Geometry properties in 3D (area, volume, moment of inertia...)

Hello, I'm trying to work with 3D discrete models in matlab (RBSM, LPDM...) and I am struggling to find certain properties necesary for calculation. For example, when I have a plane in 3D defined by points/vertices, is there a way to find its area or moment of inertia? I am well aware of my areas for improvement in planimetry or linear algebra, but if anyone could recommend me if there's a function in MATLAB or point me in the right direction, I'd be grateful.

In the past, I used the functions for polyshape objects, is there something similar for 3D?

[Matt J]

plane in 3D

Do you mean a polygon in 3D? Planes are things that extend infinitely, and have no vertices.

[Mady]

Yes exactly, sorry I defined it wrong. Polygonial face of a volume defined by its vertices (3/4/5/6... points).

[Walter Roberson]

Where's @Roger Stafford when you need him...

Answer 1

[Matt J]

You can project your planar points into a 2D coordinate system and then use whatever 2D methods you had used previously to compute desired quantities. I would suggest planarFit() from this FEX download to help,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-to-fit-plot-conics-and-quadrics?s_tid=srchtitle

Example,

V=eye(3)  %Triangle in 3D

V = 3×3

1 0 0 0 1 0 0 0 1

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v=planarFit(V').project2D(V');  %2D vertices

p=polyshape(v');

area(p),

ans = 0.8660

[Mady]

That tool looks useful, thank you. However, in my problem only partly gives the desired solution. For the area calculation it is great I think, but in case of moment of inertia, there would be one direction missing (the shape could rotate around 3 axis in 3D, which cannot be captured in projection to 2D, right?).

[Matt J]

You can use triangulation to decompose the polyshape into triangles and then add up the moments of inertia of each triangle.