Tetrahedralization of a beam

Hi there Grasshopper people,

As for my line of research, I am currently working on the numerical integration of matter by different methods.

Apart from some other developments, I have finished the attached piece of code:

discretization-transf-matrices.gh

Basically, its purpose is to geometrically prepare the basis for a set of tetrahedra distributed along a beam. The beam gets defined by two points, and the rest of its geometrical properties are hard-coded but can be easily brought out as input parameters in the component. This is just for the case anyone feels like experimenting...

I find it interesting as an exercise with rotation and translation matrices and is likely in the future I might have another using quaternions instead.

I have explained a little bit more in my blog (www.stochasticandlagrangian.com), but I think the comments in the code are self explanatory...

The images below show how a prism can be composed of five embedded tetrahedra, which we will later utilize to implement the material properties of a beam or whatever other use we want to give to it.

I personally will calculate their rate of deformation when forces are applied to them for imlpementing a Finite Volume and a Finite Element Methods environment into GH.

Well, enjoy!