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Thanks for this comment, makes feel it was worth it!

Probably you are past that point. But maybe still just try to draw like I suggested. Also, certainly everybody has to find their own path of learning, and what I have shown here probably can be learned in other ways as well

@@phipsart6424 thx. I did try the observational drawing exercise. I immediately recognized the curving of the three axes as i turned my head (due to having learned about curvilinear perspective). _But_ i will say that the observational drawing exercise gave me more insight into how depth and distance in real life are represented in a drawing. I had to see the physical distance of objects in my chosen setting (especially those overlapping each other) and judge how to represent that accurately in my drawing. So I guess it still helped me a little 😊

@@SyoDraws That's basically what this was about :)

@@phipsart6424 oh, so i got it, yay 😁

That's not what I wanted to say with this video 😁 Maybe you know what you need to practice now?

It depends on on which edge you hinge it. If you hinge it in a way that they both are lying on the ground (like here, in an other video of mine, at 8:20 czcams.com/video/Mtsv1IpjUgs/video.html& ) then it is the same situation as for the first cube: One still does look perpendicular on the guideline pointing up/downwards. But I guess you are more interested in the other case, where you hinge it with one of the edges that are parallel to the ground. So, you rotate around one of the edges that have a vanishing point on the horizon. So when doing this rotation, the corresponding vanishing point will not move. The other 2 vanishing points however do move. The second VP that lied on the horizon will now lie below or above the horizon. And now, have a brief look for example at 32:58 in the perspective video czcams.com/video/YDanHdjPJVs/video.html With the altitudes you can get the 3rd VP. You will find, that because the 2nd VP does not lie on the horizon anymore (or more general: the line connecting VP1 and VP2 does not run exactly through the middle of the image (center point) anymore), the 3rd VP will not lie in infinity. And therefore it is a 3-point perspective, and no 2-point perspective anymore. Does this make sense to you? Thanks for your comment!

​@@phipsart6424 Thanks. The way it switches from 2pp to 3pp is counter-intuitive. And in my sketches it still looks counter-intuitive.

@@a7ccel Then most likely the placement of the new VPs is a bit off. Make sure the cube is located where the altitudes of the VP-triangle meet. Or maybe also edges of the cube do not converge into VPs. Probably you should check this first. However drawing cubes with VPs is very technical on this level, and you may find an easier access to drawing cubes or drawing in perspective in general. Maybe you check out this video, the very first exercise, 'Observational Drawing'. It is a more intuitive approach. czcams.com/video/Mtsv1IpjUgs/video.html

So in particular when I draw intersecting bodies, I first draw lets say a cube with light pressure, and then I draw a cylinder over it with light pressure. Then I decide a point where they should intersect, and try to figure out all intersection lines and draw bold over everything. Does this make sense? Also, recently for example I drew mechanical tools in perspective. Like hammers, tongs, etc. These are great to study and practice since they often are made out of basic forms. You also can practice proportion and it is relatively easy to tell whether you did a good job or not since their forms are very familiar. So they give you very good feedback

@@phipsart6424 okay thank you, this helps a lot!! i think drawing tools, basic every day objects is a great idea. usually i try to find free blender models -> draw objects in persp -> compare with model but that takes too much time. i think i'll try winging it and take some photos of real life objects from diff angles. i learn alot faster when i have something to compare my drawing to. again, this helps thanks so much for giving such a detailed reply! hope your journey of becoming an art god is going great :>

Hey thanks for that feedback! Light weight - you mean line weight? Or can you give a timestamp? :)

@@phipsart6424 Yup. I type like a 3 year old. Line weight, especially on the silhouettes. The line weight on the lit side should be thinner (or even broken), and the dark side heavily (sometimes MUCH heavier).

Thank you so much! Here is what comes closest to part 2: czcams.com/video/Mtsv1IpjUgs/video.html&t

I would not say that there is true or false perspective, or that one of them is a lie. There are just different ways to do it. Thanks for your comment! :)

I am not sure if I got you right, but have a look at 8:20. The vanishing points of the green lines all lie on the red line (lets call it horizon, the horizon of these cubes). So this horizon line gives a good anchor for every cube. Other than that, you may draw a perspective grid from this horizon, which gives you a relation for the spacing. These 2 techniques still involve some guessing (like when you estimate where the 2nd vanishing point of the cube should be on the horizon), but they narrow it down a bit. With the perspective map you could get even more exact results, but it gets more tedious. But I think these measures may give you a good orientation of the relation between the objects and their behavior when you continue to draw more objects to the left and right etc. Does this help? Thanks for your comment! 😊

I don't know enough about aphantasia, but for spatial imagination I think it is a seamless transition anyways. Like, for ghosting, which helps to draw perspective grids: I reckon that with some practice you can tell whether a grid is off (lines not converging well), no matter if you have aphantasia or not. You get accustomed to some pattern - and that may be same for other skills that are considered to be 'spatial imagination'. So I think you can learn a lot about it, despite the term 'spatial imagination' suggesting no compatibility with aphantasia. So maybe 'how it should be' is the wrong question anyways ;)

@@phipsart6424 that makes sense, thanks for the vids and exercises bro !

I don't have aphantasia, but in my experience a lot of the technical stuff with drawing (even spatial reasoning) has more to do with specific knowledge of principles and patterns, such as perspective, and applying them consistently, than with imagining stuff. Hence, while I CAN imagine stuff in my head, I usually don't do that when I'm drawing. I hope this was useful to you, and I wish you the best in your art!

Totally agree!

Very happy to read that!

I dont have that much time 😅 but happy to read that!

Very happy to read that! If you have other tips or exercises feel free to share!

Haha thanks for sharing!

Sure! You also can do so below my perspective video ;)

@@phipsart6424 Thank you! I wanted to comment on the perspective video but I thought my comment would be drowned within the sea of other comments. Most of my questions are about the “90o cases and how to deal with far away Vanishing Points” chapter of the video. 1. What did you mean when you said v or w would converge to zero if the 3rd VP is close to the rim of the blue area? I know this isn’t relevant but when would v be the one to converge to zero and when would w converge to zero? 2. If the canvas converging to zero is the same as all the VPs being infinitely far away, how would it mean that you are moving closer to a one or two point perspective if all 3 VPs are far away instead of just the 3rd VP or the 3rd VP and one of the horizontal VPs? 3. What do you mean when you say that there is always a VP not farther than 2.5 times the canvas’s radius and how is this possible? Why is it that not all VP’s can be farther than 2.5 times the radius of the canvas? This kind of relates to question 2 so I may be repeating myself. Sorry for the abundance of questions, I just couldn't put my heqd around some things you said. Also, do you have a community discord server or anything similar? I would love to be able to talk with others and ask more questions. I really appreciate the work that you put into the perspective video, it helps with my perfectionism, although I plan on trying to rely more on intuition in the future.

@@DdokgaebiI read all comments, no matter on which video. Now your questions: 1. From rule 2 you get the location of the center point. If you vary the 3rd VP then this changes the location of the center point, and therefore it also changes v and w. If you move the 3rd VP to the left or right rim of the blue area, then the triangle becomes a right triangle, which means the center point will be located at the right or left VP, and this means w=0. On the other hand, when you move the 3rd VP to the circular rim of the blue area, then with Thales theorem you get that you again have a right triangle, and this time the center point will be located at the 3rd VP, and v will be 0. 2. Probably I stated that ambiguous. Not all of them can be infinitely far away at the same time. If you look right at one of them, then the others are infinitely far away for instance. Or, if you look for instance at the horizon, then the VP of the vertical will be infinitely far away. So I think you got that already right. 3.If you rotate your view through space, then VPs come in your vision and leave your vision. Have a look for example at 22:00. The view plane would be the infinite extension of the canvas as it is rotated around there. And the intersections with the lines of the true VPs are where the VPs on the view plane will be. There are always such intersections, and they are closer or farer away from the center point. And if you turn away from one, you move more towards another. What I did in order to come up with the value of ~2.5, is figuring out, that when the VPs form an equilateral triangle, then this is the situation where you look right in the middle of the 3 VPs, and so the center point will be as far away as possible from the clostest VP. From this equilateral triangle I calculated the size of the canvas in relation to v, which is this value of ~2.5 I hope this helps! If not, just ask again. And sorry, no I do not have a discord server. Would be a nice idea though

​​@@phipsart6424Thank you for taking the time to answer, I really appreciate them and the videos that you make! Still wrapping my head around the first but mainly the third answer but if I have any questions, I'll make sure to ask.

@@DdokgaebiYeah just write again if it does not get clear!

Makes me happy to read that! :)

Maybe first draw them with vanishing points. After some practice, skip drawing the guidelines, and after that skip the vanishing points. Of course there are also other things you can do. Soon I will publish a video with 8 exercises concerning spatial imagination, so stay tuned!

@@phipsart6424thanks! i'm looking forward!

Thank you so much!

Just skip it, it's not necessary in order to become good at perspective drawing :)

Haha thank you! Actually I have another video basically finished, I hope to upload it the next days

I also thought about whether one can deduce the projection we perceive the world with by looking at the geometry of the eye. However the projection plane of an eye is not a flat plane, but the backside of the eyeball. So it is not a flat projection surface, but curved. This, from a geometrical point of view may lead to fisheye effects (like compression of the outer fields of vision). I say may, because I don't know for sure, but it seems plausible. Anyways, maybe even more important probably is the processing of the brain afterwards, as it may apply any transformation that is useful to what we see. Like for example the merging of the images of our 2 eyes into one image. Or think about birds who have way more than 180° viewing angle, maybe even up to 360°. This definitely cannot be a linear perspective, because the absolute limit of linear perspective is 180°. And since we, humans have a viewing angle of 180°, maybe even a little bit more, at least some curving needs to take place in our vision. Or, to take it even further, as some watchers pointed out, probably what we see is not necessarily a 2d image, but something more deep. If you again think about animals, there are animals with 360° viewing angle, and this is impossible even for fisheye. Which is an indication, that their brain calculates an 'image' which differs to any linear perspective or fisheye or whatever perspective projection one may use. It cannot be represented by any 2d image. So, after all, I think the answer to how we see (in static view, not changing the direction of view) cannot be answered by the geometry of the eye alone. If you are interested, below my pinned comment, there are some comments related to what you were saying. Thank you very much for your comment!

Have a look at my pinned comment! Thanks for your comment

@phipsart6424 Hi tried to download the article but no joy. I think it depends on what you are trying to achieve, i.e., realist abstraction, etc. The eye is an instrument that has limitations we see upside-down and the brain corrects it. In general when drawing thay say you should keep your head and body in the same place. Photography changed the game, and for some time, the artist has to go deeper. A lot of rules went out the window. I don't think it's about capturing reality but to provoke a response in the viewer. If you feel to make a statement involving theories is legitimate if it gets you to your goal. As vangoh once said art is a lie but more literal than the truth. Cheers.

@@John-mz8rjGo on google scholar, and search for 'the art and science of displaying visual space'. There you should find it. It is highly interesting, and imo answers how we see in static view (not turning head or eyes). I totally agree, with what you say about the response in the viewer. I often like to have something like linear perspective with a bit of curving

A new video is almost done, thanks for your comment!

Don't worry! The math is not so important, I dare to say that almost none of the great artists used math. You need to get intuition for space etc. Actually I am working right now on a video that adresses this

I see. Maybe I dont on this but I do on other things Im interested to doing or try to@@phipsart6424

I think I know what you mean. But with a curved 3d canvas, do you take this as the final 'image', or as an inbetween step, before transferring it to a 2d image?

@@phipsart6424 It's the same idea as a concave mirror, so yes, it would be the final "image" depending on what you are looking for

@@SenySencomentador I understand that you can vary the distortion in a certain way by doing this. But, I am not sure how exactly one would define terms as 'parallel perspective'. If you take the approach for linear perspective as I introduced it in the video, and curve the canvas, then, from the point of the beholder you see no difference compared to a planar canvas, because all the objects still are seen in the same direction as before. Do you agree? Or do I have some misunderstanding?

@@phipsart6424 I'll explain about the concave design of the projection lines on a flat screen. The vanishing points that start from the observer as the only point of origin on a flat screen, when their origins are put in parallel with the same distance that they have on the flat screen, results in a concave design when we draw lines between the starting points of each line, this is the result of the projection angle from the vanishing point that has a 180º opening, forming what we know as "vanishing point". So let's consider the existence of the concave design in a vanishing point projected on a flat screen, in this sense, if we curve the screen to a concave shape towards the observed object and keep the lines that we made initially, we see that the height of the lines become flat as we curve the screen from the observer's point of view towards the observed object, this is basically the cancellation of the concave designs, where the concave design of the lines of a flat screen (which is the vanishing point) are canceled when added to the design of a concave screen, resulting in a straight projection known as "parallel perspective", but returning to the point where we haven't curved the screen yet, if we curve the screen the other way around, that is, curve the screen towards the observer, this causes the curved design of the lines we made instead of being canceled they are amplified, resulting in a projection called "fish-eye perspective", and that's basically what I'm talking about.

How do you mean that? Having a point in 3d space and calculate where it is on the canvas, or the other way round or something else? Thanks for you comment!

Thanks for your feedback!