Hi, sorry, I don't have anywhere else I can ask this.
https://www.reddit.com/r/ArtFundamentals/comments/rf4v63/hi_sorry_i_dont_have_anywhere_else_i_can_ask_this/
2021-12-13 02:31
hanareader
If this is against the rules just delete.
In Scott Robertson's book, How to Draw, on pg 75 he has an example of a box with a rotating flap. The box is pretty simple to draw but I can't figure out how he knows he is drawing a perfect square in perspective (in order to place the ellipse that tracks the rotating flap). I put the example of what I mean. The blue square is in perspective, the only line not foreshortened is probably the center line in red. I guessed here but how can I know for sure that it is in fact a square in perspective? Thank you for any help in advance,
Uncomfortable
2021-12-13 20:19
While the question isn't exactly drawabox related, we do tackle similar concepts so I'm approving the post.
We explore the concept of testing whether our planes are squares in 3D space in the 250 cylinder challenge, as well as in Lesson 7, but basically there's two criteria that we can check to either prove or disprove that the plane you highlighted in blue actually represents a square in 3D space (and therefore the ellipse within it would represent a circle in 3D space). Both criteria focus on the ellipse itself.
First, the ellipse's minor axis must align to the vanishing point that governs lines perpendicular to the plane's surface. In this case, that would be the right vanishing point of the scene. If you're unsure of why that is, read through this explanation of the relationship between the minor axis and normal vector in the context of ellipses.
If the minor axis is not aligned in this manner, then we'd have to change its rotation on the page until it was. Then we'd check the next criterion.
The second point involves looking at the points at which the ellipse makes contact with the top and bottom edges of the plane itself. Identify these two points, then find the line that passes through them. This line, the "contact point line" should align to the vertical vanishing point, which in this case appears to be at infinity, making all vertical lines run straight up and down with no convergence.
If we test these two criteria against the ellipse you've drawn in that plane, as shown here, you'll see that neither fit. Both the minor axis line and the contact point lines are misaligned - but that doesn't mean the plane itself doesn't represent a square in 3D space. Since both are off, it might simply be that the ellipse was not drawn correctly. If on the other hand our minor axis were aligned correctly but the contact point line was still way off, then the plane would simply not represent a square.
So, if we correct the alignment of the ellipse and adjust its degree to still touch all 4 edges as shown here (I've got a load of critiques to tackle today, so I didn't have the time to line this up perfectly, but it was close enough), then we can see that this does actually bring the contact points more in line as well. There's still a bit of a margin of error there, but it's fairly small, and could be accounted for by the ellipse not touching all 4 edges perfectly.
Alternatively, the plane itself could still be slightly off, but I'd call this plenty close enough to work from, as these methodologies aren't really designed to produce perfect results. For that, we'd rely on everything going back to the vanishing points. The approach we employ in Drawabox, and that Scott Robertson speaks to in his book, is more about having a "correct enough" perspective to be able to build up your constructions organically without having to plot every little thing back to the vanishing points.
I hope that clarifies things a little.
Airveazy
2021-12-14 02:27
Try drawing the oval on the side of the flaps vertical or horizontal, the larger one its kind of slanted
hanareader
2021-12-14 21:52
yeah, uncomfortable just showed me the big one is wrong, i never even noticed, thanks
hanareader
2021-12-13 23:48
I think so? I appreciate you taking time out of your day to explain it to me. I didn't even recognize my ellipse was wrong. I guess my question is if i wanted to draw a rotating flap, where do I start? Like if I have a box here what can I do next to get a hinge? I feel like there is nothing I can do, I need to define a perfect square in perspective to place an ellipse or use an ellipse to find a perfect square...The only thing I can think of is arbitrarily measuring the edge most closest to me because its the least foreshortened to find the top and bottom points of my ellipse and then the top edge of this rectange is my new minor axis. But how can I complete the square? Is the answer that I just guess? Thank you for your time again
Uncomfortable
2021-12-14 00:26
Here's the jist of how I would tackle that problem, using the concepts I shared previously. As with those, this is not 100% precise for reasons that will become clear.
Main things to keep in mind:
We have the radius in 3D space of the circle we wish to draw. It corresponds to one of the edges of our box. I've chosen the depth, and am going to figure out the ellipse we need in order to rotate along the "width" as our rotational axis. This would of course also require us to repeat the same process, finding another ellipse, for the corresponding depth edge on the far side of the box.
With that radius, we can find what would be "double" that distance in 3D space by using this technique from Lesson 6. The example there uses the technique to subdivide the plane at specific distances from either side, but we can use the same principle to duplicate a distance.
We cannot trust that the height of the box is equal to the radius. They look similar on the page, but we have no actual reason to be able to trust that, so we must not. Therefore we have to transfer the distance of the diameter from one dimension (depth) to another (height), and in a sort of backwards fashion, doing so requires us to actually draw the ellipse we're trying to figure out in the first place. We use this technique in Lesson 7, specifically this video to create a 3D unit grid.
This leads to the reason behind my lack of precision - I don't have enough information to draw the ellipse easily. I have the left and right vertical edges, and I know how the ellipse's minor axis needs to align, but if I draw the ellipse with different degrees, it'll impact the height of the plane that would enclose it.
I know that the points at which the ellipse touches those top/bottom edges should align towards the vertical vanishing point.
So, I draw an ellipse while trying to approximate where those contact points will fall. Without actually drawing those top/bottom edges, I can't actually see clearly where the contact points would be, but I can get rough idea. You could eke out more precision/accuracy if you had a couple rulers in addition to an ellipse guide to test it all out, or if you drew the edges in pencil, tested them with the ellipse, then erased them if they were wrong - but I've been working as an artist for a number of years and I have yet to come across a situation where that would be a worthwhile use of my time.
The ellipse I approximated did end up being imperfect (the degree should have been narrower, resulting in a taller plane/ellipse), but it was still fairly close, with a pretty small margin of error. I wouldn't be against using that as the ellipse for my rotation, or the plane enclosing it as a representation of a square in 3D space.
hanareader
2021-12-14 02:28
I see. I forgot that we can mirror the radius in space. It didn't sink in that the top/bottom points of the ellipse are aligning towards the vanishing point. I think if there's too generous a margin of error that I don't even need to hit the contact points itll be impossible for me to know if I did anything right, haha. I think I will practice more so that I can better intuitively know what degree I need. Thank you for answering all of my questions. I had been struggling with this problem for a while now.