Drawabox - Measuring in Perspective: Constructing to Scale 

To be fair, I pretty much made a career out of half-assing perspective. I make a point of doing everything I can to *not* actually specifically place my vanishing points because they're such an encumbrance! But there's some things you just can't avoid at the end of the day ):

@Slimzie Maygen sounds like you're a dedicated reader of Scott robertson haha very good

@Slimzie Maygen That's quite the extensive list I'll be sure to read through and check everything out later today I'll let you know if i have any questions

@Slimzie Maygen cheers I'll get to watching this later today

This is all insane , i'm fascinated are you open to further discuss this topic? is there a way to contact you privately?

I'm glad I was able to lay it out in a manner that made the material click for you. It's definitely an important concept, and once it starts to make sense, it opens a lot of doors.

I'm glad to hear that! I was just about to write up my answer to your other comment, when I noticed this new one, and that the other had been deleted. I figured the issue was that you weren't correctly keeping your ellipses' minor axis aligned to its specific vanishing point, as that is a common mistake when students end up feeling that a wide variety of ellipses would ostensibly meet the given criteria.

@@Uncomfortable Yes, that was pretty much my issue, as well as getting the contact points mixed up with the major axis (oops). I figured there's no need to clutter the comment section of the other video so I just went ahead and deleted the comment, thanks for still helping out others years after the making of the videos, means a lot!

I'm glad it helped!

a little confusing in the end , there no exact solution for finding back sides and corners of a box ( the not visible ones) , right ?

@@kssnkr Since you already have a bunch of lines converging towards each of your horizontal vanishing points, you can indeed find the back edge. It's just a matter of having your back edges converge towards the same "implied" vanishing points.

Glad it was useful to you! I actually learned this from Scott Robertson's "How to Draw" book, which covers quite a bit of useful material. I figured it could use a little more direct explanation though.

👍

Glad I could help!

I'm glad I could help! The book 'How to Draw' by Scott Robertson also covers this material, and much more.

Hahaha, thanks. I honestly didn't actually realize til now just how much of the video has a blank canvas... ._.

Thanks!

Glad I could help!

Hahaha, I'm glad you liked it. 'Sketchup for your head', that's a good one!

I wish I could take credit for it - but all that credit is due to Scott Robertson (or whomever he learned it from). But it is indeed quite clever!

You are most welcome!

You're certainly right that measurements have to be made in order to construct an ellipse that perfectly represents a round circle. That's not really what I'm after though - I'm not sure if you've dug into the other lessons on drawabox.com, but I tend to promote the importance of a more organic grasp of how things sit in 3D space. By organic, I effectively mean imperfect. Having to measure everything out constantly seriously impedes the design process, so being able to draw things that may not be entirely perfect but happen to be good enough for the purpose of visual communication is an important skill to learn. So, in those lessons and in these videos, I try to take the various rules and leverage them in a way that can still be used in a way that doesn't terribly impede one's ability to design fluidly. That said, it's not too often that I find myself using this technique in particular, because even it tends to go a little too far into the technical side of things for my taste.

Uncomfortable for flowing design process this approach seemed good! :) i didn't mean to stomp on this tutorial by any means. I just figured that I could try to discuss a few things.

Don't worry about it! The feedback is always valuable.

Lattamonsteri r

Haha, I know the feeling. I'm glad I could help clarify this stuff.

:D

Adjusting the degree (width) of the ellipse, if you maintain the same minor axis (aligned towards the correct VP) will throw off the alignment of your contact points. You'll only have those contact points aligned, and your minor axis aligned with the VP at the same time at one specific degree.

Okay, I was forgetting about the minor axis.

I'm glad you were able to figure it out!

@@Uncomfortable This is confusing me too. I have been through ScoRo's book over and over, google searched everywhere. At 19:39, you add the width ellipse, however it appears there is no minor axis defined when you added it. In order to define where the minor axis would be - you would have to have an already completed plane (to find it's center, so you know where the minor axis should run through). I'm confused because if this is true, you need the minor axis to define a plane, and you need a plane to define a minor axis. It would be so helpful to me if you showed how you placed the circle at 19:39, because you have not drawn the minor axis (as far as I can tell, I am a moron though).

​@@nokkturnaldev So the reason some of that is missing is because I was using a tool to construct my ellipses (Lazy Nezumi's ellipse constraint) which actually displays the major and minor axes of the ellipse before you actually draw it. I aligned the tool's minor axis towards the implied right-side VP. Given that my vertical VP is at infinity (2 point perspective, all vertical lines running straight up and down), all that was left was to set the tool's degree to something that would result in the contact points with the top/bottom edges sitting directly above/below one another. The use of this tool is more or less equivalent to students being allowed to use an ellipse guide through the lessons where the concepts in this video are introduced. Everything needed to place the ellipse is essentially already available - you don't need the containing plane in order to drop it into place. You just need to know that the ellipse is going to be fitting between those top/bottom edges and that the minor axis is going to converge towards the right-side VP (which the other lines are also converging towards, despite the VP itself not having been drawn explicitly).

I don't think it's your lack of understanding - just the reduced precision of the physical tools you used. Fortunately, digital tools do give us a bit more accuracy, and I used my digital ellipse tool to determine that the ellipse on the left has a degree of 37 and the ellipse on the right has a degree of 53. This does appear to total to 90 degrees. Logically I see no reason to doubt that the degrees would add up to 90, given that the degree corresponds to the rotation of the circle in 3D space (and therefore if the two circles are perpendicular to one another, they should add up to 90), but I don't actually know enough about technical perspective to confirm your hypothesis definitively. This would be a question for someone far more experienced with technical linear perspective, whereas I'm really just sharing the tools that I've learned within the context of this course, which generally relies more on organically working through spatial problems where we can.

Yup - in the video description I mention that what I'm explaining here builds upon the "Perfect Circles in 3D Space" video ( ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yFjrSddZiv4.html ) - although more recently the video on drawing cylinders also goes over this information: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RBwHU72-Abk.html

Unfortunately that would only work in a void - meaning, if you have nothing else already present in the scene/on the page. The reason being that we can draw an ellipse and *assert* that it's meant to represent a circle in 3D space, but from there everything else would have to be consistent with that. Once you've already got things present in the scene, then you already have a field of view and other properties of the camera established, and so what you draw from there must remain consistent. The technique demonstrated here is one thing we can do to ensure we maintain that consistency.

@@Uncomfortable Thank you I understand :)..... have you considered creating a "100 circles in perspective challenge"? ... I think it would help us practice this. Because its quite hard to nail that ellipse right at the first try ;)

@@toucandoit The cylinder challenge actually has quite a few elements of that, and fits in between Lessons 5 and 6 - so most students tackling the concepts covered in this video (which are introduced in Lesson 7) would have already had that experience/mileage, along with having drawn ellipses throughout Lesson 1 and their warmups since then. Conversely, in Lesson 7 we actually allow students to work with ellipse guides to avoid having their attention split between the challenges of nailing their ellipses and the actual focus of the lesson.

In this video, I reference the "Perfect Circles in 3D space" video which you'll find linked in the video description. It goes over the specific criteria our ellipses need to fit in order to represent an actual circle in 3D space (based on how it's meant to be oriented in the world). That determines how stretched out the ellipses need to be, along with their rotation on the page.

I don't quite follow what you're describing - could you draw a diagram?

Unfortunately yeah - you start to develop a sense for it once you've messed up on it a bunch.

This video is presented as part of Lesson 7, where students are allowed to use ellipse guides, so there is more room for that kind of precision - though even if there isn't, there's a big difference between 100% winging it and working with approximations.

So as explained in a previous video that I reference here ( ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yFjrSddZiv4.html ), there are specific relationships between an ellipse and our box's vanishing points that we can check to see if our ellipse actually represents a circle in 3D space (based on the orientation those vanishing points assert). If it is in fact a circle, then the plane that encloses it *must* be a square - since circles are as wide as they are tall. It's a complicated concept (which is why it is introduced all the way at Lesson 7 of the Drawabox curriculum), so it may take a fair bit of thought and attempts at applying these principles to properly be understood.

Well I kind of do empathize with Penguin (I'm ridiculously short), though I haven't seen how he's portrayed there specifically. Now I'm a bit afraid to find out.

Believe me this was not meant as an insult (in fact he is the best character in the show) though a little sociopathic among other things.

As mentioned in the video description, this video relies on some of the concepts covered in this video about how to draw an ellipse that represents a perfect circle in 3D space: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yFjrSddZiv4.html There I explain how to determine the width/degree of the ellipse that would be correct in that situation.

Your wording is somewhat unclear, but I suspect you're misunderstanding what's going on here. If by "vertical axis" you're referring to the major axis of the ellipse - which is the span across its widest dimension - then it does not remain perpendicular to the horizon, that is not a predefined rule that needs to be followed, and I'm unsure where you're getting that impression from. If that's not what you mean by 'vertical axis' (and the more I read through your comment, the more I think you perhaps didn't mean that), then I'm not entirely clear on what you're trying to say. Could you try explaining your point again? As a side note, what I explain in this video is not my own concept. It's merely an explanation of a technique from Scott Robertson's book, "How to Draw".

Here you go: drawabox.com/lesson/6/1/subdividingthirds

While it certainly is useful information, I'm trying to spread out the amount of technical information a student is faced with at any given lesson. Being hit with the transition from organic to geometric is pretty tough to begin with, so I prefer them to focus on the more basic techniques before thinking too much on measuring things out.

The program I was using there is called Lazy Nezumi. While it's primarily made for cursor stabilization (though I kind of hate how it does that), it's got a bunch of constraint features that allow for ellipse guides like this. It's quite handy, especially considering the fact that it's a pain in the ass to freehand one's ellipses when working digitally (compared to working traditionally). Alternatively rotating the canvas is something that can make different ellipses easier to freehand, but it's not a workflow I'm a fan of. Luckily digital media affords a great many tools to provide alternate solutions to such problems.

Uncomfortable thank you so much. I'll have to check it out. Pen stabilization is definitely my challenge when working in a digital world!

When it comes to stabilization, I'm actually quite fond of the 'smoothing' added in Photoshop CC 2018.

The whole idea behind this course is that everything can be simplified into basic forms, and the most basic of all is a box. So an arm can still be represented as a box, which allows you to employ more basic perspective techniques to it.

@@Uncomfortable right i understand that but when foreshortening im not sure how to measure it out. do you have a video about that? thanks for the help :)

@@theartofcompetition5965 I don't get into figure drawing. For that, you may want to look at Proko on RU-vid.

Well, you'd need to be able to at least estimate where your vanishing points are. Don't need to measure angles, but by following the criteria for what makes an ellipse represent a circle in 3D space (as explained in the how to draw a cylinder 2 video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RBwHU72-Abk.html ), you can produce a circle which by definition is as wide as it is tall. From there, it's a matter of enclosing it in a plane, which itself would be a square.

There actually is a way , page 74 of scott Robertson's how to draw in chapter 5 , it requires drawing a perfect circle because it's obvious when its imperfect, anyways you draw it in such a way that all the axis add up to converge with the edges of the circle using the vp's. This will yield a perfect square if encased in one after you double check it's correctly in the criteria above.

@@Uncomfortable woops sorry my dude i hadn t read the entirety of your reply and repeated what you said lol

@@jinxxpwnage Hahaha, no worries. I actually based this whole video (as well as another) off that section from Scott Robertson's book.

Thanks mate! :D Just found it

I didn't watch the whole video, just the part you mentioned, but I suspect I may have missed something when doing the explanation. You are correct - the minor axis of that ellipse would be pointing towards the vanishing point. When doing the demo though, I was basically just showing hidden layers, so I would *assume* I had drawn those lines with the vanishing point already in mind. I'll be sure to explain that whole issue more thoroughly when I evenutally redo the video to make it more succinct.

@@Uncomfortable thank you :D

This video, and drawabox as a whole, is about avoiding the use of a lot of the standard technical perspective concepts, allowing us to delve into technical rules in a limited fashion rather than having to build out entire scenes that way. Long story short, this isn't the place to ask questions about those kinds of things, and you should look for a resource more geared towards fully exploring linear perspective.

:)

Nvm, found it :)

Tilting the minor axis (which is what happens when the circle we're representing is rotated in space to turn towards or away from the viewer) would be compensating by its degree getting wider or narrower, allowing those contact points to align vertically. This technique basically ties together the rotation of the ellipse and its degree. When one changes, the other must compensate, in order to continue to represent a circle in 3D space.

11:18, I talk about a different video I had published that explains the concept of drawing perfect circles against set perpendicular vanishing points, and using them to create perfect squares. Since I covered it there, I didn't reexplain it here. It seems you missed that moment, resulting in your confusion through the rest of the video. The video is here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yFjrSddZiv4.html though both of these videos are somewhat outdated. I explain it more succinctly here: drawabox.com/lesson/7/1/perfectsquare

This technique is predicated on the concept that we can know whether an ellipse we've drawn is an oval or a circle in 3D space when comparing it to other points of reference we've established (like vanishing points, boxes, etc.) I explain the criteria an ellipse needs to meet in the Perfect Circles in 3D space video, although I also go over it in the newer video on cylinders here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RBwHU72-Abk.html Understanding what defines an ellipse as representing a circle in 3D space in turn allows us to build a unit cube in space (and is a key part of transferring that measurement from one axis to another). Once the cube is built, you can expand that on any of the three axes. This is pretty advanced stuff though, so if you're jumping into this video without tackling the other drawabox material, I wouldn't recommend it just yet.

@@Uncomfortable awesome! I'll check those videos too. Don't worry, I have the knowledge to do what I mentioned in the comment, but I didn't understand this method using ellipses. I don't know if you know a PS plug in called, Perspective Tools, I'm trying to use it to skip some part of the process of measuring and your method called my attention. By the way, thank you for taking the time to answer my comment, I thought it would be ignored

@@ketimporta7799 Is that Sergey Kritskiy's Perspective Tools? If so, actually used it a fair bit years ago, though it was an older version that didn't have a lot of the fancy features it does now. I only really used it to build out perspective grids that had alternating line weights, as I found it easier to design with those than the standard ones.

@@Uncomfortable Yeah, that one! But there are not many fancy features now, I think the only new feature it has incorporated is that you can morf smart object to fit the grid in a selected area. Do you know the Gary Meyer's perspective course that he made for Gnomon Workshop? I learned the basics from that course, and I was looking for a way to use his principles along with Perspective Tools

I use Photoshop, but the ellipse guide tool is specifically a program called Lazy Nezumi.

@@Uncomfortable Thanks!

What do you mean by "the three point" ?

All my demos are done in Adobe Photoshop, though I encourage my students to do most of my lessons on paper in ink.

Considering that you're using Photoshop, what is that ellipse tool you're using? Is that a plugin?

Ah, yes. I mentioned it in one of the videos I did this weekend, I guess it wasn't this one. I use Lazy Nezumi - it's made for smoothing your brush strokes (I don't particularly like how it does this) but its real strength is in its various constraints settings. There's one very flexible one for ellipses that allows you to modify your degree, angle, size all independently. You can find it here: lazynezumi.com/. It's not just limited to Photoshop (it's a program that runs independently and just controls your mouse position, but it does hook into Photoshop nicely and is more or less made for it). No Mac support sadly, and it's $35 USD.

@Slimzie Maygen hahaha! Nice , did you have trouble with mirroring rotated tilted planes Across a mirror plane? The book takes quite a jump in that part

@Slimzie Maygen well yeah that way you don't have too much or too little distortion by having those 90 degrees and staying inside the 60 cone prevents excessive distortion. What do you think of spiral staircases?

I'm definitely not the one to ask about specific, mathematic approaches to such things. Most of my lessons are about how to approximate things reasonably so as to keep your mind on what you're drawing/designing/communicating. This video's pretty much the most technical I'll ever get.

yes i loved your video. My only concern was how should I somehow get the relationship between the vertical line and line connecting to vp. www.automotiveillustrations.com/tutorials/perspective-foreshortened.html .. please lemme know if you know .. I am an architect by profession but also learning the 3d graphics by programming. I dont wish to use any predesignated tool. Thanks.

What I mean is if I have 3ft verticle line, how should I draw 3ft line on vp(vanishing) direction. Is there any direct formula? the relationship//

So you're basically asking how to create a 3ft by 3ft square in 3D space? I would draw my vertical line, then a line going from each end to the vanishing point (A), giving me the three sides of my square in 3D space, and leaving me just one more line to draw. In order to draw this line, I draw an ellipse between those three lines such that its minor axis goes off to the other vanishing point (B) and its contact points to the lines going to vanishing point A are aligned vertically. If both points of this criteria are met, this means that the ellipse represents a perfect circle in 3D space that is enclosed by the three lines we drew previously. Therefore this perfect circle has a diameter of 3ft. All that's left is to draw that one remaining line such that it fully encloses the ellipse. I explain this in detail in this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yFjrSddZiv4.html

What I just explained is how to find the point 3ft in that direction, but since it relies on you drawing the correct ellipse, it is not a direct formula. As I mentioned earlier, I am not the person to ask if you're interested in the mathematics of it. I can't give you the answer you're looking for.

I use Adobe Photoshop. When I need to draw an extremely accurate ellipse, I also use Lazy Nezumi, which is a piece of software that can work with many different drawing softwares, as it constrains the cursor rather than the brush inside the program.

I use Adobe Photoshop.

I don't really have the hardware to film myself live, so beyond the explanations I give in the lesson, I can't do much more. That said, the problem is generally that people feel weird when drawing from their shoulder, rather than them not understanding how to do it. They assume that since it feels weird, it's incorrect. The fact is that it feels weird because they're using muscles that aren't activated often, so it naturally feels awkward, and causes them to get tired quickly. In order to get beyond this however, you need to stick with it. One trick I used to employ was to hold my hand in front of myself and pivot it back and forth from the wrist joint, just to get familiar with what it means to move from the wrist. Then I would lock that joint, and do the same thing from the elbow joint, feeling the wider radius of motion. Finally, I'd lock that joint as well and pivot from the shoulder. This is something you can do for just a few seconds to remind yourself of what it means to move from the shoulder whenever you feel yourself slipping back into drawing from the wrist.

thanks. I'll try

Hey, if you ever had a plan for live video to show a small bit like that, there are many tricks for getting a reasonably good or at least okay video quality from a ghetto-tier gear, like a lamp and a phone camera. All you need is a phone ( hey, it's not the 1980s, I assume you have a phone :P), a stand to get a stable shot which you can even make from cardboard, it just needs to hold a phone and you need a light. A rather strong light. With a single layer of a white napkin in from of it you get nice, soft, but dispersed light. Then set the ISO to the least you just can and fix the white balance. Almost all android phones can do that, not sure about others. This should get quick and steady focus, sharp edges, no blurs over motion and less image noise. Almost every camera can take a good picture in my opinion, you just have to know how to set up an environment that's near perfect for a camera and its adjusting software. I hope I could help :)

Thanks for the suggestions!

In this video I'm working in Adobe Photoshop, although I use Lazy Nezumi for drawing the ellipses.

Looks like he's got a lot of very cool exercises! Thanks for sharing.

That is Photoshop, but the tool is a non-photoshop-specific tool called Lazy Nezumi. Windows only, but it'll work with any drawing app.

@@Uncomfortable Interesting, I'll check it out. Thanks!

Aaah! * Covers it up with his hands *

If you "plan" out everything in whatever type of perspective you're attempting; all you wind up with is a very stiff drawing. Eye-balling perspective when practicing perspective trains the mind & hands to create an alive-ness to your perspective drawings. Yes! You should strive for some sense of exacting perspective in your conceptions; but if you're allowing yourself no room for guesswork expressiveness - then all you're creating is a dead looking drawing / conception...which would be easier to achieve by just taking a photograph of the intended object & letting it go at the photograph. Unless you're an actual concept architect say doing an exact rendering off a blueprint for a builder, then there is a such thing as getting too bogged down with some much exactness to the point of being ridiculous. And Slimzie; who are you to state what is absolute & what isn't the "proper way to draw"??

I repeated the same process I used for the first ellipse. The minor axis goes towards the right vanishing point, and the ellipse fits snugly between the two horizontal lines going towards the left VP and that one corner vertical. The only remaining criteria I then have to match is that the ellipse's contact points with the horizontals above and below it should rest exactly above/below each other. It's this last part that's important - the contact points being aligned vertically. I explain this around 12:08, where I mention that not any ellipse will represent a circle in 3D space.

I was wondering why you didn't use the method of projecting a schematic using a Stationary Point. I thought you were working around this in a way, then I got surprised when you didn't repeat or explain what you did, is all.

My general approach to drawing tries to stay away from the standard tools of perspective - that is, vanishing points, stationary points, etc. I acknowledge the presence of vanishing points, but I usually imply their position rather than explicitly marking them out on the page. The lessons I post on drawabox.com are really more about eyeballing perspective for the most part, and this video is by far the most technical I've ever bothered to go.

believe me, I only eye balls perspective unless there's some architecture that needs it so I know where you're coming from.

Hahaha, seriously. I'd just up and quit my job if I had to contend with a thousand vanishing points in a single scene.

The measurements are relative. It's about capturing accurate proportion without relying on vanishing points directly. The first two units are arbitrary, but using the circle method, we do establish a unit square in space. The rest is a matter of repeating it in perspective.