Fix missing PSD projection of mollified m≤0 hessian blocks

[zfergus]

Problem

NormalPotential::hessian() has an early-return for the mollified case when the mollifier m == 0 (exactly parallel edges):

if (collision.is_mollified() && m <= 0) {
    const double f = (*this)(d, collision.dmin);
    const MatrixMax12d hess_m = collision.mollifier_hessian(positions);
    return (collision.weight * f) * hess_m;   // ← returned WITHOUT PSD projection
}

Every other return path applies project_to_psd, but this one did not. For positive weights the block (weight·f)·hess_m is PSD, so skipping projection was harmless. However, IMPROVED_MAX_APPROX produces negative-weight collisions, which flip the block to negative-(semi)definite — so the assembled "PSD-projected" hessian could contain non-PSD contributions. This was found via a GPU-vs-CPU hessian parity mismatch that reproduces on the cube (axis-aligned edges → m == 0 exactly) with IMPROVED_MAX_APPROX + area weighting + CLAMP/ABS projection.

Fix

Project the block like the other paths. Because m == 0 (⟺ ‖cross‖² == 0) is a global minimum of the mollifier, hess_m = ∇²m is PSD, and f = f(d) > 0. The block is therefore a scalar multiple of a PSD matrix, so its PSD projection reduces to projecting the scalar weight·f:

• NONE → weight·f · hess_m
• CLAMP → max(weight·f, 0) · hess_m (negative weight → zero)
• ABS → |weight·f| · hess_m

No eigendecomposition is needed, so this is also cheaper than a general projection in the common parallel-edge case. NONE behavior is unchanged, so existing finite-difference gradient/hessian tests are unaffected.

Testing

• Added a regression test that asserts the assembled CLAMP hessian is PSD for a cube under IMPROVED_MAX_APPROX (exercises the m == 0 branch). It fails before this change and passes after.
• Full [barrier_potential] suite passes (7418 assertions, 13 cases).

🤖 Generated with Claude Code

[Copilot]

Pull request overview

Fixes a missing PSD-projection in NormalPotential::hessian() for the mollified m <= 0 early-return path (parallel-edge case), which could previously inject non-PSD blocks into the assembled Hessian when using negative-weight collisions (e.g., IMPROVED_MAX_APPROX with CLAMP/ABS projection).

Changes:

• Update the m <= 0 early-return branch to apply PSD projection by projecting the scalar (weight * f) and scaling hess_m accordingly (avoids eigendecomposition for this case).
• Add a regression test asserting the assembled Hessian is PSD for a cube under IMPROVED_MAX_APPROX with PSDProjectionMethod::CLAMP.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
src/ipc/potentials/normal_potential.cpp	Applies PSD projection logic to the m <= 0 mollified Hessian early-return block via scalar projection.
tests/src/tests/potential/test_barrier_potential.cpp	Adds a regression test to catch non-PSD assembled Hessians caused by the m == 0 early-return path under negative weights.

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[codecov]

Codecov Report

❌ Patch coverage is 83.33333% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 96.58%. Comparing base (aa89460) to head (f9e4ef2).

Files with missing lines	Patch %	Lines
src/ipc/potentials/normal_potential.cpp	83.33%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #244      +/-   ##
==========================================
+ Coverage   96.51%   96.58%   +0.07%     
==========================================
  Files         163      163              
  Lines       16651    16656       +5     
  Branches      920      922       +2     
==========================================
+ Hits        16070    16087      +17     
+ Misses        581      569      -12     

Flag	Coverage Δ
unittests	96.58% <83.33%> (+0.07%)	⬆️

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