Intercept method - "Random" Lines
This is getting down to nuts and bolts a little bit here, but I'm trying to investigate the biases that different sampling methods have, and I'm curious. The algorithm that generates random lines for sampling object intercepts... How does it work? Related: https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)
I've found that for this kind of random generation:
Select a random point in the image
Select a random angle to draw this line at, starting at this point
The center of the image is biased by maybe ~85%, ish. Not that this is a bad thing, but I am curious.
If random points outside the image are allowed to be selected as the center for the line this bias decreases, but it's less likely that a given line will actually intersect the image at all.
I'm trying to write a short technical paper that describes this. What does MIPAR do to generate these lines?