Drawabox: Perfect Circles and Cubes in 3D Space
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- čas přidán 23. 09. 2016
- This is something that's confused me immensely for quite a while, and I've seen that a lot of people have felt the same way. Since I don't deal with plotted perspective much, I've mostly just ignored it but it has had some negative impacts on my work in the past. So, here's the results of some research I've done into the subject. In looking into how to properly construct ellipses inside of planes, I also discovered some neat tricks that allow us to easily construct perfect cubes in space - a very handy tool for building up grids and doing measurements.
Drawabox is a series of free structured drawing lessons that explore the basic mechanics of drawing, along with the fundamental skills of capturing the illusion of solid form and constructing complex objects from their simplest components.
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YAY finally, as a person with absolutely no background in drawing, I really struggled when doing homework using just "instinct" and basic perspective lessons, this helps not just a lot but like A LOT.
I'm glad to hear that.
Actually on that note, you may be interested in picking up Scott Robertson's How to Draw book. It's got loads of explanations of more technical concepts like this one. I use it as a reference whenever doing my perspective by eye doesn't quite hold up.
Thanks a bunch !! Sorry for not replying sooner I didn't had internet, I will absolutely dive into this as soon as possible :) I hope you're getting better from your surgery !
Thank you for the hard work. Every thought and idea you share with us is very beneficial.
I'm glad you find these videos to be useful!
So you need perfect circles in order to make a perfect cube, and you need a perfect cube to make a sphere
Sounds weird but seems to work
14:28 is exactly what I needed to hear today.
I was wondering how to draw perfect square before. Thanks a lot! Dunno why, but I chuckled at 14:00 when you were ghosting ellipse for a few seconds and then proceed to draw a line
uncomfortable its been almost 4 months since i discovered you and you have saved my life i consider you a very good teacher and greatly appreciate your free lessons. i finished dynamic sketching last week and i wait for your updates to figure drawing before i move forward. thank you for teaching me how to draw. i feel i deeply understand everything from your lessons up to this point, and after all this practice i can apply them with ease and success. everything but this video.... cant help but keep coming back to it..
PLEASE READ THIS
its the first time im doubting whether you might be making a mistake.i really dont understand the concept of this... how can u randomly set both vanishing points after your random ellipse aaand having the true verticals of the plane be vertical to the horizon line aaand expect it to always be a circle??
i mean (talking about the first one you start to draw) you 1.drew an ellipse with random degree and random angle 2. randomly placed its height on the horizon line to create the first vp where the horizon intersects with the ellipse's minor axis, 3. randomly placed another vp on the horizon line, 4. you are in 2 point and you are having all your verticals be verticals to the horizon line, meaning if the plane your ellipse is on was the side of a cube, the cube would be just standing on the ground/its horizontal lines would be parallel to ground. so how can all of these things be randomly placed with the restriction that your plane must be vertical to the ground, and still having it be a circle? i mean if you had made the angle of the minor axis greater, there's just no way you'd get a vertical alignment of the tangents with that specific vanishing point and that specific degree. how i see it i think the first one you did just accidentally almost had vertical tangents. cuz they werent really vertical... the ellipse's angle was just too small so it seemed like they are....
i understand the concept of making a random ellipse and setting everything after it so that its a circle, but i dont see how you set it up all at once randomly right from the start and expect it to be a circle. shouldnt you be finding one thing after another in relation to each other, so that you construct the setup for the random ellipse you made to be a circle? how is the way you drew that second ellipse different from the way you drew the first? you just did the steps in a different order. (no point in trying to align that ellipse with that specific vertical. was still just a random vertical you could have placed it after the ellipse. the result would have been the same amount of random as long as you had a set minor axis. the degree would have been different but still would be random. just a diff order of random.) i dont see any difference besides that the angle is greater so now the tangents really dont seem vertical. the vp to the right is still random. that ellipse would have worked with a different vp, just like the first one only happened to almost seem to work with that random one.
the way i understand it is that u can do this but by leaving one parameter for last, and leave it up to how the ellipse came up. i mean how else can every ellipse you make be a circle if u set everything up yourself from the start, and just connect them after? so in the case of your second drawing, it could have been a circle if its plane wasn't vertical to the ground. so you'd find the line that connects the tangents and get the true verticals of the plane from there, rather than expecting them to be vertical to the horizon. in the case you really wanted it to be vertical, you'd leave the second vp for last, and move it around to find where its tangents with the circle align vertically. or move the horizon... i really cant understand it any other way and i ve been over this thing all morning...
im not saying you re wrong, im really hoping you'd answer and explain and prove me wrong... i just want to understand. thats just the only way i can see it.
i mean, why does this even prove that the ellipse is a circle on a perfect square?? couldn't that be ANY ellipse centered to a rectangle?? meaning that it makes tangents with the rectangle right at the four true midpoints of each side? ellipses in perspective arent even perfect ellipses on the paper, only circles are. they're kinda deformed especially if the distortion is extreme we dont even draw them as ellipses. we draw them by connecting nodes with curves right? like, when u have a really long box with an ellipse centered to the long side and you see it really distorted, you cant draw an actual ellipse with the minor axis you find from the 2 centers of the sides of the box, cuz the further half of each side is just too small and the close one too large...
this got too long sorry, i hope you read this and clear some things out cause im really struggling with understanding circles and ellipses in perspective, i cant find any other videos that explain this... and im such a psychotic piece of sh!t that i cant even make a loomis head without suffering deep inside knowing that i havent really sorted out circles in my mind...
Actually, it is more a drawing hack, that has no mathematical base.
Each one, the circle and ellipse, can be in position, where their major axis is perpendicular to the ground plane. The difference is: in 3d world, when we will begin to rotate each one, the circle will remain visually exactly the same as it was, while ellipse will begin visually recognizable rotation (you can test this in every 3d software).
But the trick is: when we draw, we make a still 2d illusion of 3d space. So you can construct an ellipse that stand "straight", declare it a circle and construct whole picture/world around it. And there will be no mistake, because drawing illusion has no mathematical basis in this case.
So, a straight ellipse is a circle only because it's your drawing (=illusion) and you've claimed it to be so.
I must confess, I cannot make head or tails of his explanation here either, or how the VPs are set up or why they are where they are, etc.
wow that wall of text took longer than the video!
My problem is his 3 clicks to finish a line and misses then has to redo it like 3 times because he can't get it right the first time. Just use the line tool like damn.
5 yrs ago and this comment still hasn’t got any answer from Boxman himself :(
question: what program do u use? that doesnt seem like ps, and that ellipse tool looks really handy. thanks
It is Photoshop, but the ellipse guide is actually part of a program called Lazy Nezumi (lazynezumi.com). In addition to its main purpose, which is to steady brush strokes (I've never really found any software that does this particularly well and lazy nezumi is no exception so I don't really use it for that) it comes with some adjustable constraints, like the ellipse tool. The program runs on top of other software, so it's not tied to any one application. Very handy.
I got the Lazy Nezumi trail and set up a 2pt perspective scene in ps. Using the Ellipse Ruler I aimed the Minor Axis at the LVP and also set up 3 Vanishing Lines coming in from the RVP (Top Middle and Bottom). No matter how much I tried to adjust the Degree I kept having difficulty with getting the Ellipse to come out right. The book "How to Draw" by Scott Robertson at the start of Chapter 5 talks about how to meet certain conditions like with the Vertical Magenta Line and and the Horizontal Cyan Line, but I wasn't able to line them both up properly... It wasn't until I discovered that Lazy Nezumi had a Perspective Ellipse Ruler which allowed me to meet the Vertical and Horizontal conditions... When I switched back to the normal Ellipse Ruler and tried to match the Ellipse that I just made using the Perspective Ruler, I noticed that the Minor Axis was not lined up correctly with the LVP...
Not sure, but what led me to this video was so that I could learn why certain steps need to be taken with a given method to create a Cube. I still don't know if this Ellipse method can help me with that...
5:30 When Peter tried to throw the bullfrog out of the window.
8:06 I think in left example ellipse also is not perfectly aligned (parallel to VP at infinity), top touching point is slightly on right and bottom touching point is also slightly to the left. Seems to me that if the ellipse is having a minor axis from VP1 at any angle there will always be this misalignment.
You can check that if VP (minor axis) is closer to ellipse/plane with extreme angle and ellipse is of narrower degree.
Thank you, that bugged me while drawing cylinders. I always saw that some of them looked flat like that they are looking from in front not circles. I wanted to be sure that they are tube like. Srry, cant explain it in english very well. Anyways, thx!
Free but informative,I wanna indtroduce you to all my art mate I know
Hey this is great but I have a question as a beginner. Is it best to draw the ellipse first then the vanishing points or the other way around?
Try to think of this in the case of drawing ellipses on something that's already half-drawn. Your vanishing points will already be established (either explicitly or implied), so you're going to have to make sure the ellipse you're adding conforms to the parameters that have already been laid out. So when drawing an ellipse, I'll start by drawing a minor axis (which goes off to one of the VPs), then establish three of the lines of the plane (aligned to the other VP) in which I want my ellipse to sit. Then I'll draw the ellipse, minding my contact points and ensuring that it aligns correctly to the minor axis, and finally I'll draw the fourth line of that plane.
Thanks so much! I appreciate the help.
ive rewatched this video 3 times now and i.. i am still so confused.. how can the ellipse be at an angle and ahve the major axis be like perfectly perpendicular to the horizon line..? D: i.. what..? can someone explain to me pleaseeeeeeeeeeeee..?
vcxlll You are confusing the contact points to the enclosing plane above and below the ellipse with the major axis. They are not the same thing. We don't actually use the major axis for anything important.
IMMORTAN JONES NOTICED ME.
hmm.. but the widest points(major axis) of the ellipse should be touching the.. "true middle" of the top and bottom lines of the plane containing the ellipse, right..? i.. but it's at an angle so the widest points are at an angle too, right..? i'm so sorry i know i'm probably understanding everything wrong but i..
like in the treasure chest challenge, the "minor axis" for the "ellipse-for-swivelling" is based on the back edge of the box, but shouldn't it be the.. side edge of the box that's closest to us?
vcxlll like I said - the major axis has no bearing on anything. The contact points with the enclosing plane do not have to be the ends of the major axis, and those contact points don't need to be at any "true middle". The only two criteria you need to follow are:
1. Minor axis runs to one of the side vanishing points
2. The two contact points of the ellipse with it's enclosing plane's top and bottom edges must align towards the vertical vanishing point
I appreciate the thought here, but I think you have it backward. Establish a perspective cube--using measure point method--then draw ellipses withing. I am now trying to determine how the measure point method id derived.
The reason for this approach makes more sense when seen in the context of the other lessons on drawabox.com - basically, when drawing we avoid plotting too much back to vanishing points, measuring points, etc. because it tends to make each drawing very cumbersome, and stunts one's ability to design and think creatively. As a result our drawings tend to be less accurate (inferring an implied vanishing point from the perceived convergence of two lines definitely leaves a lot of room for error), but we're able to leverage it better when constructing our designs and communicating things visually. So here, while I refer to the vanishing points, in practice I wouldn't be.
Because of these limitations, I basically *have* to work backwards. If my goal was to be completely precise and accurate with my measurements, you'd be absolutely correct - nothing beats plotting everything out perfectly. In my experience as a concept artist however, this is not always practical.
You can see this in practice in the 'Constructing to Scale' video here: czcams.com/video/ERQ-_Xfz3yk/video.html
I have done the ghosting planes assignment and when i’m starting to do this, one of that page is missing
Not a big deal - just do another page of planes to replace it.
How it works for 3 points perspective?
It works the same as it does in 2 point perspective, except instead of being able to rely on those verticals being parallel on the page, you now have the added complexity of factoring in convergences for that axis. Although I should add that while in practice it's still largely the same, the use of an ellipse to represent a circle in 3D space does start to distort/break down somewhat. It's still close enough to be the better choice (in the sense that worrying about accuracy to reality beyond that wouldn't be of any real benefit), but it's worth mentioning it anyway.
So... how do I know it's actually a "perfect" circle (in perspective) and not a random oval especially if I don't use a circle/ellipse tool? Wouldn't I technically have to construct a perfect square first in order to make sure the radius of the circle is the same on every side? I know this demonstration isn't 100% accurate but "close-enough", just wondering...
That's unfortunately outside of the scope of this course, but if you're asking about just generally drawing a perfect circle freehand, a lot of it comes down to practice and mileage. Meaning, trying to draw circles, analyzing where they're off, and then using that information to help inform how you need to adjust your approach. And of course, going through that process a lot.
I'm sry but i hv a doubt. So to make a perfect cube u need a perfect circle...but when drawing a circle... can't that be squeezed sideways...so how do u knw it's a perfect circle?
Keep in mind that we're talking about a circle in 3D space - which is represented in our 2D drawings as an ellipse. If you're unsure of what I mean by that, then you may be diving into a concept that is far more advanced than you think. You can learn more about the relationship between circles in 3D space and the ellipses that represent them here: drawabox.com/lesson/1/5 . This video is actually part of Lesson 7 of the Drawabox course - so if it doesn't make sense to you right now, then it's because you're missing everything that leads up to it.
As to your actual question - how do we know if the ellipse we've drawn represents a perfect circle in 3D space - then that's pretty much what the video goes over. It explains how there are specific characteristics (in checking the ellipse's minor axis and the lines that pass through the points at which it touches the edges above and below) that allow us to check if it actually represents a circle in 3D space. Only one ellipse would match the given vanishing points.
@@Uncomfortable thank u for taking ur time n replying.. i've started the drawabox course..i hope I'll understand better. Thanks
I don't think you did what you think you did with this explanation.
When you said you wanted to make sure it was a perfect circle, then just aligning them to whatever plan lies perpendicular or parallel to the horizon is simply not related to having a perfect circle in perspective. Your first example demonstrates how that elipse was not on the same plane as the "perfectly circular" one, but it did nothing to prove it wasn't a perfect circle, or that the first one was.
And then, your method of creating perfect circles in perspective is pretty wrong, and should be obviously so. You can have an infinitely long elipse that fits an infinitely long rectangle in perspective, and have them align " perfectly" the way you described them. Being perpendicular or parallel to whatever horizon you want it to be in says nothing about its shape.
You cannot begin with an elipse for this, and I'm not sure why you'd want it in the first place. Establishing a perfect cube is pretty easy even without plotting it all out with VPs and PDs.
Well, all of this is assuming you aren't expecting people to be using tools that can make perfect elipses, right? Because I would dare any one here to be able to distinguish a distorted elipse from a distorted circle in perspective. If the goal is to be able to estimate when you draw, without tools, then this doesn't really help with perfect circles.
I'll preface this by saying that I've just gotten home from work, so I'm a bit too tired to sit through the video and try and determine which parts your comments relate to exactly. That said, it does feel like you've seriously misunderstood what I was trying to convey, especially given that I don't even mention "horizon" once throughout the video. Now I'm certain the content of this video could have been communicated more effectively, but in essence what I'm trying to convey here is a method by which one can check, against a predefined set of 3 vanishing points, whether an ellipse represents a circle in 3D space. This isn't a method I invented, it's the one explained in Scott Robertson's 'How to Draw' - though many of my students had some difficulty understanding it there, so I tried to explain it a little differently.
A circle, or the ellipse that represents it, relates to these three vanishing points in very specific ways. Firstly, its minor axis points directly towards one. Secondly, two of the edges of the plane enclosing said ellipse run towards another. And thirdly - perhaps where your misunderstanding lies - the points at which the ellipse touches the two edges mentioned previously line up towards the third.
If we're talking about something like a wheel on a vehicle, which is the configuration I use to demonstrate this concept in the video, then the minor axis will point towards one of the horizontal vanishing points, the two edges of the enclosing plane (the top and bottom edges that is) will converge towards the other horizontal vanishing point, and the two contact points of the ellipse to those edges will run towards the vertical vanishing point, or if we're working on 2 point perspective, they'll run perpendicular to the ground plane/horizon line. Now to clarify, as this may be where your confusion arose, that isn't to say there is any relationship between *any* ellipse being circular and it sitting perpendicular to the ground plane or horizon. That's just in this particular two-point perspective configuration, where the vertical vanishing point is at infinity.
In order to match up all three criteria, we can modify two properties of the ellipse - its orientation (and therefore the orientation of the minor axis) and its degree. Most often students will run into problems with their ellipses' contact points being off (the third criterion), and this specifically suggests that the degree is incorrect (as demonstrated in the first example at the beginning of the video).
Given that there are other lines that will need to use these same vanishing points (due to them running parallel to the components of the ellipse used above), the challenge is to keep everything consistent. If the wheel, that is supposed to run parallel to the side of the vehicle, is only circular when compared against other vanishing points, then it's either not circular or it's not lined up correctly.
As you noted at the end however, drawabox still focuses as much as possible on being able to estimate and achieve results that are "close enough", and the techniques mentioned here have limitations as far as they can be applied before the ellipse is actually drawn. It does help a fair bit if you're using an ellipse guide, but that's not specifically the point. Instead - and this will be a part of the revision of the cylinder video which will come out in a month or two - it provides a means to check for mistakes afterwards, similarly to how we use line extensions to this effect with our 250 box challenge. Having a set way to test these properties gives us a clear path forward. We make several attempts, test them against our criteria, and identify where we've made mistakes and try to find patterns that suggest what we're misunderstanding. Then we try again. Over time this builds up a more intuitive understanding of 3D space, which can then be applied to more successful constructions.
I hope that helped clarify the video. Ultimately I still struggle with ways to communicate this particular concept, so if it's still unclear I'd recommend checking out Scott Robertson's "How to Draw", specifically page 74 (at least in the edition I have).
@@Uncomfortable I suppose I was not very successful in transmitting what I wanted to say, either. But I do not think your delivery is at fault here.
I'll begin with an image so that you can have a sense of what I want to convey with this criticism. I can't have a video rebuttal of your explanation, unfortunately. That would have made things much easier.
imgur.com/a/EAoAYQj
In that example, you can see that there is a pretty convincing elipse in a clearly not perfect square plane. When I said aligning those points meant nothing in regards to certifying the circularity if your elipse, this is what I meant. When you don't use tools to ensure you have a perfect elipse, you can very easily create one convincingly enough that is just as aligned as you want it to be, and yet definitely not be a circle inside a square. This gets trickier when the elipse is closer to being a circle, but still not quite there.
Perhaps Scott Robertson drew this method from traditional perspective manuals that do certify their measurements, and then extended the principle to his technique, which in turn made you do the same. The principle is not what I'm criticizing. I understand it. But it just doesn't work when you're free handing elipses and you're a mere student that can't really see clearly if your elipse *feels* wrong, flattened, not circular enough.
The misalignment of the elipse would only really happen if you were so good at free handing elipses that they'd always come out perfect.
Perhaps what I wanted to take out from your lesson here is not what you intended to deliver anyway. It's still useful to know those principles.
@@BIZEB Thanks for taking the time to provide an image, I definitely appreciate it. One thing that comes to mind, when looking at this, is that the ellipses you've depicted there do not have their minor axis aligned correctly.
I probably forgot to mention this in my last response, and I may not have even mentioned it in this particular video (I touch upon it in the cylinder videos which are meant to precede this, but I really should have mentioned it here). The minor axis itself represents a line in 3D space that is perpendicular to the surface of the ellipse - so it's coming right out from its face, and aligns to the matching vanishing point. In physics and mathematics terms, it represents the "normal" vector of that surface.
In this case, based on the orientation of the ellipses, that vanishing point would be the far right horizontal one - though the minor axis is going straight up.
Let me know if I've misunderstood you again, and I'll try to address it.
@@Uncomfortable Thanks for the reply.
I'm wondering, how did you determine that the minor axis aren't going straight to the right VP? I didn't draw them.
Why couldn't I simply trace one back from the VP through the middle of the elipse and call that my minor axis?
imgur.com/a/IO6t5r9
That way they'd be functioning as the minor axis of the flattened elipse.
@@BIZEB Oh that one's easy - the minor axis isn't an arbitrary line, it's an actual feature of the anatomy of an ellipse. The minor axis is the line that cuts an ellipse into two equal, symmetrical halves down its narrower dimension (with the major axis being the one that does the same down its wider dimension).
As shown here: drawabox.com/images/lesson1/example_ellipseanatomy.jpg
I don't think this is correct. Mainly at 4:10. You mention it's a perfect circle because the top and bottom are parallel to each other and "not set at an angle and they don't touch at different verticals" . This isn't correct, as they actually SHOULD be at an angle. An ellipse in two point perspective is slightly rotated depending on the minor axis alignments with the 2nd vanishing point, even if it is a perfect circle.
Any ellipse that isn't directly in the center of the horizon line is going to be slightly rotated (So the top and bottom will NOT be a straight line up and down to each other) due to distortion because the minor axis needs to align with the 2nd vp. Lookup "Ellipses in Perspective" by "Drawish studio" for the explanation.
You're confusing the major axis and the contact points of the plane around the ellipse. These are not the same thing. It has to be the case that where the circle touches the plane, the line connecting those points has to be vertical in 2pp, or it's not a square. Drawish is just pointing out that the major axis doesn't bisect the center of the plane, which is true and not contradicted here.
이거 보는 영어잘하는 한국인 없나요? ㅋㅋ 진짜 의역으로 듣는데 당쵀 먼소린지 하나도모르겠네... 댓글보니까 소실점이 어쩌고저쩌고 각도 어쩌고저쩌고하는데, 이게 소실점으로 인해서 단축효과가 들어간 평면 안에 원을 맞게 그리는법임????
Really? Dude, do u believe in that? Now I understand why those wheels on your cars lock so lame. I... Can't believe it that you dare teaching.
Ps. I also find that you don't understand the concept of projective plane, when you talked about rotation, like VP shift by same distance shit.
Can you elaborate further?
@@chevynxu362 Idk I feel like the hole course is a bit inefficient. It teaches you how to compose things from simple shape. But it doesn't train that much of intuition of those simple shapes. Like an assessment, draw ribbons, maybe for people who afraid too much of white list it's ok to do something they don't get, but I like to do things on purpose. For example in proko anatomy, they teach like everything should make sense, if you draw from that angle then this, this converge there not here etc. Like making analysis is important. Not jus draw that ribbons but think of convergence points, to simply it, to get intuition, of what you are doing.
Which program do you use for correct elipces?
When I need a very precise ellipse when working digitally, I'll use Lazy Nezumi. It's a windows-only app that constrains the mouse to specific paths, so it can be used for a wide variety of things (including ellipses) and works with most drawing software.