I don't know how many times I've watched this video... And over a month! But this time I think I finally got it.... PHEW.

One Point Wide Angle Tests.

DOES THIS WORK? the top of the box is divided in four parts by the x made by the two vps crossing over it. I imagine that the box is made of some gelatinous substance, stretchable. If i imagine myself standing over the whole thing like a giant standing behind the viewer ( the whole thing, so viewer and box and vps as drawn on the paper are like on a table in front of me ) if i move the two vps closer together by sliding them in the pp I have to bend forward towards the pp (bend over the table where the paper is) so i move closer in a way to the pp, also if the cube is made of a gelatinous ans stretchable substance, it can stretch along the mouvement of the x, and what happens to the portion of the top of the cube as delimited in-the top section of the x? well it's compressed by the pinch mouvement of the x.. the said section becomes narrower and as a result the substance extends toward the pp. i wish i had the time to animate this: i bend down, i push the vps closer together and the part of the cube inside the top section delimited by-the x goes "sprootch" and extends towards the pp, so i get closer to the pp the vps get closer and the box get narrower and extends more towards the pp - do i make any sense? english is not my first language so apologies. all this to create the sensation of closer to pp for viewer leans closer to pp for back edge of the box and vps getting closer together. apologies

Here's a rule to remember: In 1-point perspective, the distance between the two vanishing points (called, "distance points") is twice the distance between the station point and the picture plane. As these distance points move closer together, the station point moves closer to the picture plane, and visual rays between the station point and the object being drawn become increasingly oblique to the picture plane, resulting in increasing image distortion. The distortion is correctly foreshortened when it is viewed from the station point and it seems to disappear because of it.

I'm really enjoying the discussion here, especially the excellent contributions from @Anthony Hernandez and @Dedee Anderson Ganda, as well as the rigorous solution-hunting by @M C and @Michael Giff. I'd like to toss in my two cents, in case it helps anyone. Let’s take a simple case: projecting a square in one-point perspective. Setup: We start with a square. We choose the viewer’s position and decide where we want the projected square to sit on the ground. We have three tools in our perspective toolbox: 1. Projecting points from the orthographic (ortho) view down to the picture plane (PP). 2. Lines of sight that converge toward the central vanishing point (VP). 3. Diagonal lines at 45 degrees to the square, converging to two side vanishing points VP1 and VP2. These are the red points in Marshall’s video. By combining any two of these three tools, we can construct the one-point perspective view: 1 + 2: Use verticals from the ortho and lines converging to the central VP. 1 + 3: Use verticals from the ortho and lines converging to VP1 and VP2. 2 + 3: Use just the lines converging to three vanishing points, VP, VP1, and VP2. In every case, we end up with the same projected square, as expected. 4. In the third method above (2 + 3), let’s strip away the ortho entirely. We’re left with just the base of the square and the three vanishing points. 5. We can still reconstruct the same projection, just as Anthony beautifully demonstrates in his diagram below. This is what Marshall is walking us through in the video. Now, what if we move the viewer farther from the picture plane? 6. Using the 1 + 2 method: the farther the viewer is from the PP, the flatter the projected square appears. Distortion is controlled by how close or far the viewer is to the PP. The closer the viewer, the stronger the stretch. 7. Here's the fun part: moving the viewer by a distance d away from the PP is equivalent to moving VP1 and VP2 by the same distance d away from the central VP. That’s why adjusting the spacing of those red points controls distortion. And that’s why we can get away without the full scaffolding of orthos once we understand the system. 8. We can always recover the viewer’s position from the two red dots, or the two red dots from the viewer’s position, because there is always a fixed relationship between them. The distance of VP1 and VP2 from the central point VP is the same as the distance of the viewer from VP.

I think I got the gist of it. But when I imagine rotating the box and made it into two point, while using the same trick, it should lead to the same result. But it feels wrong. It might be too much of a workaround method, since its better to move their original vanishing points instead of the diagonal lines right? But on top of that, I think the mystery is not finished? When looking at the zolly app's result, the more closer the viewer is to the box, the more distorted the upper X lines of the box. They grow wider horizontally. I think what happened is that in zolly preview, there are 2 vanishing points instead of 1, the 2nd one is for the Y lines!!! Ohh my goshh, I GET IT. What happened is: The distance between horizon line's vanishing point and the 2nd (Y) vanishing point shrunk! But wait a minute.. I can get that when the 2nd (Y) vanishing point gets closer, the upper angle gets more acute.. But why does the upper X lines grow wider??? This is mind boggling

Thanks for the explanation, have I got this thought correct? So this is the how rail tracks, fences, trees etc, going into the distance are sized with respect to the viewer in perspective using diagonals is derived ?

I think I got it. I wondered why did we not point to the center of the object, but I realized that would only work if you are fully center. If there is some displacement to the left, such that it is still 1PP but not fully center, it will not work. I experimented with it, and sure enough, I got A solution.

Are we essentially setting vanishing points for measured angles onto the horizon line. In this case a 45 degree measuring point or vanishing point which we can use to draw any square with the same distortion within our created world so to speak? If we chose. I believe if this was a rectangle and not a square we could still measure the diagonal, set the same angle from the view point and then project it onto the picture plane then transfer it onto the horizon line. Is this correct?

is this satori? help welcome

crying in my vegan root beer! I dont get it anymore, my viewer (cyan) is all over the place! help

me again: trying to do things without math as Marshall said to intuite;. Once again: THE VIEWER CAN'T POSSIBLY BE THERE!!!! what have I drawn????? this is scary! help!

Have I mentioned that this dunce hat is very heavy? I know it's just a paper cone but I've been wearing it for 8 months, it has to be someone else's turn by now. Why do we care about the wedge shape that appears on the box? My whala moment is more, wha? than la.

as authorized by Marshall: here is my imagination wild! Do I make any sense?

OH MY GOD!!!!!!!!!!!!! 🙀this is BIG!!! suddenly I can FINALLY imagine the acute to obtuse or to flat etc etc dance around the horizon! I CAN FEEL IT!!!!!!!!🙀🙀🙀🙀😻😻 next step: imagining this dance with a figure in the box like kim jun gi (something that is scifi for my brain) many thanks Marshall Sensei! (or Marshall Sifu if you prefere kung fu to karate lol)

Is this the whole using one point to find different 90 degrees sums to find boxes at different angles. I remember all this it was in my how to draw book.