#61 Moments of Inertia wrong?

[Jens Biele]

Hello,

I have the suspicion that the Moments of inertia (tensor/axis momenta) are not calculated correctly by Meshlab,

Example sphere (result is well-known: all axis momenta must by 2/5, since radius=1 and mass=1)
I created a sphere with Filters/Create new mesh layer/sphere. Radius 1, subdivision level 4.
Then, Filters/quality measures and computatinos/Compute Geometric measures give the output below, with correct volume, surface, center of mass, principal axes (well, just weirdly ordered), but axis momenta of 1.67 which should be 0.400000000000. The ratio between these values is approx 4*pi/3=4.1888 - coincidence?

kind regard,

Jens

Applied filter Sphere in 37 msec
OUT OF SCOPE
Mesh Bounding Box Size 2.000000 2.000000 2.000000
Mesh Bounding Box Diag 3.464102
Mesh Volume is 4.179739
Mesh Surface is 12.551390
Mesh Total Len of 7680 Edges is 579.833069 Avg Len 0.075499
Mesh Total Len of 7680 Edges is 579.833069 Avg Len 0.075499 (including faux edges))
Thin shell barycenter 0.000000 -0.000000 -0.000000
Center of Mass is -0.000000 -0.000000 -0.000000
Inertia Tensor is :
| 1.669487 -0.000000 -0.000000 |
| -0.000000 1.669487 -0.000000 |
| -0.000000 -0.000000 1.669487 |
Principal axes are :
| 1.000000 0.000000 0.000000 |
| 0.000000 -1.000000 -0.000000 |
| 0.000000 0.000000 -1.000000 |
axis momenta are :
| 1.669487 1.669487 1.669487 |
Applied filter Compute Geometric Measures in 140 msec
Started Mode Get Info

[Jens Biele]

I think I found the solution: Meshlab assumes unity density, not unity mass, thus the Moments of inertia have to be divided by the volume of the mesh, then it's for unit mass.
Then you get 0.4 for a sphere as should be.
J.