Nonlinear CCD

[zfergus]

Description

This PR adds a generic implementation of the nonlinear CCD (of linear geometry) algorithm from [Ferguson et al. 2021].

Generic nonlinear trajectories are specified through a NonlinearTrajectory virtual class. By default the maximum distance between the trajectory and a linearized version is computed using interval arithmetic. That is

$$ \max_{t \in [0, 1]} \Vert p(\mathrm{lerp}(t_0, t_1, t)) - \mathrm{lerp}(p(t_0), p(t_1), t) \Vert_2 \leq \sup(\Vert p([t_0, t_1]) - \mathrm{lerp}(p(t_0), p(t_1), [0, 1]) \Vert_2) $$

where $p$ is the point's position over time, $\mathrm{lerp}(a, b, t) := (b - a) t + a$ and $\sup([a,b]):=b$. Because this can be an overly conservative approximation, users can override the NonlinearTrajectory::max_distance_from_linear function to compute the max directly in closed form if known.

We perform interval arithmetic using filib which has been shown to be "the only library that is correct, consistent, portable, and efficient" [Tang et al. 2022].

Type of change

• New feature (non-breaking change which adds functionality)

How Has This Been Tested?

New unit tests checking for rotational trajectories.

Test Configuration:

• OS and version: macOS 14.0
• Compile and version: Apple clang version 15.0.0

Checklist:

• I have followed the project style guide
• My code follows the clang-format style guidelines of this project
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[codecov]

Codecov Report

Merging #72 (3fa224e) into main (7d04a5f) will increase coverage by 0.01%.
The diff coverage is 96.49%.

@@            Coverage Diff             @@
##             main      #72      +/-   ##
==========================================
+ Coverage   95.11%   95.13%   +0.01%     
==========================================
  Files          82       87       +5     
  Lines        7105     7251     +146     
==========================================
+ Hits         6758     6898     +140     
- Misses        347      353       +6     

Files	Coverage Δ
src/ipc/broad_phase/voxel_size_heuristic.cpp	95.58% <100.00%> (-0.13%)	⬇️
src/ipc/ccd/ccd.cpp	95.53% <100.00%> (-0.16%)	⬇️
src/ipc/ccd/nonlinear_ccd.hpp	100.00% <100.00%> (ø)
src/ipc/ccd/point_static_plane.cpp	86.48% <100.00%> (-0.36%)	⬇️
...c/ipc/collisions/collision_constraints_builder.cpp	94.30% <ø> (-0.02%)	⬇️
src/ipc/utils/eigen_ext.hpp	100.00% <100.00%> (ø)
src/ipc/utils/interval.cpp	100.00% <100.00%> (ø)
src/ipc/utils/interval.hpp	100.00% <100.00%> (ø)
src/ipc/ccd/nonlinear_ccd.cpp	95.31% <95.31%> (ø)