EVSM

[monte165]

Can someone explain this paragraph from here http://www.punkuser.net/lvsm/lvsm_web.pdf ( 7 Other Warps)

“For instance, it is interesting to consider the exponential warping function e^(cx) (where c is a constant) as suggested by [11], but still using a second moment and Chebyshev’s Inequality. This warping has the effect of relatively moving object B toward object A which reduces the above ratio. The resulting exponential variance shadow map (EVSM) has greatly reduced VSM-like light bleeding while still avoiding any bleeding near occluders.”

I can see why the ratio reduces using exponentials, but I don't see why is it because of this - “This warping has the effect of relatively moving object B toward object A". The paragraph right after that one isn't the clearest either but I would like to understand this first. Is there some shadows expert here that could explain this?

Thanks.

 

[monte165]

Just to be clear, I don't understand how why does this happen and what does it mean - " “This warping has the effect of relatively moving object B toward object A".
But what I think I understand is that using exponentials, the ratio will get smaller than without exponential because
ratio of exponential ratio and regular ratio is always less than 1:
(c-b)/(b-a) * (exp(k*b) - exp(k*a))/(exp(k*c) - exp(k*b)) < 1 for a < b < c.
As you can see, that ratio mentions object C depth, but paper mentions only A and B in that paragraph.