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What I would like to achieve is the generation of a mesh of data points (of some resolution) on the faces of a polygon/polytope. I specifically need points ON the faces as I would like to do a transformation of the initial shape through some equation.

The problem is closer to linear programming than geometry, per say, as the initial shapes are defined by inequalities. I'll use a simple example of what I want to achieve:

For the inequalities;

x,y,z > 0

x,y,z < 1

x+y+z < 2

a unit-cube is generated from which the one corner is 'cut off'.

The vertices of this shape are;

(0 1 0), (0 0 0), (1 0 0), (0 0 1), (0 1 1), (1 0 1), (1 1 0)

and its clear that it has 7 faces (4 triangular- and 3 square-shaped). It is on these faces that I would like to generate extra data points (seeing that I only have the 7 vertices at the moment).

My example uses just 3 dimensions, but eventually I'll go up to even more, so my approach needs to be rather generic.

At the moment I am stumped, as all the routines/algorithms I've looked at are very data-driven and focus little on extra data generation. Any suggestions, ideas or pointers to other sources will be greatly appreciated.

Ideally I'd be looking for Python modules, but if writing a wrapper for some C/C++ code gets me what I want then so be it.

Thanks

André

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# Tiling the faces of a polygon/polytope

Can you offer guidance or do you also need help?

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