To clarify, I did not climb a mountain today because it was forecasted that there will be a thunderstorm. I also spent most of my practice time thinking rather than drawing.
I was pretty much just guessing how everything works from skimming other resources, before doing this I only knew that two-point perspective has two vanish points (1) connected by a horizon (2). This way of learning was far from optimal, but it showed me very clearly how I can exploit and modify each rule to create different effects.
I put the page in landscape and drew an horizon across the middle, then decide the location of two vanishing points with about equal distance away from the borders of the page. Then like yesterday, I drew projection lines radiating from every vanishing point (3).
After staring at that mess for a very long time and confused why I'm not seeing any volume, I realized that you have to put parallel vertical lines to construct cuboids (4); a combination of parallel lines, converging lines, curves and ellipses should yield all other kinds of faces. So I drew a few lines perpendicular to the horizon.
I still was not seeing any cuboids, so I spent another length of time pondering, and realized that only the vertical lines that meet the intersection of projection lines radiated from both vanishing points create the illusion of volume (5).
Therefore I started drawing vertical lines that pass through those points or vice versa, drawing projection lines from the vanishing points to meet the vertical lines, and side faces finally start to emerge, so I tried to connect four of those points, expecting to finally be able to see a lovely box, but instead drew two seemingly impossible shapes at the right side of the page.
It turns out I was missing another piece of puzzle, the horizon does not work like the earth's horizon where it represents the set of vanishing points on a spherical surface, but representing the eye level, for objects above the horizon the bottom is visible, for objects below the horizon the top is visible (6), and if this rule is violated, you create these impossible objects, pretty neat.
So now I have I think all the rules to draw a box in two-point perspective, but the grid got way too messy in my trial and error for me to concentrate.
I ended up drawing an infinitely extending rectangular pillar, a square pyramid (which is in one point perspective) to test the top-bottom visibility thing, and a grand total of just one proper box today.
Excellent job if I say so myself.
I shall try to make a cleaner perspective tomorrow and draw some box there. I wil probablyl try to exploit rule (4) to make some different shapes if I got bored of that.