0
$\begingroup$

There is a sampling pattern used in FEM method for triangles, which can be seen here:

enter image description here

The rough description is that at each edge we have n samples (containing the endpoints) and then in the interior the number of samples remains roughly uniform.

The equivalent for the square is just a regular grid of points, like this one:

enter image description here

What I am looking for is, given a number $n$ and a regular polygon with $n$ sides, a rule such that:

Each side of the polygon has $n$ samples (including the endpoints), the interior is regularly sampled (i.e. the minimum distance between points is bounded).

I am not having much luck finding out how to do this.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

If it is a regular polygon its barycentre $c$ can be found by calculating $$c = \frac{1}{n}\sum_{i=0}^n v_i.$$ Then you can construct $n$ triangles $c,v_i,v_{i+1}$ which can be regularly sampled like the triangles you showed.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.