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No matter how much I fiddle with it, I can't seem to grasp fully how to use the perspective: 4 points FX.

I've looked in the book and there's not a whole lot of explanation.

That bar that floats around in the background of the 4 points, what's that supposed to be and why does it swing around wildly when I'm adjusting one or two of the points?

What are the specific definitions of each of the 4 points? I.e., what do they represent exactly?

Does anyone have a solid grasp of this FX? I think it's probably superb, but when I use it, it's a hit or miss thing - I don't really know what I'm doing.

Thanks for your help; you're always there when I need you.

That blue line is the horizon, when you set it to "fill", not "once".
There are two handles on that blue line, they represent the vanishing points of the perspective.
You can move them.
It is much easier to understand how it works in "fill" mode.

Oooooh! Now I get it! Thank you so much, ematecki. You've succinctly cleared up the mystery for me.

I can't seem to find where I 'set it to "fill," not "once."' Where do I do this?

Added note: I'm not using the perspective FX for drop shadow, but I was hoping to use it to make an image diminish in size toward the horizon.

At the top there are tabs called "Position" and "Render".
In the Render tab there is a check box called "Fill", that's the one.