Refined P3P solver, and a new implementation for rel_pose_upright_3pt

[yaqding]

Refined P3P_ding solver. Compare with default solver with Newton refinement: without Newton refinement: Performance on real dataset. Slight improvements over the existing solvers. First sequence AUC5 89.57 vs 89.48 and more efficient. Latest implementation: Default P3P solver: Original p3p_ding by Mark Shachkov:

A new implementation for rel_pose_upright_3pt solver based on intersections of conics. Default solver: New implementation:

[pablospe]

Check C++ formatting: https://github.com/PoseLib/PoseLib/actions/runs/7908740484/job/21612424100?pr=93

You can run this line at the top-level in the repo: https://github.com/PoseLib/PoseLib/actions/runs/7876199471/workflow?pr=92#L31

[yaqding]

Thanks! It should be fine now.

[S-o-T]

@yaqding thanks for refinement!

I took a quick look over changes and found out that ensuring BC is largest is enough to make current implementation as stable as lambda twist (according to poselib internal benchmark).

Regarding posebench results - i failed to reproduce numbers you posted, all 4 implementation yielded the same AUC5=89.48 on eth3d_130_dusmanu, but it looks a strange given that current implementation is a bit less stable then lambda twist. I will try to find some time to recheck that.

[yaqding]

@S-o-T The little difference in the posebench is possibly due to the different random samples in different machines. After using std::array instead of std::vector, now the runtime is ~209ns.

[pablospe]

It seems it is still complaining about the formatting. https://github.com/PoseLib/PoseLib/actions/runs/7927921250/job/21649068111?pr=93