particle.

5. Sample air particles. Similar as volume sample. Using surface particles as seeds, sample air particles outside the surface within a single-smooth-kernel layer with the help of level set.

The result so far looks like this:

The green particles are ghost particles, and blue ones as fluid particles.

The next step would be transplanting all the calculation parts in my previous SPH simulator into this new one.

My understanding for the paper might not be 100 percent correct, now I still have a few confusion related to this paper. I'm contacting the author recently and hopefully they could unravel my questions.

I'll keep updated.