For reference: I'm incapable of thinking spacially. Not sure why. Nonetheless, I've been on an adventure to basically teach myself to think spacially using a bunch of dirty geometric tricks. This is one of them.

One of the problems I've always had comes from trying to figure out how a given shape is supposed to be bent into perspective using foreshortening techniques. The question that's always been in the back of my mind is "well, where is it supposed to end to make it accurate?" I've never really gotten much of a clear answer. Most of the time it's "it comes with practice" or "you'll figure it out," that sort of thing. And, while true, sure, you'll eventually just get a "feel" for where the proper point is supposed to be, it's unfortunately not how my brain works. So I set out to try and discover where, exactly, that mysterious "point" I've been looking for is.

This actually combines a lot of technical things I've learned along the way with inference in perspective. But for now, I'm only going to focus on the orange and blue circles you see in this piece.

The vertical lines parallel to the black line represent the two-dimensional measurements of the lines to be twisted into their representative vanishing points. As an object is rotated, it is done so in a circle. This means we can use the line we want to transform to represent the radius of a circle. To eventually draw out the vanishing curve, only a quarter arc of the circle needs to be drawn. That's the first outer circle you see.

The outer curve represents where the transformed line is supposed to land without foreshortening. This will assist us in trying to understand what happens to the line we want to transform into perspective as it winds up being rotated.

We know that as we rotate an object, its outer lines shrink eventually into oblivion. Why? This is because that while the rotation can be represented as a circle, our line actually shrinks as it's being rotated. Thus, as the circle is being drawn, the radius is shrinking as well. As a result, this can be represented as a sort of odd half-circle. Drawing half the arc of the original, then drawing the curve as shown will then represent the vanishing curve.

Where the vanishing curve meets the vanishing line is how far you must draw your line in order to give it accurate foreshortening.

Really fun trick I've learned! I hope you find it useful. :)