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I am an engineering student trying to write a simple visualization program for a rigid block model subject to earthquake loading (using discrete element method). Now my DEM code is capable of outputting the displacement for each of the vertices in each block (each block being a 12-sided prism). However, I would like to minimize the data that I write to the disc and was trying to see how many vertices per block are needed to completely recover the displacements at all vertices and calculate their position (thus finding the entire block position and orientation).

After thinking about this problem I realized that I will need at least three points. It is embarrassing that it took me a while to figure this out since it seems rather obvious and this is stated everywhere (you need three non-collinear points).

Now I am trying to understand how I go from the three-components of displacements at three vertices to calculate displacements at the remaining vertices. So if I imagine a cube, this means that I will need to calculate the displacement of the 5 remaining vertices and then move those points to the appropriate coordinate to get the final block position.

As you can see I am not the brightest bulb around, so I would appreciate a very low-level explanation with as much real examples so I can understand what is going on. I had taken a linear algebra class many years ago and I was pretty bad it even then. Hopefully I can start over again.

Regards, Al

PS: I asked this question on mathOverflow and it was recommended that this is a better forum for this type of question. Hopefully that is okay.

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    Your blocks are 12-sided prisms? What shapes are the cross sections? Are the displacements associated just with the block itself, or is there a unique displacement for each vertex?2012-06-21
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    Well most of the blocks are 12 sided. The cross-sections are irregular convex polygons. The displacements are associated with each vertex but since all blocks are rigid, they really describe the motion of the block itself.2012-06-21

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