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Hello there fellow deviants,

Perspective is probably one of the most difficult concepts in art to grasp. I suppose pretty much everyone has or has had problems with it, even some more experienced artist. I can tell you I'm not exception to that. Even thought I wasn't extremely bad at drawing, it still took me 6 years to even figure out where I needed to work on before I could address the deeply rooted issues I had.

I have basically based all of my artistic understanding on perspective and 3D. Although I can't say I'm perfect in my execution, by looking my gallery you can see that pretty much all of my drawings tries to convey the feel of depth and 3D. I think that's one of the factors that make my drawings stand out and maybe you also feel that way. Drawing depth has become a second nature for me.

You may also have noticed that I have about four tutorials (depending on how we define perspective) that tries to explain a thing or two about perspective. I have also few practices/demonstrations about perspective. Here they are:

I feel I haven't been able to convey my understanding quite as well as I have wanted though. I have a decent idea what makes perspective so difficult for many, but I'm also having problems with translating my own understanding into tutorial format. It's like there is a missing bridge somewhere that I haven't been able to tell you about. I'll keep trying to find it.

The first challenge I have is that my way of thinking might be so out of the box that it doesn't make sense to others unless they know all the factors about it. Things I find very straightforward and self-evident probably are very alien for an average person. I can relate to this to a degree because I originally didn't think the way I do now and I'm sometimes perplexed with my own findings.

The second challenge is that my approach is pretty much completely opposite to how perspective is commonly addressed. I don't think about vanishing points or guidelines (in fact, they were the reason I initially went astray), but I have confirmed that the way I think doesn't violate any of the rules of traditional perspective. I think in very spatial way, as if I personally were within the drawing and then I just analyse how I see or should see the objects in the scene. It's a lot more difficult to draw a good perspective drawing without using perspective guidelines. I tend to draw reference objects (bounding box) trough eyeballing and its reliability depends solely on my ability to get look somewhat right. I think my approach makes perspective feel more lively and real. I often see very well executed perspective drawings that are... how to say it... dull and artificial. That's not to say my approach is ultimately a better choice, but it has served me surprisingly well because it's applicable in any possible scenario.

The third challenge I have is how to tie concepts and reality together. It's good to note that I didn't figure out perspective from still images or examples. It dawned to me trough motion and movement (I worked on a 3D model and orbited around it) and witnessed how the rules of perspective changes the view). That said, if I truly wanted to explain my understanding, I would need to present an animation or other video material to truly express my ideas (later in this post you will find my best attempt to demonstrate the idea). I think that normally people aren't able to piece things together from several still images. Hence there are life drawing courses where you can actually "orbit" around the model and see how the subject looks from any angle, that's the whole point in those courses in my opinion. Also, if things are too simplified and conceptual, the examples lose their meaning. People have no problem understanding how the real world unfolds in front of them because there are so many visual cues, but to make them perceive something specific in just one simple cube or plane... to make them see something that isn't there... that's a huge challenge. These were the biggest obstacles for me to figure out, not to mention how to actually work on them.

I believe that you won't go too badly wrong if you try to ponder these things as well. If anything, it's worth checking out.

The fourth challenge is that even if you figured a thing or two, you still need to transfer that into your drawings. That requires a lot of practice which isn't exactly tied to perspective alone. It's also up to you to identify your deeply rooted issues, they may be different from what I have found myself.

I have had some quite deep discussions with some people who have asked me about perspective in comments. In these discussions people often have had some sort of enlightenment. Here is a short comment thread you may be interested to read trough:… (I should have saved all such instances, now I should browse trough all the comments to find more). I don't know to what degree it has been thanks to my understanding, I feel the people I discussed with have figured something out on their own while they have processed things in their mind or experimented on their own. I suppose it's important for everyone to find their own way to approach concepts like perspective.

If there is something common with several people I have talked with, it's the "pole" concept. Like on the aforementioned comment thread, the person comes up with the infinitely long pole that vanishes at the horizon (horizon is infinitely far away). You could say there is a vanishing point there. If you move that pole around, its other end still vanishes somewhere. That means that where ever that pole ends, there has to be a vanishing point. So if you anchor the other end in place and just rotate the pole along that anchor point and plot every vanishing point, you form a spherical point cloud (that pole is the radius of the sphere). This image shows how that spherical point cloud could look:


So the idea is that you as the beholder are in the center of the perspective system, i.e. in the center of that point cloud of vanishing points. The point you are looking at is the other end of the pole (the one that is infinitely far away). You only need a handful of vanishing points from that point cloud when drawing though. Which particular vanishing points you need depends on the orientation of the objects you are about to draw. I think traditional perspective tutorials that focus on 1-, 2- or 3-point perspective fail to explain this and it can seriously cripple your ability to learn perspective. A cube has 6 vanishing points in total, because if you have one vanishing point, say, above, then there also has to be one below. The same apply with left vs right and front vs back. Here is an animation I once made (modelled in Sketchup):
All the guidelines point at vanishing points, make a note how they move when the view changes. Also note when the horizon appears briefly

Does this make any sense to you? Did you find the bridge or just another cliff?

I'm interested hearing whether I managed to show you the missing bridge or not. Maybe I still wasn't able to define the bridge properly. Maybe some more animated examples would do the trick. Maybe I should explain the rules of a cube in meticulous detail, because its essential to understand how it behaves in order to understand how any other form behaves. Maybe I'm still missing something absolutely crucial.

I hope to find that out.

Nsio of the Hermit Mystics
Here is my attempt to explain few things about perspective once again. I really feel I haven't been able to do that in my previous tutorial.
Add a Comment:
dipsydew Featured By Owner Jun 26, 2018
Neat animation! I think it shows how vanishing points can be anywhere, not just on the horizon.

What is difficult about perspective for me is how much depth things should have. Like I can draw two lines converging at a vanishing point, but if I draw a square using those lines, I don't know how distant the near and far lines should be. You can figure it out if someone already drew a square for you, and you just use tricks to keep the next square proportional. But with just lines going to a vanishing point, if the near and far lines are too close together, it looks like a rectangle seen from its long side. Too far apart, and it's a rectangle seen from its short side. And I have no way to tell where that "magic" distance is, that makes a square look square.

For that matter, which vanishing point lines to use is confusing. If the angle between them is too obtuse, the square will be much huger than you intended, and if they're too acute, it's much tinier. And there's no way I know of to figure out the proper width for objects relative to the guy holding the camera. It seems totally arbitrary!

Another difficulty is when things go from above you, to below you. Everything below you is below the horizon and you can see the top of it, and everything above you is above the horizon and you can see the bottom of it. Except if that thing you see is rotated with the top facing you or the bottom facing you. Something below you can rotate so you see the bottom, and something above can rotate so you see the top. Trying to imagine a rotating thing also rising up, transitioning from "below" to "above" is... really difficult.
infinipede Featured By Owner May 4, 2018  Hobbyist Digital Artist
While I worry a lot about whether or not this'll really be an epiphany for me, I like seeing different ways to learn about and explain things that I've only ever seen taught or explained one way. I especially liked seeing your demonstration of the 4-point or "fisheye" perspective.

I sometimes beat myself up over never improving as fast as other people seem to, even if I try to put effort into it. I have terrible spatial reasoning (thanks autism) and my mind's eye essentially looks like an escher lithograph. I even see myself from a 3rd person perspective in a lot of my memories. Having a different way to approach something that hasn't worked for me in the past is at least a better path towards understanding it myself.

I like your tutorials a lot but I've never been able to work with the "start from the very beginning" approach. Personally I need something I'll actually do. I can't make it feel like a job for myself, so I try and put it in the context of things I like to draw.
monmoshi Featured By Owner Mar 23, 2018  Hobbyist General Artist
tha's very useful^^thank you
Marini4 Featured By Owner Jan 22, 2018  Hobbyist General Artist
Hello Nsio senpai super sorry if you are busy I thought I just wanna let ya know that from your drawing tutorials I keep coming and coming to your deviantart for tutorials and refs. Throughout my studies for Diploma Architecture semester 1 until semester 3 is Design manually a.k.a traditional work, I use your perspective tutorials and aced my design. Your tutorial really helped me passed my design which tbh is only 20+/40 students passed because some of my friend cheated traced using sketchup and when my lecturer asked how I draw (to make sure I didnt cheat) I showed them YOUR tutorial and tell them you and architect. My lecturer is praised by ur tutorial and my lecturer used some of your tutorial practice for Graphic Design class for semester 1 students as like a notes/tips and tricks. My design not only that I remember from your journal "Why I choose Architecture" I comment I wasn't sure If i made a right decision to be an architect but seeing your love of drawing, the proportions, the angles and perspective while you still on architecture makes me wanna go the same path as you, right now I'm applying for Degree but part-timer I draw my comics and the technique and tutorials you provided still in my head until today! Just wanna say thank you so much for your tutorials and everything. If werent for you i don't think I ever pass on my diploma ^__^ cheers!
Nsio Featured By Owner Jan 23, 2018  Hobbyist Digital Artist
Cool! I remember your comment on my journal, it's great to hear you are doing well there. It's also cool that even your lecturer found my tutorials worth mentioning, it shows that I'm probably doing at least something right :D. Keep up the good work and spread the word to your fellow classmates about my tutorials so that they could ace their designs as well :)
Cestarian Featured By Owner Jan 10, 2018   Digital Artist
Well, no idea why I didn't see this journal sooner but for me after our last talk the major difficulty I have is applying perspective to more complex forms than say cylinders and cubes, making the leap between there and being good at drawing boxes is quite challenging :stare:

After that talk however the conclusions I came to were quite a bit different from what you described with the pole :D it's pretty much the same principle though but rather than having the horizons next to the beholder, they would rather be in the distance, so the sphere would encompass the beholder and all the objects in view, in other words guidelines would still work the same.

Also something i realized during our talk (though this part was not actually from you :meow:) is that objects that are paralell on the vertical axis (for example all boxes that have their bottom plane facing the ground directly) will use the same horizon line, but if they are rotated they will use separate vanishing points, it was a result of this discovery that allowed me to understand what you were talking about to me, that if objects were not parallel to the ground I'd just have to create a new set of horizons for it in order to make it work... It also helped me create more dynamic looking distortions by thinking of the horizon line as a horizon circle :nod: (this was all you :la:) which made me start sometimes drawing in curves rather than straight lines, it's way more fun (although it looks more like a camera shot with a distorted lens than realistic).

And now that I'm talking about this I'm making even more realizations for example where that new horizon should be placed; it wasn't clear to me before but it should be centered from where the vertical horizon and main horizon would cross :la: so all of the tilted horizons should cross at the same point. I don't know if this lines up with your idea but it's clearly a slightly different way of thinking, as I'm clearly still thinking in guidelines. I'd very much like to be able to convert to your method though since I really am not a big fan of guidelines Sweating a little... But it's still somewhat beyond my understanding.

It's kind of amazing how your chats can help people reach their own conclusions that differ from your own. Maybe you should try explaining things with 3D models rather than drawings.

BTW since I just stopped drawing for 2 months and started again the other day after realizing that what's hindering my progress is lack of perspective understanding (ESPECIALLY the thing I said first, about translating perspective from simple objects like cubes to complex objects like say robots or bodyparts, so haaaard) and I noticed this youtuber that had exceptionally good perspective, and he said he learned his stuff from a how to draw book by scott robertson which I have now picked up and am reading and intend to follow to see if I discover anything new. Scott Robertson is a textbook example of traditional perspective done right, to the point where a lot of his drawings look like actual 3D models :stare:

I'm not exaggerating, this is not a 3D model… (I don't think I've ever seen anyone do cast shadows so perfectly) but the guy seemingly uses a lot of guidelines every time he draws.
Nsio Featured By Owner Jan 11, 2018  Hobbyist Digital Artist
I don't see any difference to my way of thinking and the way you explained your thoughts. In fact, it's exactly the same. I don't know, maybe I didn't explain my views as well as I should have if you find it different. And that's what I'm always concerned with my explanations, because bad interpretation can potentially lead people astray. It's good to hear that you came to the same conclusion trough your own thinking.

The effects you mentioned are direct consequences of the rules. If an object rotates along its vertical axis, the same horizon line still works. I recall explaining this on more conceptual level, in a way that apply any particular situation, i.e. rotation along any point/axis. Though it's easier to understand the concept trough more concrete example and then expand the idea to all possible situations, that's how I figured it out at first as well.

Also the point where vertical and main horizon would intersect is merely a consequence of the rules. If there are two circles with the same radius and center point, and one of them is rotated along the center point, then the two circles will intersect at two points. If the other circle is rotated 90 degrees, then yeah, vertical and main horizon intersect each other and two vanishing points are located on. If you rotate the vertically oriented circle 90 degrees along vertical axis, then you have three circles and 6 intersections. That's 6 vanishing points.

I think that the only difference we have is that you (currently) think the rules are external and therefore projected on the objects you want to draw (so constructing a cube with horizon, vanishing points and guidelines), which I find as the traditional or typical way to perceive it. For me the rules are embedded in the objects I draw, (so I construct horizon, vanishing points and guidelines with a cube). I've learned to use my own drawing in progress as references for the rest of the drawing. It's organic process where everything is subject to change. I look for middle and end points, middle lines, dividers, right angles and try to take "shape equality" in account (more about that here: Nsio Explains: Introduction to Guidelines . I can see the guidelines in my mind and I attempt to take them in account, because they are direct consequences of the perspective rules. Drawing complex shapes is just about breaking them into basic shapes and then making sure the drawing follows the rules.

M way isn't reliable, but it's more intuitive and fun in my opinion. I'm sure you could adopt that sort of method, it merely takes a lot of practice to be accurate with it and even then there will be inaccuracies. I suppose a mix of the two is the most useful.

Yeah, that guy is awesome with perspective. Although the guidelines are definitely working, it's tedious to actually construct them. I may say that just because I want to avoid the tediousness. I have done similar drawings before, but not very often. But for example: 
Racincar Guidelines by Nsio
This isn't even close to the awesomeness of what Robertson can do... but merely a simple test of drawing without meticulously constructing the perspective. I only drew a quick grid by free hand and a simple projection to get an idea. There are mistakes (most noticeably the air intake above the seat with bad orientation, the cockpit is also clearly off-centered), but I'm getting better at noticing them and preventing them.

Here is another example:
The CoDD Concept Art: Dispatcher MK IV by Nsio
I drew this without any guidelines. Sometimes I just start drawing something random, usually just for fun and warm up. I usually draw one side and then try to analyse how the other side would look if it was symmetric. It's difficult, but definitely good practice for both the hand and eye.
Cestarian Featured By Owner Edited Jan 11, 2018   Digital Artist
It's amazing to me that you could draw something so complex yet symmetrical looking without using any guidelines :la: but at least it was difficult for you :nod: what I wouldn't give to learn that tho :stare:

I'm glad to hear I'm on the right track for it, if you'd make a new perspective tutorial I'd gobble that shit up like a hungry wolf right now :D

Anyhow, I think maybe if you want to have a higher success rate maybe you should try to make your perspective tutorial with the assumption that the reader doesn't even know how to draw a box or cylinder yet, work from the assumption that someone trying to learn to draw for the first time ever in his life is reading your tutorial, and moreover is 12 year old and doesn't have any real background in mathematics :stare:If you start from the bottom and work your way to the top at a gradual pace instead of trying to do it all-in-one it will probably be more understandable to your readers, you might have to make a bigger project than your usual tutorials to do this tho.

Perspective is probably the most complex concept in drawing and the most important one at the same time, there's an extreme lack of good tutorials about it not because nobody's trying, but because nobody is covering it in enough depth. Also the bottom line of drawing is that things can only be learned with practice, therefore exercises to practice the concept are necessary in order for people to successfully understand it.

I'm often told I'm a good teacher and my only secret to doing so is that I always start from the assumption that the one I'm teaching knows absolutely nothing, and work my way up from zero. Maybe that's the kind of attitude you need to take to make the kind of perspective tutorial you want to make, think of it as if it is going to be read by a bunch of children with runny noses that don't even know what 3D means :D
Nsio Featured By Owner Jan 13, 2018  Hobbyist Digital Artist
I just take up the challenge. The more one does something, the better one becomes at it (eventually). After 7 years of application, it has had a noticeable impact and the impact would have been even greater had I spent more time on applying it. Robertson has draw hundreds of perspective drawings. As his page says, he has over 18 years of experience in teaching, so he has to have even more years under his belt before that.

You have put a lot of your own efforts and thinking on understanding perspective. That's a must in order to learn anything to begin with.

You know, that has actually been my strategy for a long time, to assume people know nothing about anything. However, doing that literally makes the project much bigger than my usual tutorials as you pointed out. That would lead to the Book of the Hermit Mystics with hundreds or thousands of pages :D. Not only it takes a lot of effort on my end, it also requires a lot of perseverance from the readers. It's difficult for people to stay interested if the subject at hand has nothing to do with the actual topic, because they won't see the connection at the time, or by the time I get to the point, people have already forgotten the preceding things for they fail to see the importance to memorize them. Effectively that means several read troughs which multiplies the readers efforts. What they will choose to do? They will keep looking for tutorials that claim to do the trick easier and faster, people will always try to find the easy way out. I would need God-tier methods to convince people to keep reading my tome instead and I know I won't have the time and effort to spare to make something as perfect like that, not to mention all the things that I have yet to figure out.

Making a series of tutorials starting from zero is also problematic for the same reasons. People most likely will get interested by the time the series actually start covering things about perspective so they essentially miss the foundation. it's not feasible to start every tutorial from zero either, at some point we just need to assume people know at least something.

You know how in maths there are functions like a+b=c, L=2a etc. I'm not especially talented in maths, but mathematical truths are beautiful. I like how they are applicable in any situations, like no matter what the dimensions of the cube are, we can just say that the length of each edge is "a". Or we can say a=2b, essentially dividing the cube into 8 smaller cubes where the length of each edge is "b". However, I didn't come to understand and value the beauty of the math until I had figured out my way of approaching perspective and witnessing that it works and follows the rules. The reason is that people don't see objects, they see meanings. I started to see meaning in those mathematical stuff. When something is broken into universal concepts, people fail to see the meanings, even if they are told what they are supposed to see there. They need to learn to inject meanings into those letters and formulas, otherwise they will not mean anything to them. But if they never see the connection, how they will ever learn it?

Therefore we can argue whether using a cube for perspective demonstrations is truly beneficial. A cube is the most useful way to demonstrate the rules of perspective and geometry but on the other hand, it's so simplified form that people have hard time injecting any meaning into one. In a similar way a simplified drawing, while delivering the idea, isn't really as tangible as a real object with real meaning. On the flip side, using a real life object like a car is so complex that people won't know where exactly they should put their attention on (while also taking so much efforts to draw just for the sake of demonstration). In short, using too simplified and conceptual examples lack the meanings to make them understandable, while too complex and meaningful objects fail to deliver the idea loud and clear. That's why there are usually examples on how to utilize the formulas and a lot of exercises to apply them.

Maybe it's for the best to just spark inspiration and make people think on their own after all. You didn't completely understand what I was trying to say about perspective, yet you put your own thoughts into it and filled the confusing gaps I failed to explain and came to the same conclusions. Maybe the interaction between the apprentice and the master, the student and the teacher, is in fact the best way to make sure people will learn, because trough the discussion teachers can determine where the students are lacking, effectively helping them to focus on developing those areas.
Cestarian Featured By Owner Edited Jan 13, 2018   Digital Artist
Haha yeah that makes sense, people always want that magical shortcut, myself included... And it took me years to reach the realization that the shortcuts are all trash, and doing the hard work, and doing it seriously, for a long time, is the only way that you're gonna get any real shortcuts :stare: those will be shortcuts developed in your head to do this hard thing with less and less guidelines, when I was starting out I like most never listened to people who said this, because I didn't want to hear it, but now that the training wheels fell off for me I can see the error of my ways, as I fall flat on my side. I bet however that there's plenty of people who have ended up here, maybe even a majority of self-taught artists, and those who do either have the same level of thirst as me (which drove me to swallow my pride and read another "how to draw book" :nuu:) or they were never gonna end up doing anything good with it anyways.

People have shortened attention spans, people glaze over details often, I'm no less guilty of this than others, in fact there's only three tutorials you've made where I've read every letter. 2 perspective tutorials, and the 1 about boobs (cus you know, it's short, and has boobs) Usually I just look at the pictures and try to see what you mean from that. I didn't really want to admit it, but I'mm just as affected by attention deficit as everyone else who has had the internet since they were kids :saddummy: I know I am capable of focusing longer but I need to put my mind in order first Even if I'm reading a book about perspective, I'm just glazing over everything in the second chapter (perspective terminology) only stopping my eyes if I see something I don't get (these things so far have been cone of vision/field of view and drawing ellipses around the minor axis :nod: I found a way to practice ellipses, I'm really bad with them so I'm somewhat happy about that. But pictures, (at least your pictures :D) are fun to look at therefore peoples eyes will be drawn to that rather than text, therefore the format of maximum images, minimum text may be the best to keep reader attention, you can make short descriptive texts beneath each image and then maybe add more detail for certain things that may need more explanation in the description. (I'm not saying you don't already do this btw)

I think maybe the best approach is deciding how many parts there should be (I recommend 3 parts, each building upon the last; beginner, intermediate, advanced) then take as long as you need (days, weeks, months...) thinking about what needs to be covered in each part, what is the best way to cover it, maybe even write down those ideas for each part so you don't forget them, until you feel like they would be satisfactory, and then start slowly working on them, piece by piece, day by day. This way you can go into a lot more detail visually (in the tutorial) and verbally (in the description), so that most people will grasp the concept, and those thirsty enough to read the details in the description will properly understand the concept. How does this format sound?

Also, I wouldn't mmind buying a book about drawing by you hehe, maybe you should do it :dummy:

I agree with what you said about math, but I just haven't reached that point yet, not in math anyways.

I think I agree with your idea that maybe a cube isn't the ideal perspective teacher, it is both "too simple" and has too little meaning to anyone. And also I can only draw cubes because I practiced only cubes (mostly) so it becomes a problem in and of itself if too heavily relied on.

You may have sparked inspirations and gave me enough information to fill a bunch of gaps myself, but I did not fill all the gaps :stare: my perspective knowledge is still half baked, even if it's 10x better than before I talked to you (and that happened overnight) 10x 1 is still only 10/100 :dummy: or something. I think you might be right that the interaction between a student and teacher is the best way to learn, because that's 1 on 1 teaching, that can be tailored to the students specific needs by answering the student's specific questions. But most people don'tr ask these questions, most people think in terms of "I understand" and "I don't get it" and if they don't get it, they think they don't get the whole concept, rather than narrowing down which part they don't get, therefore because not all students question, not all students learn. But I at least do narrow it down, and right now my biggest weaknesses are: cylindrical shapes, complex shapes and imaginary guideline's accuracy.

I think with some practice I can solve the former two, but since when I draw with what you taught me I use guidelines I see in my head (or rather, I decide where the horizon is, and where the initial VPs are, and draw based on that; my current plan is to learn what guidelines Scott Robertson uses and then imagine these as well to solve problem (probably 1), 2 and 3 but there's no guarantee it will solve 3), and you say you draw a first object and base the perspective of the rest off of that first object, using my method I can indeed draw this first object without issue, I can even draw the others albeit with some difficulty, so if I were to ask you to explain anything to me now, it would be how you base your perspective off one object rather than on horizon + vp mental guides?

How did you figure out this technique? What goes through your head when you execute it exactly? How does it work? Can I do that too?
Nsio Featured By Owner Edited Jan 13, 2018  Hobbyist Digital Artist
Yeah, sometimes when people ask guidance from me, I would just want to say they should start from scratch. That's hard to swallow and no one wants to hear that. However, I don't have a curriculum to follow, the "learning order" tutorial is closest to what I have managed to come up with so far. There are so many things to learn, but by doing wise choices it can be done easier. What comes to me, I just wanted to learn drawing quickly, so I focused on concepts that would allow me to get started. As long as I'm drawing constantly, I can build up my confidence and accuracy and venture beyond my comfort zone.

I have tried to compile my tutorials in a way that they would be captivating to look at. Boob tutorial definitely does the trick lol :D. But on a more serious note, there are many psychological things that when taken in account can draw the attention of people. Artists are masters of manipulating the viewer to see what they want and guide their eyes to the key points.

Those students who think on their own, ask questions, come up with their own ideas and experiment are the ones who learn. And those teachers who can identify the weaknesses of their students and know how to steer them towards the right direction are the best teachers. Since I know what kind of issues I had, I assume people have very similar issues as well. And as you pointed out, there are many people who have walked the same path of arrogance. Even the most given facts are to be questioned and dismantled for closer look to grasp the secrets.

I think I started to understand how perspective works when I was at the university and working on CAD modeling. Slightly orbiting around the model made it look more three dimensional. I also noticed how hard it was to fit things within the field of view when making 3D renderings. The lines are just too straight. If I forced 2 point perspective, things on the ground and close to the viewer look skewed. When you take a picture with a camera, there will be very slight distortion. I realized that "mathematical" perspective, while true in its own right, has its limitations. I started to pay more attention on the distortion.

My childhood home is next to a railroad so in one occasion I observed how a train looks when it passes me at close distance. When the train goes past me, where does it go? If I turn around, it goes away from me, obviously. But the interesting part is what happens between those two views. The transition is the key here. If the real world worked like mathematical perspective, the train would become larger behind me. But when I turn to see what's behind me, the rules change dynamically to meet the new conditions. So this is how I found that there are vanishing points at both ends of the axes and the guidelines has to bend so that they will recede at both points. The guidelines are parallel, but mathematical perspective makes them "literally too parallel" so to say.

I've done similar experiments with some handheld objects (like remote controller) and observed how I see them when I move them in different places in my field of vision. When it's directly in front of me, then that's where the horizon and "vertizon" intersect. Then you could imagine that cross divides your field of view into four quadrants. Technically you can just study how the object behaves in one quadrant, the rest of the quadrants are identical but the effect is mirrored. Let's imagine that the quadrants are number from 1 to 4 in clockwise order. So if the cube is on the right and seen from below, it's on the 1st quadrant. On 2nd quadrant that same cube would be still on the right, but now it will be seen from above. On 3rd it's on the left and still seen from above and on the last quadrant it will be on the left but seen from below just like on the 1st quadrant.

If you have a small cardboard box, it's good for this kind of observation (for it's clearly rectangular).

Anyway, I just started to apply simple rules. So if I draw a cube in certain orientation, what does it tell me about the relation between the object and the beholder? Is it above or below, left or right, i.e. in which quadrant the object is? How far or close it is the beholder? It's for the best to assume the bottom (or top) face is in fact horizontal, because it will then give a tangible hint of the world it exists in). I decide where I want it to be and after that I will start to see where the rest of the image should be in relation to the first object and the beholder according to the rules. I have learned to feel where the horizon should be. Like "I see the bottom, front and left face of this cube, so if I move my eyes to the left and down, the intersection of the horizon and vertizon ought to be somewhere in there. I have also learned to feel the "fan effect" of the lines as they recede towards the vanishing points. The larger the difference between the guidelines (or the edges of the reference cube), the closer OR larger the object is. When these same lines are nearly parallel to each other, the object is far away OR small. Basically there are multiple rules affecting the view at all times which can flip or rotate the view depending on how you perceive the image. In real world, we happen to refer to horizontal plane because everything are technically bound that horizontal plane, so our brain has no problem with figuring out how to perceive the world. 

I actually cover these things to some degree in this tutorial. The pics at the bottom with the tiles seen from above, below, left and right.
Nsio explains: Perspective by Nsio

In this practice I also apply the "quadrant mirroring" by "rotating" or "flipping" the rules. If you look at the vertically aligned cubes, you could imagine that they are seen either from above or below. Since they are only simple cubes with no meaning and there isn't any background to refer to, I don't know if people are able to see the rule flip (I tried to draw those figures pointing at the direction they are looking at).
Nsio Practices: Perspective + 3D by Nsio

Anyway, this is the strength I have. I can see the objects in different orientations and I can also flip the view in my mind. I can also invert the view in my mind to some degree, like reverse the depth cue (inverted cube looks weird if you think that the closest corner is actually the farthest, this is what I tried to demonstrate on the aforementioned tutorial). If I draw just the horizon and some vanishing points, I have no idea where the view I'm imagining in my mind is. This is one reason I originally abandoned the perspective system, for I had no idea how to set it up. My own method still follows the same rules though and I have confirmed it many times.

If that makes any sense to you, you can adopt the same method. For me it has become a second nature, it just makes a lot of sense and works in all scenarios. In fact, I'm so accustomed to see this way that when I see a drawing like the racing car example where there are two pics next to each other, I feel there is perspective mistake in there. You know, in that pic there are two racing car pictures in identical orientation. I however tend to see such images as if it was one image, so to me it looks as if the car on the right is rotated slightly. It just shows my perception works as intended :D.
Cestarian Featured By Owner Jan 16, 2018   Digital Artist
Whew, that took a while to digest, I started by reading the first half, then for some reason I was getting tired so I waited until I was in a learning mood to read the second half. Your method makes sense to me logically, and the more I think about it, the more I feel like trying to see if I can do the same in practice, I also however see that there are a bunch of gaps in my knowledge (which is where I guess 3D modeling came in handy for you :P ) I suspect that like you, if I don't start getting it soon I should probably try picking up 3D modeling again and learn the rest from observation by myself.

I think this method could end up being really useful since it has a few obvious benefits.

  • It allows you to go straight into drawing without overthinking your perspective or drawing a bunch of guides
  • Enforces the idea that every object in the image is connected, helping you create a more cohesive (and therefore pleasing) image by default
  • Allows you to account for distortion more easily since you're looking at the image, not the guidelines, over time it no doubt develops into a 'sense'
  • Makes it easier in practice to focus on where the object is, in the image, rather than where it is from the perspective guidelines, casting an illusion on yourself as you would on your viewers :D which should in turn make drawing a more immersive and enjoyable experience overall.
There are probably more good things, I think when I first saw that tutorial you linked to a couple of years ago, I thought "that's what I want to do" (which I still do think) but at the same time decided I wasn't ready for it (and I was right) now however I am ready to start practicing it :meow: mostly thanks to the guidance you gave me last year. Now once again I must thank you for your guidance, Nsio Sensei  :la:
Nsio Featured By Owner Jan 17, 2018  Hobbyist Digital Artist
Yeah there are benefits in this method which make it more intuitive. I don't think it's significantly easier, though it forces you to process the idea. I'm sure that all good perspective artist have this skill to some degree, they just rely on guidelines for accuracy which is harder or more troublesome to achieve with this method.

I figured I didn't even explain how I embed the rules on the objects. I onlyexplained how the objects are related to each other in space.

If we start from the core idea of any system or method, it has to be reliable and applicable in any situation. The less complex it is to put in practice, the better. A good system or method builds on basic principles which form a solid foundation and which can be extended for complex tasks. It's imperative that the rules can be used to check the drawing for errors.

Perspective has many rules and some of them are technically very easy to put in practice. The horizon, vanishing points and guidelines create a very solid system that just works if followed trough (when the guidelines are drawn with a ruler and they meet at vanishing points, then you technically can't go "wrong" there). It however requires more deep understanding how to setup the scene to meet specific needs and one has to take the limitations in account. This is where most people just fail.

My method is automatically less reliable because there aren't straight lines for guidelines. Therefore I have to embed the rules into the objects themselves to make sure I get them right.

Basically there are still many rules borrowed from the perspective system, or rather, facts about geometry. I'm sure these are obvious to you, but I'll explain it anyway.

A cube has 6 faces that are identical. Therefore I can focus only on one face. The edges form 4 corners, each with 90 degree angle (right angle). Therefore all faces have right angles in relation to any other faces. Therefore when there are two or three faces visible, I have to keep these rules in mind. The more I see one face, the less I will see the other faces. If I see one face directly from the front, I won't see any other faces. The hard part here is to make sure those corners are in right angle at all times while also taking in account the depth, because my method doesn't provide as reliable guideline as traditional perspective system does (because it technically takes the depth distortion automatically in account, it's built in the system).

So I need more rules to make sure the corners are in fact in right angle. I need to make sure that the edges are parallel or perpendicular, for that's a direct consequence of having a right angle. Two lines that have  a right angle and intersect are perpendicular, two opposite edges of a square are parallel. This isn't any different from traditional perspective, but the thing is that I will use these aspects as a way to check my drawings for error. If you draw straight lines but they aren't parallel or perpendicular, there won't be a right angle. This is easier to grasp with isometric projections because then you don't have to worry how depth affects the view.

The next important thing is to find the middle points. Middle points are in the middle, it's just that simple. It shouldn't be hard to find a middle point of a line even by eyeballing. And hey, you can use them to check for errors as well. If you draw a line between two opposite edges along the middle points, then it has to be parallel in comparison to the other two edges. Draw two lines (horizontal and vertical) along the middle points and they will intersect in the middle of the face. Draw two diagonals between the two opposite corners and they will also intersect in the middle. If all 4 lines you drew intersect exactly at the same point, you know you are doing well.
The middle lines also provide yet another way to check the drawing for errors. I call this "shape equality". Any shape that is truly divided with middle lines will be divided into 4 equally sized shapes which are 1/4th of the original shape. So a square will be divided into four smaller squares. If each shape look identical, or at least very similar, it's likely that the original shape is drawn right and you have also found the middle points. Now you can just start "flipping" and "mirroring" the original shape. It won't reveal whether you have drawn the shape in right orientation, but it's already something noteworthy.

Of course,when moving from isometric projection to perspective, you will need to "break" these rules a bit but still maintain the idea of parallel and perpendicular lines, middle points and lines and shape equality. Now depth is just one more rule to keep eye on. I basically see a hand fan in my mind: "…" . Like, imagine the pivot point is a vanishing point, the slats are guidelines. Technically that's what perspective system does. I try to keep that effect in mind and subtly change the angle depending on where the beholder is looking at.

And that's just a cube we are talking. There are more rules when it comes to complex shapes, but even they can be broken into the same rules as in squares and cubes, but going trough all possible shapes and forms would be too much in one go... and writing it without drawn examples is futile for me.

To put it short, the big idea is to have multiple rules which you can then use to cross-reference each part of your drawing, one by one.  In fact, these geometric facts are part of perspective system as well so these same methods can be used to check for errors in constructed perspective. Contradictions between rules need to be analysed to see which rule(s) you didn't follow.

That said, I can't draw a good perspective drawing in one go. It's a process where even already drawn objects may still change.

I think the hardest part here is to avoid letting your own mind interfering the process. I check this by first assuming that whatever I drew is drawn correctly and then I imagine what that would look. I try to imagine how the drawing looks from different angle, how it would really look if it truly looked like the way I drew it. Since I won't let my brains think what it wants, I easily see clear abnormalities which I can try to fix.

Here are some examples of imagining object from different angle. I've drawn some illustrations for people to explain what I see in their drawings. In first pic I shoved how the arm would look from above. On second pic I saw the book as if it wasn't on a horizontal plane. On the third pic I pointed out how the arm  should be posed according to the limitations of the joint articulation.
Some way to fix stuff by Nsio Object On Ground by Nsio Raised Arm by Nsio
I'm good at seeing errors like these, which is why I'm not doing blatantly obvious mistakes very often. I wouldn't be this good at this if I didn't force myself to approach drawing like this, in fact, I did the same mistakes as everyone at first. Years of experience have done the trick.

You're most welcome. It's always fascinating to talk with people who are truly trying to understand these things, because I also need to put my thoughts in order.
(2 Replies)
HorseLeafsCabbage Featured By Owner Dec 23, 2017  Hobbyist Filmographer
I feel like the application of 3D modeling (even if rudimentary) can help with an understanding of space and persp.

I recently came to the conclusion that that is a key missing factor in my ability to bring my ideas to life; a good intuitive grasp on the space and depth of a drawing.
Rixks Featured By Owner Edited Dec 2, 2017  Hobbyist General Artist
I would say to explain the cube in more detail, and use some more sample animations. Although, I get the idea of the point cloud, but to me, that's kind of a given; not to discount your findings, btw. Perspective is only hard sometimes because I've not studied enough from life and photos to be able to properly justify my liberties taken with it. I like the idea of technical accuracy, but being obsessive about it feels too stiff to me. All those extra points just feel overwhelming to consider.

I feel like art is more about having something interesting to show--what the camera or the eye can't capture, rather than explain what's already there right in front of us. Reality is important, sure, but it's your toybox to play with once you have a good enough grasp on all the concepts you need to learn. Making things that aren't real is what's exciting about it.
Nsio Featured By Owner Jan 11, 2018  Hobbyist Digital Artist
Sorry for the late reply.

Many of the things that I have discovered are in fact so obvious and given that its actually embarrassing. I figured that I had to study them in order to bypass automatic filtering of the brain. And when things got too complex to handle, it was necessary to find the ways to simplify.

What you are saying about art vs. realism is true, but one has to be careful with such statements. Does that statement stem from real artistic understanding or from something that's just said to be that way? For a beginner that will most likely be an subconscious excuse. That's not to say it wasn't possible to make great art without understanding about perspective, but it surely rules out many options.

Anyway, my goal is to figure out concepts and rules that apply in all scenarios. You will never need to plot a point cloud to construct a perspective, the point cloud just refers to the idea that there are infinite options for you to set the perspective.
Rixks Featured By Owner Edited Jan 12, 2018  Hobbyist General Artist
It's cool, man. Anyway, to answer your question about my statement:

I feel that my answer stems from what I've gathered in artistic understanding. In my opinion, a beginner (completely wet behind the ears, mind you) needs to take these concepts very seriously. For example, I wrote off a lot of stuff when I was beginning because I believed there would be an easier way to get where I'm going than what most people have done...but from asking around, trusting my eyesight while taking note of my observations, I've learned that I have to do obsessive studying to get the idea I want to convey in a medium as close to the image in my head as possible. Also, my definition of obsessive means to go far and well past the means of getting a handle on something than having to know every minute detail about it. I'd say that take on studying something varies from artist to artist, though.

Over the last four and half years, I've been building on my own intuition trying to make my mind more malleable. Sure the ideas and truth of the world are pretty obvious and blatant, but it's a lot tougher to put them into practice, at least from where I'm standing. Half, if not most of what I had been learning at the start was still confusing to me, and I didn't quite believe that what I was learning was true in my head, or made sense enough for me to properly explain it on paper. I was a lot less observant then, too. Concepts like "How do I make sure all of my character's body parts make sense in space?" "How far apart are they?" "How am I supposed to consider and see all of that at once when that's a lot of things?" Then I went back to someone saying "You need to see 2D and 3D at the same time." Still, I was lost, and then it clicked for me when I realized that I was supposed to be reading everything I studied or drew like a flat image or silhouette the whole time--like I had unconsciously from the start.

I have to draw as if I'm witnessing an action happening before me. I have to feel it and anticipate it, and when I'm not completely sure how to explain something, I go right back to study.

With all that said, I think your method explains a lot, but it still all boils down to each artist and how much they're willing to learn about a given subject.
Rixks Featured By Owner Jan 14, 2018  Hobbyist General Artist
I'd like to amend a line from my prior statement:  Also, my definition of obsessive means to go well and far past the means of getting a handle on something than just understanding enough of it to get the point across.*
Marcotonio-desu Featured By Owner Nov 15, 2017
You lost me completely with the dot spheres, specially the first ones going out of bounds from each other.
From my understanding, if you look at the visible tip of the the pole, you'd manage to make a "dome" out of the positions where this tip sits at in space, but for it to become a sphere you would have to either reverse the tips (and go infinitely towards the other side) or, taking what you said about the pole being a radius, project one new sphere for each pole position.

Maybe if there was a one~two~three points in space picture before plotting the whole sphere it'd be more clear what's going on, and what each color represents.

I did read the comment thread you posted, though, and I understood that discussion just fine. It's kinda like being inside of a round cage, each bar being one "slice" of your horizons and "vertizons" based on how off-center it is.

That always makes me think about stuff that doesn't bend; imagine an infinitely long pole, but it's not touching the ground; it's instead going upwards. Where does it converge to if outerspace isn't rounded like the Earth?
This is how I'd project its perspective, but it doesn't feel right, specially the fact that I can stare at the vanishing point. Shouldn't it vanish on my personal zenith, thus never being visible? But then if I look up I feel like I will be able to see "above" the infinitely long pole, and it will not converge to the former zenith anymore, but more to the curved horizons just below it. Really confusing stuff. Maybe I have some misconceptions caused by 2D art often representing those deformations in visible ways, so I find it normal to see a bent tower and am assuming my own eye would be able to see that deformation even when moving my head. ANIMES RUINED MY HEAD. HELP.
Nsio Featured By Owner Jan 11, 2018  Hobbyist Digital Artist
Sorry for the late reply.

I searched for an example pic that would closely represent the idea I was after. I actually thought it might have been for the best to explain what to look at, because there are some unnecessary blue dots there. I however assumed that people would understand that I'm referring to the "red" sphere. I also thought my explanation would do the trick: "So the idea is that you as the beholder are in the center of the perspective system, i.e. in the center of that point cloud of vanishing points."

Representing 3D on 2D has it's limitations which is why it's difficult to actually demonstrate the effects. A 2D representation is static, therefore it shows only one particular view. If we wanted to show more than what our field of vision allows, then the perspective has to bend in order to follow the rules. This isn't how we are used to see though, because when an object is out of our field of view, we turn to look at the object. The view isn't static anymore, it changes and this transition from the original view to the new view causes the bending on 2D image.

So the vanishing point of the infinitely long pole (that's vertically orientated) is above you, which is in fact your "personal zenith" as you said. However, to see this vanishing point you need to turn to look at it. Now this vanishing point is in front of you, even though from your perspective it's still above you (because we are subject to the gravity and therefore refer to horizontal reference plane, i.e. the ground). So the pole isn't vanishing at different vanishing point, it's just your view that changes.

Think about a panorama image. To take such a pic, you have to rotate the camera which then compiles the image into a panorama view. The camera can't see the whole scene if it doesn't rotate.
Marcotonio-desu Featured By Owner Jan 17, 2018
No worries about the delay, I myself owe a few people some replies on dA. >_>

I think I understand it better now. I was thinking since the pole doesn't bend (like the Earth's surface), there would be no converging to a certain point in space, and even if it was extremely foreshortened forwards, as long as it had a slight tilt upwards it would keep going up, just taking billions times more pole to reach the "out of bounds" of my field of vision. But I thought about how Limits work and I saw where I was wrong - it is still going up forever, but it's going at such a slow rate that it never passes the vanishing point, even if it's infinite. And the converging is not caused by the curvature of Earth as I was thinking for some reason.

That was an insightful exchange!
davichiz Featured By Owner Nov 9, 2017  Student General Artist
The tutorials are great but people actually have to put it to practice daily to grasp it. That can't be taught. Take yourself for example, you understand these things because you've spent countless hours putting them to work in your illustrations, when you started out it would have been difficult and everything probably looked terrible but over time you improved and so did your understanding.

The problem is that's not something you can teach. You can explain it but the mileage earned by actually learning these principals is what everyone needs to do.

I've been learning to draw everyday for almost a year now. I started off thinking I could watch a tutorial and then know how to do this or that but if I've learned anything this year it's putting these things to practice is what makes improvement.

I stopped posting on my page in late july and decided to buckle down and if I watch/read something interesting, make a point of drawing it out without the tutorial and repeating it until I grasp it.

I think spent a good 15 hours straight rotating things on a dividing line to see overlap etc, I finished about 30 pages in that day. They started out terrible and by the time I finished I actually knew how to do something like that. 

People underestimate how much shear mileage makes for improvement, If you're reading a tutorial and then moving along to the next like you learned something you just won't improve. You need to practice those principles.

Great tutorials btw! You should keep them coming if it's what you enjoy doing. Maybe throwing in more assignments would get people to actually test these things out.
Nsio Featured By Owner Nov 30, 2017  Hobbyist Digital Artist
True, many concepts require a lot of experimenting to truly get the idea. I'm hoping I could find a way to help people find the key to great revelation. People are so different that finding an universal explanation may pose impossible after all. I still remember how blinded I used to be with very straightforward and obvious things that it still amazes me. Technically everyone are struggling with the same issues.

Practicing an unfamiliar concept is also hard because one can never be sure whether they are on the right track or not. Some concepts may even be impossible to learn before grasping some other skill. In those cases 15 hours or even weeks may be fruitless practice (or the effects will not be visible until years after). On the other hand, how could someone learn drawing a difficult viewing angle if they never draw one? Although one should learn the basics first before going for the advanced things, it maybe necessary to stumble with challenges to actually realize what are the basics.

Thanks! Sorry for taking so long to reply
Skimbleshankx Featured By Owner Nov 8, 2017  Hobbyist Digital Artist
I'm pretty sure that my problem with perspective is that I get drawn into a) what are the actual physics behind it, b) trying to rationalize the three dimensional object as a series of lines on a two dimensional plane, and c) getting frustrated from lack of progress within a short time. I have learned the classical three dimensional objects: cube, sphere, pyramids, and cylinder. I can reproduce them well enough, with or without drawing a proper set of vanishing points. But I just can't seem to make the jump from that to anything else without getting bogged down in stuff like 'what angle of light do I need in order to create this level of shadow', 'how do I show where the edges are on an edge-less (rounded) object', or 'why doesn't my drawing look professional already'?

I've never played with Sketchup, that I am aware of, but your little model is cute. I think I have most of your old tutorials saved to my favorites. 
elitassj4 Featured By Owner Nov 8, 2017
Any thoughts on streaming on Twitch or Picarto ?
sakpalamey Featured By Owner Nov 7, 2017  Hobbyist Traditional Artist
That I don't have a future.
jose123xdxd Featured By Owner Nov 7, 2017  Hobbyist Artist
En mi caso yo aprendí lo básico de perspectiva para saber dibujar en 3/4 pero aun así no he mejorado mucho aunque me a sido muy útil lo que e aprendido 
HarmonyRainWingCat Featured By Owner Nov 7, 2017  Student General Artist
I never had too much trouble with vanishing got pretty hard for me beyond four- and five-point perspective though! XD

What helped for me was understanding that the Earth is round (no shiz) and that looking forwards is like looking at a sphere, you'll never see what goes beyond the curve and that's why the points grow smaller in certain points. I know, I know, elementary stuff, but it seems to do a lot for me personally. It's still pretty hard to understand where to place my vanishing points though, thanks for the diagrams! Peace Bunny Emoji-72 (Kawaii) [V4]  xxx
Nsio Featured By Owner Nov 16, 2017  Hobbyist Digital Artist
I need to confirm one thing, do you find that the horizon in the perspective system is the same as the horizon of the Earth? That once anything reaches the point where you can no longer see the ground due to Earth curvature, that's where the horizon and vanishing points are. Is that what you are saying? I want to be sure I understood your point properly because to me it sounds you have a big misconception here. Of course, if you just want to continue with this conversation.
HarmonyRainWingCat Featured By Owner Nov 17, 2017  Student General Artist
That's pretty much what I said yeah :P

I'm still a bit (very) lost when it comes to the legitimate reasoning and placement of vanishing points, so this really helped me.
Nsio Featured By Owner Nov 17, 2017  Hobbyist Digital Artist
I see, well the horizon of the Earth and the horizon in the perspective system are two different things. Things do get smaller by the time they reach the the horizon of the Earth for sure, but they don't vanish there. You see, you can still see the masts and sails of a sailboat even when it has already crossed the horizon from your point of view. 

The concept of perspective doesn't take in account the Earth curvature at all. It assumes the ground is completely flat and the horizon is infinitely far away. Its horizon is your eye level and the guidelines receding there are completely straight. So if you want to take the curvature in account, you need to adjust the methods of constructing perspective and make the rules bend along the Earths curvature. That will make it much harder though because you can't use a ruler to construct such perspective anymore. On the other hand, if you can do that by free hand, it can look even more believable and lively.
HarmonyRainWingCat Featured By Owner Nov 22, 2017  Student General Artist
Thanks so much! >w<
JellyBX Featured By Owner Edited Nov 7, 2017  Hobbyist Digital Artist
Actually i have a better understanding at perspective thanks to this tutorial:
Nsio Explains: Learning Order to Human Drawing by Nsio
Because of that tutorial i backtrack all the way into drawing lines to improve my skill Meow :3 
After im satisfied with my lines, i draw tons of boxes which contribute a lot in my perspective understanding
I even draw a lot of scenery using only boxes for that exercise until the point i can draw boxes with determined vanishing point from any place and angle
Yet drawing boxes with perspective actually isnt enough for me to apply it into actual scene
So i watch this tutorial which was referred by BBstudies, and it kinda inspire me about how to draw people with perspective into a scene:…

However there is another problem with perspective, like how to apply it if the vanishing point itself is outside of canvas? :o (Eek) 
This one kinda drives me crazy
Until i found this turorial which is made by KNKL…
That trick is kinda clever and works pretty well for me

As for now i can easily determine how perspective distort the shape by combining my perspective knowledge and imagining stuff as simple box, then start working from there :) (Smile) 
Whenever i got a difficulties in imagining object with perspective, i draw it as boxes Wink/Razz   
Nsio Featured By Owner Nov 16, 2017  Hobbyist Digital Artist
Yeah, it may not need anything other than more experience about drawing in general. Technically speaking perspective is just about putting the lines in right places reliably. So even if someone didn't know about the vanishing points and how to use guidelines, it still possible to draw cubes that look alright. It's then possible to find the rules governing perspective from there.

The first video was cool and that artist seems to be quite a pro. He did good job demonstrating the effect of vanishing points and guidelines, though he didn't really elaborate why it is in certain place. For beginner it's really difficult to decide the place of the vanishing points to get the desired effect. On the other hand, practicing like this will make the artist familiar with the effects he has chosen to use (whether they work or not in that particular case you want to pursue).

The second video demonstrated the limitations of the system, scalability and how the unfavorable rules can be mirrored to make it work in different scenario (like the effects of using the 3rd vanishing point).

Neither video didn't elaborate how we really see things though... and the second video even claims as if we still don't know how we see the world beyond our field of vision. The effect he demonstrates is purely because of following the rules of mathematical perspective literally beyond its limitations. That distortion takes place only because converting 3D space on 2D canvas will never be completely perfect and seamless if you venture far enough.

Take a look at this image:… here you can see a cube unwrapped into 2D space. As, you can see, there has to be gaps on the corners. You can't connect the left and right together either, so the world just sort of  "ends" there. In addition, the points where the faces connect each other look a bit weird. If you wrap this flattened cube back into a 3D cube and imagine yourself inside this cube, you would perceive the sky and ground just fine, without and gaps or discontinuity (though the corners may still look funny, for this is a cube we are talking about). In a similar way, if you wanted to flatten the Earth on 2D space, it would look somewhat like this:… . For practicaly use that just looks rather weird, so we tend to use mercator projection instead:… . It looks alright, but the closer you get the poles, the more distorted the continents become. For example, Greenland seems to be larger than Africa, but in reality it's hardly 1/6th of the size of Africa. Similarly, if you go beyond the limitations of the perspective system, things will start to skew and distort.

That said, we simply can't see more than our field of view allows us to see. Images where the distortion takes place merely show these areas we can't see unless we actually turn our eyes or head to see the area, in which case the area will be within the limitations of the perspective system again. That said, every time you move your eyes and/or head, the rules of perspective will change as well to meet the new conditions. In fact, they have to. Therefore there is nothing weird happening in the areas that are beyond our field of view. If we literally believe the mathematical rules of perspective, it will just lead us astray, for if the rules don't change depending on where you look, then the perspective gets broken.

You can witness the rules changing on the animated box. In each frame it looks alright, because the rules keep changing while the view changes.

That's one reason I didn't get perspective at first and abandoned the system for a while. I however figured that rules keep changing when the view changes and they actually have to bend if we flatten the image. Even then it won't be perfect, but it will make things look more natural. You can actually see this bending if you try to see what happens in your peripheral vision (without moving your eyes). If you look at the the corner of wall and ceiling and focus on looking at the two wall corners on left and right without moving your eyes, you ought to see edge between the wall and ceiling bending slightly. The larger the room or the closer you are the wall, the more prominent the effect is. You can also perceive this if you are walking on a floor with tiles. If you keep walking, the tiles seem to bend around you.
JellyBX Featured By Owner Nov 20, 2017  Hobbyist Digital Artist
Thanks for your reply! :) (Smile) 

Indeed, the perspective will always change if we move the camera or our eyes since the vanishing points will also move from our sight which basically also change the object shape in our perception.

Actually something interesting which i realized during my exercise in drawing tons of boxes is vanishing point exist like in the direction of where the box come from, but that fixed point wont moving pretty much even if we change the view.
Something like if we assume that a box comes from fixed point in horizon line, if we change the view a bit lower near the box, obviously the horizon line will be placed lower while the box stay in its place and naturally it'll seems that the box distorted (like an above view) because we retain its vanishing point which is moving along the horizon line.
I think the same rule also follows if we move the camera higher and so on I am a dummy! 

Yeah maybe thats a basic understanding about perspective which i got from drawing boxes, yet i dont quite understand about how to bend perspective until it reach something like curve shape or something like that Sweating a little... 
FireShika Featured By Owner Nov 7, 2017  Student General Artist
I had to reread some passages but this does make a lot of sense to me. Personally I fail to think in "lines" while drawing because then I just end up thinking 2D if I try to break everything up into forms. I just try to imagine going around the object/character in 3D space inside my head ... yeah ... try ...

However I like this approach. Especially the last animation is a very good idea. To bring your point across however i'd make I'd extend the canvas so you can see the two vanishing points on the horizon, also not just moving up and down but also around the block will get the idea across better.
Nsio Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
I'm thinking ways to illustrate the idea more thoroughly on Sketchup. Since it follows strict mathematical perspective, it's difficult or impossible to demonstrate some things that I would like to emphasize. Showing two vanishing points at the same time is one of those things that's problematic.
Technemancer Featured By Owner Nov 7, 2017  Hobbyist Digital Artist
I read your 6-point perspective tutorials with no clue how the hell perspective worked. Then this came out and I finally understand.

FREE YOUR MINDS GUYS! (thanks Morpheus)
Nsio Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
Good to hear that this could shed some light on the subject :D
Technemancer Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
speaking of lighting, your shading tutorial was great Wink/Razz 
Rainbow-Skybird Featured By Owner Nov 7, 2017  Student Digital Artist
My problems with perspective have basically been trying to apply it to complicated shapes. :( Of course everything CAN be broken down into simple, 3D shapes, but when it comes time to actually rendering the details (such as muscles, curves, etc), it's easy to kind of lose the idea because we rely too much on these rigid, blocky shapes and that can make our art very rigid.

I do believe in just experimenting with it and trying to focus on 3d objects as a whole, without strict point guidelines, but it's definitely tricky for a reason. More animated examples would be super nice actually. :) Many artists are visual learners, so SEEING something in perspective move may help more than just reading a bunch of text about it.
Nsio Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
That's when its essential to start approaching the subjects from the opposite angle once you got your cubes in place. For example, look your own hand and try to imagine its faces within boxes. It's like associating complex forms into easy to remember boxes so that you can then just fill the boxes with whatever you want. Obviously it takes quite some time to form extensive visual library in your mind, but the more you keep doing it, the more useful it will become. I used to spend all my down time on observing things around me (while I was on bus for example).
Rainbow-Skybird Featured By Owner Nov 10, 2017  Student Digital Artist
Thank you for the response! :) I think it's better to just expect perspective to be hard to grasp so it isn't as discouraging when struggling beginners like myself don't quite get it right for a while! I'll definitely look into visualizing such things more often. :salute: It can be overcome!
DarkLored123 Featured By Owner Edited Nov 7, 2017  Hobbyist Digital Artist
I agree, the main reason in my opinion that perspective is difficult to grasp is that people who create tutorials simply give you the information as it is, and don't necessarily explain the deeper concepts of what perspective is based around. Just like you showed with that spherical diagram with the poles, only after realizing that the vanishing points are located on the endpoints of the X, Y and Z axis was I able to truly grasp the concept behind the illusion.

I also think why perspective and art in general are so difficult to learn is because some artists tend to glorify their understanding, not saying that most are, but from what I've observed some people simply make drawing seem intimidating to learn as if it is some sort of subject that only 1/10th of the population can learn. I found that art was much easier after I let the mindset of it being so hard to learn die, it is like any other subject of study that exists in this world and is well developed enough for anyone to learn.

After having some discussions with you privately and you making it aware to me that perspective does not have to be done by using the actual perspective grid is what opened my eyes as well, it is just so much easier to get decent results without the grid and only theory since I personally do not aim for technical accuracy as to say in terms of it having to be accurate, as long as it is believable I am satisfied, right now it is just a matter of practice for me. 

What I personally find difficult about drawing in perspective is to keep it consistent within all the objects, especially when you talk about animate beings since some body parts face different orientations but the hard part is to have them still be apart of the general perspective. That is my take on the matter at least.
Nsio Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
Yeah, I think typical guides tend to make people limit their horizons. Perspective works only when then person knows how it works and what they want to achieve with it. Neither is something a beginner could do at first. Even more experienced artists have to stay alert constantly to avoid making mistakes. They just have the advantage that they can usually tell quickly if they are doing something wrong.

By not relying on a grid that you can't get right in the first place, you avoid limiting yourself. When you start getting things somewhat in place, you will get the usefulness and limitations of all the guidelines and rules. Discovering things on your own will make it stick to your mind as well.

I have the same difficulties as well. I haven't let that discourage me to draw, in fact, I have tackled with those difficulties even more vigorously.
DarkLored123 Featured By Owner Nov 10, 2017  Hobbyist Digital Artist
I think the grid is effective in teaching how perspective affects objects in different situations. It can be a useful exercise to beginners, but eventually they need to learn to get rid of the training wheels, and apply perspective by theory. 
parameciumkid Featured By Owner Nov 7, 2017  Hobbyist Digital Artist
I never had much problem with vanishing points. If there's anything hard about perspective for me, it's applying it to blobby organic structures such as people's limbs - when a character is pointing toward the camera, what shape do I make her finger so that it looks like a foreshortened finger and not a tumor? How big do I make her hand to make it look like it's in the foreground and she doesn't just have a really stubby arm or a weird monster hand? What do all the facial features do when viewed at extreme angles?
Nsio Featured By Owner Nov 9, 2017  Hobbyist Digital Artist
You clearly just need references to address the points you mentioned. Either real life or drawn ones. If you have a mirror in your house, spend some time just observing yourself. I used to take poses in front of the mirror, I still do at times.
Itsukarine Featured By Owner Edited Nov 7, 2017
Despite "understanding" perspective I find it incredibly difficult to put into application outside of single point. It's probably a mix between laziness because i hate using guidelines and finding them time consuming... though I guess laziness fits both of those. And getting scale right.

I particularly have it hard with bodies; I think that with hard unmoving objects it's very self-evident to work with and the only restriction is imagination, but with bodies I find myself often making the perspective really extreme where it shouldn't be; to the point where I feel as if I'm just feeling my way through anatomy placement. (I tend to just kind of place shoulders always one lower than another for example, half symbol drawing half "perspective") and my perspective's pretty bad in almost every case that's not an extreme low or high angle since it's not subtle and the "pole" is easy to visualize.

I wonder if it's just application not being enough or I'm really weak on certain things; it took me far too long just to realize that multiple vanishing points could exist so I'm probably just an idiot.
Nsio Featured By Owner Nov 9, 2017  Hobbyist Digital Artist
Laziness surely is a problem. I could easily spend +10 hours on drawing daily, so I could gain a lot of mileage. But trust me, I hated using guidelines as well. Therefore I wanted to find a way to draw where I wouldn't need them. I can now see them in my imagination, though occasionally I will need to draw them. It's significantly easier now and while my abilities aren't perfectly reliable, I keep honing them with each new drawing.

If you can identify your tendencies, you should start working on them. If you wanted to improve that is. Also try doing "the opposite". So if your perspective is too extreme, experiment what happens with no perspective at all. Easy viewing angles and isometric projections could be ideal for you.

I think we all are idiots at first. The answers are literally littered all around us, yet we fail to see them. Many concepts I have figured out are actually very straightforward, the difficulty is to tie them all together and to actually draw them out.
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