Optimized curvature calculation

[Miraclelzk]

The original curvature calculation only rotates the coordinate system to the three directions of x, y and z to fit the quadratic curve.
It is modified to rotate the coordinate system to the local normal direction.

The curvature of a sphere

Before modification

modification

Avoids systematic errors in coordinate system fitting and provides better calculation results

[dgirardeau]

Good catch! However, in addition to the syntax, we would also have to fix the fact that 'm_quadricEquationDirections' shouldn't be a simple set of 3 dimensions (indexes). We should probably remember the rotation matrix as well... I'll work on this and push an additional commit.

[dgirardeau]

And now I realize it's not possible to store this matrix as it depends on the local normal 😅 . I'm a bit puzzled to understand how this works without changing m_quadricEquationDirections ...

[dgirardeau]

Ah no sorry, it's just that you were re-calculating the rotation matrix for every point, but actually it's a constant matrix and should only be computed once! I'll keep pushing in this direction then.

[Miraclelzk]

What I did was actually rotating the coordinate system of the quadratic curve.
I hope this will be of some help to this project.

[dgirardeau]

See my other version here: #118

With:

• syntax fix
• no new method initFromParameters
• proper management of the case where the normal is close to (0, 0, 1)
• improved numerical accuracy
• an unrelated bug fix (in SquareMatrix::inv)

I realized that the choice of 'Y' (named 'axis' in your PR) changes quite a lot the results... So I eventually kept your way of initializing Y/axis as it gives an (almost) consistent behavior on the whole cloud.

[dgirardeau]

Ok I've merged the other PR (118). So normally your commit and my updates are already merged into master. I'll decline this PR.

Thanks for the contribution!