i made this diagram of using special vanishing points to measure out a cube in perspective. how exactly does it work. i know that it works, and in my diagram swinging an arc of a line from the left vanishing point to the station point up to the eye line makes kinda makes sense to me. but it's the right measuring point that i'm having a harder time visualizing. when the vanishing point is so far off canvas that drawing a line to it is inconvenient, this method where you divide up lines to make a perspective grid, and then use the halfway line and run a perpendicular line through it running from the station point to the eyeline is the part that's harder for me to internalize. i get that it works, but why?
upon further thinking, i realized why the perpendicular line works. if you slip an arc in half, and then run a perpendicular line through that bisection with the end points being the station point, and its intersection with the eyeline(RMP), it intersects at the same point as running the arc of the line from the vanishing point to the station point up to the eyeline.i guess my question now is, why is it that a line equal to the distance from the vanishing point to the station point on the eyeline allows you to use it as a vanishing point for taking lines out of flat space and into perspective.
after another day of deep thought and some geometry, i understand why it works now.in flat space, the angle that would divide the vanishing point line by a certain amount on a measuring line is parallel to the line running from the station point that is derived from the arc of the line running from the vanishing point to the station point up to the eye line. and given that all lines coming from the vanishing point are parallel in perspective to that angle in flatspace, it reasons that so to is the case for the lines that come from the measuring point and intersect those lines in perspective. thanks /ic/ i knew i could count on you to answer these sorts of technical questions.
Dude perspective is so fucking based. It's literally a rigid methodical process you have to follow to a T. People who think "artists" are so heckin creative and free-spirited never produced a single image in their lives that had correct perspective.
>>7996972I mean, it is a hard answer. I tried to come up with something, but the picture plane is just as flat a representation of our world as I see it. The angles work because they are projected to the flat world. However, your question is way deeper than just the formal perspective that we use for art, as you want a more geometric understanding of WHY these angles work. Some of us aren't engineers enough, my man.You might have better luck letting your questions on >>7987435I saw people go deep on how geometry/perspective works for the vanishing points there.
>>7995940Lol do you need a paper the size of a table to do that? I feel like this is more of a traditional CAD method. Your canvas is 80% grid and guides and 20% your drawing.
>>7996972I had a crack at it when you first posted. More than half the time I spent was trying to interpret what you were asking. What you write is mostly unambiguous after some work, but it doesn't come easily. There's a reason geometry folks refer to points, angles, and segments the way they do.Your diagrams certainly help but it takes some work to interpret them. The use and implications of your two green 45 degree triangles in your first image, for example. You're really relying on someone's familiarity with this process here. So you limit your pool of responders to geometry buffs who are also perspective buffs.To be fair, though, had you phrased the question in a more friendly way, you may not have received any answers anyhow.Interesting questions, though. I read them and attempt them sometimes.
