> - Choose a basic probability p.
> [...]
> - Calculate the area A _OF THE IMAGE_ that the triangle P0-P1-P2 would
> [...]
> - Put a tree with probability p/A. Beware of division by zero.

I was previously in a hurry. Here is a more refined version:
Let A0 be the area of the image between three ,,adjacent'' rays.
Let d be the desired density of trees, i.e. in average there
should be one tree in an area of 1/d.

Then put a tree with probability d*dx*dy*A0/A, i.e. choose p=d*dx*dy*A0.

Regards,

  Mark

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