What's difficult about perspective for you?
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: comments.deviantart.com/1/5940… (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):
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
The CoDD: Tiamat6A1 character description v1.1
I'm practicing Perspective now because of the advice you gave me a long time ago. It's very hard. I believe because volume I feel that perspective is very hard because it's subtle. You have to take into fact the shape, form, and volume. It's hard cause the littlest detail matter so much. I am continuing my perspective journey, so thank you. How do I test my perspective is correct? Do I just have to develop my artistic eye? I don't know maybe I'll figure it.
My biggest issue with perspective is to find a practical way to keep proportions of complex elements (like a scene with several human figures with different body types in dynamic poses) in perspective.
The way that I do now involves a lot of eyeballing and trial and error. It ends up draining a lot of energy and time that could be spent in other steps of the illustration process.
I've researched several ways to solve this issue and found some that could work ( like the one from cushart that moderndayjames uses here: www.youtube.com/watch?v=DaG-cB… ), but they are simply too complex to be used in a real environment.
So far, a way that I believe that works is to build a simple 3d mock up of the scene and use it as reference. This one have the added benefit to change the camera around and test different views. I still need to build some 3d models and test it to see how it goes.
That's it, cheers!
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.
After that talk however the conclusions I came to were quite a bit different from what you described with the pole 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 ) 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 (this was all you ) 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 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 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
I'm not exaggerating, this is not a 3D model www.artstation.com/artwork/wby… (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.
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:
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:
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.
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
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 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
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 . 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.
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 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 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 ) 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
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 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 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?
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 . 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.
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).
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 .
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 which should in turn make drawing a more immersive and enjoyable experience overall.
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: "www.designsponge.com/wp-conten…" . 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.
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.
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.
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.
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.
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.
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.
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.
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!