Cross field singularity index violates Poincaré-Hopf theorem
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Description
Describe the bug
The singularity index computed via igl::find_cross_field_singularities is always positive, which leads to the violation of Poincaré-Hopf theorem (section 3.2 of [1]).
The original discussion and unit tests is from https://github.com/libigl/libigl-python-bindings/pull/295
Platform
- Windows
- macOS
- Linux
[1] Vaxman, Amir, et al. "Directional field synthesis, design, and processing." Computer graphics forum. Vol. 35. No. 2. 2016.
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Research direction
Start at the implementation of igl::find_cross_field_singularities and review the discussion and unit tests in libigl-python-bindings PR #295. Reproduce the reported all-positive indices on the relevant cross-field examples, then verify that the corrected signs satisfy the Poincaré-Hopf theorem and that regression tests cover the result.
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Assessment
- Tech stack
- cpp
- Domain
- computer-graphics
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Quiet
- Clarity
- Mostly clear
- Newbie friendliness
- 48/100