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

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Mady
Mady 2024-11-13
评论： Matt J 2024-11-13
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?
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Mady
Mady 2024-11-13
Yes exactly, sorry I defined it wrong. Polygonial face of a volume defined by its vertices (3/4/5/6... points).

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Matt J
Matt J 2024-11-13
编辑：Matt J 2024-11-13
Ran in:
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
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
v=planarFit(V').project2D(V'); %2D vertices
p=polyshape(v');
area(p),
ans = 0.8660
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Mady
Mady 2024-11-13
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
Matt J 2024-11-13
You can use triangulation to decompose the polyshape into triangles and then add up the moments of inertia of each triangle.

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