Fillet filter in LevelSetFilter.h

[ghurstunither]

Adds a fillet filter, which rounds off concave edges to create a smoother transition between surfaces.

Fillets a level set by

• offsetting at locations with a negative principal curvature, proportional to its magnitude
• leaves locations with non-negative principal curvatures untouched
• this filter converges to the convex hull if iterated enough times

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Example

Union 2 spheres:

FloatGrid::Ptr grid1 = openvdb::tools::createLevelSetSphere<FloatGrid>(1.0, Vec3f(0, 0, 0), 0.1, 3.0);
FloatGrid::Ptr grid2 = openvdb::tools::createLevelSetSphere<FloatGrid>(1.0, Vec3f(1.4, 0, 0), 0.1, 3.0);
openvdb::tools::csgUnion(*grid1, *grid2);

std::cout << grid1->evalActiveVoxelBoundingBox() << std::endl
[-12, -12, -12][26, 12, 12]

Visualization:

7 iterations of filleting:

openvdb::tools::LevelSetFilter filter(*grid1);
for(int i = 0; i < 7; ++i)
  filter.fillet();

// non-shrinking filter!
std::cout << grid1->evalActiveVoxelBoundingBox() << std::endl
[-12, -12, -12][26, 12, 12]

Visualization:

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Tube radius stays the same after filleting:

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Note, only concave corners are filleted:

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A level set with a single connected component will transform into its convex hull after indefinite iterations of this filter. Unfortunately it's not practical in most cases, but it's still a neat fact. For example it took 16000 iterations to reasonably approximate the convex hull here:

[richhones]

LGTM @apradhana feel like this covers some similar ground as the smooth union (e.g. https://iquilezles.org/articles/smin/) but imagine there is still place for both of these operations?

[ghurstunither]

LGTM @apradhana feel like this covers some similar ground as the smooth union (e.g. https://iquilezles.org/articles/smin/) but imagine there is still place for both of these operations?

That's a good point! I think we should include both features.

1. The fillet filter operates on a single object, and so is not a blending operator.
2. These type of blending operations can sometimes cause undesired 'bulges' where regions have significant overlap near their boundaries. Here's a comparison combining two tubes, where the smooth/blended union shows the bulge:

3. The smooth union functionality has advantages, like finer control with extra blending parameters, as well as running much faster for large fillets since it isn't bound by a CFL-like condition.

[apradhana]

Would be great to add @details that provides a reference to where the technique comes from. If I recall correctly, it's from one of Sethian/Osher's book.

[danrbailey]

@apradhana @ghurstunither - I think this was merged prematurely, it doesn't appear to have a unit test or a changelog message? At the very least, it would need a couple lines in the unit tests that evaluates this method, but better still of course would be something that validates the results.

[apradhana]

Thanks for pointing this out @danrbailey. I will add a unit test for the new feature and submit a PR. We are lacking unit tests for all the level set filters methods in the LevelSetFilter class in LevelSetFilter.h. It's a good time to start adding tests for those methods.