# moment of inerta tensor for polygonal objects

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I'm working on an open source progect with a game engine that was developed sevral years ago, and we were not given all of the code for all of the tools, we've done quite well with what we were given, but a thing that has been a problem for some time now has been the moment of inerta settings for the object files. it is in the form of a 3x3 rotation matrix, wich I have been over the last few days learning is a tensor, and I have seen a bunch of poorly explained formulas for calculateing it, so now I will pose this question; what is a good way to calculate a moment of inerta tensor for an object composed of polygons(assumeing dencity is uniform)? I'm thinking if the object is broken down into triangles and I integrate each triangle as it is scaled to 0 summing the volume each makes (inverting the volume of triangles that face the origin) all I'd need is something that could give me a moi tensor for a triangle in 3d space (or the described volume made by it and the origin) the values I've got for the exsisting models are extreemly small, in the 10^-4 range for the central diagnal, and 10^-8 for the product of inertas on an obect in the < 50 meter size, the bigger it gets the smaller these numbers get. [Edited by - Bobboau on October 2, 2004 8:15:03 PM]

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Brian Mirtich developed a nice technique back in 1996, documented in the Journal of Graphics Tools, Volume 1, Issue 2. Here is a web page with a downloadable version of the article, as well as C code. I'd suggest you consider using this!

Fast and Accurate Computation of Polyhedral Mass Properties

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