How To Draw A Perfect Cube In Perspective
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- Опубліковано 25 сер 2024
- This video explains step by step how to draw a perfect cube in perspective. This is helpful to create a scene that has an accurate sense of scale, or the first step to construct an ellipse, as well as other uses. It is a simple technique with great value to your drawings!
The video references these other Drawsh videos on perspective, if you want see detailed explanations of these techniques, click the links in the video or below.
Dividing planes with the "X" Trick
• How To Divide Planes U...
Perspective Basics
• Linear Perspective Basics
2 Point Grid
• 2 Point Perspective Grid
Tracking Size
• Tracking Size in Persp...
Or watch the perspective play list:
• Linear Perspective Basics
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im gonna need to watch this 100 times
I understand, it is a lot of steps for one box. :)
In 3 minutes, you explained something to us that I hadn't understood for years. Thank you
Wow, happy those three minutes helped so much. Thanks for taking time to let me know!
Average educational UA-cam content
are you serious
it is interesting that a perfect cube in 2 point perspective will appear rather stretched horizontally when it is drawn close to a vanishing point
Yes, anything drawn near a vanishing point will appear distorted. But helpful to know a way to measure to make sure it is actually square :)
I can see where this can be very useful. Lots of potential for perspective in comics and cityscape drawings. Thanks for explaining what to use it for.
Yes! Lots of uses for this. Glad you liked it :)
This is explained incredibly well! I've watched dozens of videos about drawing in 3D space, but this one is the best I've found! Thank you!
Wow, thank you for the kind words, happy it was so helpful to you:)
10 out of 10 for simplifying a not-so-simple exercise!
Much appreciated! Happy it was so helpful to you :)
I really appreciate this straight forward explanation. Can I ask where can I learn this formula and other logical explanations for perspective? A lot of times instructional resources tell the how without the why because the reasoning is so complex. I'd like to try learning the why. Do you have any good references I can start with?
There are a lot of great texts I have learned from over the years, but also great teachers. Marshall Vandruff is on of those teachers and he is currently producing a comprehensive series on perspective which I think will be the most valuable resource out there. Scott Robertson’s books are also very technical and have great information. An older book I love is joseph d'amelio perspective drawing handbook. Hope that helps.
Awesome vid, extremely clear and straightforward!
Thank you, very happy you enjoyed the video!
@@DrawshStudio is there any way to determine the relationship between the right vanishing and the left? I saw this video cover how it can be applied to determining the height of a cube, but how can i determine If i wanted to make a cube one inch bigger, how would i measure one inch to the other vanishing point?
Thanks, this is awesome.
I have trouble to rotate a rectangle and be sure if it stay the same size, really trick.
My pleasure, happy it was useful and thanks for supporting the channel!
I had been looking for video like this
Thank you so much
My pleasure, glad you found it!
(Notice how at no point in the video where he defines what the hell is a "station point" or what the hell is a "cone of vision")
Thanks for the interest in my videos! If you watch my perspective playlist I have videos that explain all these concepts in clear detail.
Thank you. Great job.
You are very welcome, thank you for the comment :)
thank you!!!
You're welcome! I appreciate the message :)
FINALLY!!! THANKS
Happy you enjoyed it, thanks for taking time to comment :)
What two lines are you measuring from? Because the 45 seems smaller than the 30 degrees
The 45 degree line won’t be actually 45 degrees because it “represents” 45 degrees in perspective. It will depend on the specific you have chosen.
The 45° is half of the right angle at the bottom
It's purposely 45 degrees to be parallel with the diagonal of the square, because the 90 degrees bottom triangle has it's laterals parallel with the future square.
The 45 degree will slice the square diagonally, so the point hitting the horizon will be the vanishing point for any diagonal of squares parallel with the large triangle.
Could you please explain why you take the distance from a VP to the SP and project it up to the horizon line to find the Measuring Point at 1.25? I follow what you are doing and realise it works but I don't understand WHY that should work. Everything else in the video makes sense apart from that. Please clarify.
Thanks for the question, but I’m not sure if I have an answer for you that’s better than “it’s just geometry”. In the same way we can use geometry to find the area of a triangle by using specific divisions, perspective works in the same way. It has these ways in which we can use lines and points to figure out correct geometry. It works because it works. We have to learn these methods like we learn formulas in math to creat convincing spaces.
@@DrawshStudio Thanks for your reply. Everything else in perspective makes sense - it all seems rational - but this measuring point placement seems to be plucked from thin air - although I acknowledge it works! Can you shed any more light on it to help me visualise 'why'? Or can you recommend a good text book I could refer to? So, far all books I have consulted seem to make the same assumption without explaining why... I would love to know why!!
It isn’t picked out of thin air though. It’s based off of the distance from the vanishing point to the station point where viewer is standing. It is basically akin to a mathematical formula that we have discovered to be true. That specific distance in the context of the perspective scene will also be the measuring point to base the perfect cube off of. There may be an better explanation out there but I haven’t seen a book go deeper into that unfortunately.
@@kennethleriche that can be easily found, if you would look at the cube from above (it would be just a square). Draw the lines going out from the SP parallel to the sides of the cube and its diagonal. In that case in perspective view those lines would cross the extensions of the sides in VPs. Now, if you draw the segment line from the square vertex closest to the SP which is parallel to the horizon line and then connect its end with the another vertex, you will get a isosceles triangle. The same triangle shall be drawn from vanishing point (that what you see on video), to find needed vanishing point. Check this picture to understand better, what I mean www.dropbox.com/s/djuvp18ur9qaxcm/idealcubein%20perspective.png?dl=0
@@andreyostr Thank you very much for your explanation - and diagram from an aerial view.... now I understand!
You're videos are great but I don't get how you got the vertical measurement.
The series of steps laid out in this video give the vertical measurement. It is a complicated set of steps, and only necessary if accuracy is needed within a drawing.
The height that you rotated up, would it be the same if you wanted to rotate it down?
Yes! The explanation as to why is covered in my video “tacking size in perspective”.
how do you do perfect 3 point perspective, do you place the third vanishing point randomly or is there some rules?
There are definitely rules, there’s always rules in perspective :) The third vanishing point will be directly above or below the center of vision point. For simple three point this will work. But in reality, three point means the viewer is looking up or down, so things like the cone of vision must be moved. There point grids are more complex as well.
@@DrawshStudio My gosh, Legend just replied!!!, Hi Legend, about this question, i still feel like it's a little bit vague, imaging constructing a scene with a perfect cube in 3 ponit perspective, putting the 3rd vainishing point up or down only determine the vanishing point, but didn't determine the length , for it to be a perfect cube, all the length has to be equal. but i don't know how to do that, i wonder if there's any book covered this topic?
You are correct, it is a vague answer :) your question is a very technical and complex process, and a UA-cam reply isn’t the easiest format to teach complex concepts. When I’ve thought this we spend several weeks going over these ideas. What you would want to search for is how to make a 3 point grid, Scott Robertson teaches some of the more complex processes, I would look into his teaching and books :)
Would this method also work for heavily distorted perspective?
Generally perspective becomes distorted when it moves outside of the cone of vision. If that is what you mean then yes, it will still work but it won’t look correct to the eye.
Thanks :)
My pleasure, thanks for the support!
Which program was used to create/animate this video?
Photoshop and keynote.
Three sides to the ground is where im lost. How do you choose this.
You choose those three sides (going to the vp obviously) and the rest makes it a perfect square. :)
0:45 if you do degrees i think you should include an animation of the line rotating out from the VP toward the 45 degree VP. I got kind of confused whether you measured the 45 degrees from the leftmost line or the SP line, but im assuming you measured from the leftmost line
The line emerges from the center of the two vanishing points at the station point. The line goes through the corner of the blue box. Since the vanishing points are a 90degree angle at the station point, the 45 degree vanishing point cuts them in half, no matter how they are oriented. I have another video that talks about the 45 degree vanishing point as well.
Laws of geometry make eveything hard to draw!
Hard yes, but magical i what they help us achieve, also yes :)
Please help, @ 47 seconds you place a 45 degree angle FROM THE STATION POINT... there are already two 45 degree angles from the station point and that explains the blue box. Help me to find this new 45 degree angle (the angle you drew seems very small from any reference point existing on the page at the moment) ... I see many people asking the same question. do you mean the new line you draw will become a 45 degree angle? Thank you!!!😇
When the video starts, you see a blue box at the station point with lines coming out on the edges which give us the 2 vanishing points. When we cut this box in half it is the 45 degree vanishing point for this perspective. The 45 degree line that you reference cuts the box in half (half of 90 is 45). I hope that helps. I have a video on this in my perspective playlist that might help.
Thank you for replying! I will watch he video also...@@DrawshStudio 😇
Can you please explain the height determining factor with the proper reason - "why this way"?
Its good otherwise
I can’t :) I don’t know a way to verbalize the logic as to why this works. It’s essentially a mathematical formula played out visually.
How to do this in 3 point perspective?
That’s a great suggestion for a future video :)
How did you make the square grid just from the base of the cube?
m.ua-cam.com/video/3n3gpGX_v2s/v-deo.html
Can anyone explain or link me a mathematical proof for why all sides have equal length.
Also for some reason i can't quite wrap my head around circles in perspective to be perfect elipses. It feels like the part facing us has to little curvature compared to the face away from us, but i guess the elips is rotated just enough to cancel all that out?
I’m not sure what you mean by mathematical proof. In perspective, you can’t rely on mathematics because the variables are to numerous. For example, slightly higher or lower to the horizon changes things. So we rely on steps like this to create something correct in perspective.
Ellipses are strange. But it is true they will be a perfect ellipse in linear perspective. Remember tho that linear perspective is an approximation of life to appear correct to our eyes.
@@DrawshStudio by mathematical proof I mean a reasoning for why all sides must be equal length. When I turn a cube in three dimensional space it corresponds with a unique projection on my retina, so surely there's some projective geometry thingy going on.
A cube by definition has equal sides. This method is a way to do that in perspective. The lines aren’t literally equal, but represent equal lengths in perspective.
@@DrawshStudio I know that, what I wish I could find somewhere is a mathematical proof that this method results in a cuboid with all equal sides.
I have had similar questions and I’m always a little confused by them. Perspective exists outside of mathematical numbers, it is sort of the point. When people ask this I’m always a little unsure of the concept in their mind they are looking for. But I wish you luck in your journey.
What is the 45 degree vanishing point and what is it used for (besides how it is used in the video)? is there a video explaining this?
If you watch my perspective play list it will explain it for you :)
I was so looking for this tutorial, it sounds like gibberish for my foggy brain but it'll watch it again and try to pay more attention.
Thank you so much for doing this! I noticed that your vanishing points are at a 90 degree angle from the station point I think which you can see from the flat blue square touching the station point. So then for a perfect cube would the vanishing points always need to be at 90 degree from the station point then or could you make them at a different angle and that wouldn't matter when you make the 45 degree angle to make the square?
If I understand your question, to be “correct” vanishing points should be at a 90 degree angle from station point. That angle can rotate, but this keeps all the 2 point vanishing points consistent in a scene. I cover this in a previous video as well :)
@@DrawshStudio D'oh! It seems like now that should have been more obvious to me! THANK YOU SO MUCH for responding! Your videos have been such a help at understanding perspective form me and "fill in the gaps" from some of my books
There is a logic to perspective but it isn’t always obvious at first, and it takes a lot of sources to piece it together sometimes :) glad you are making progress and thanks for supporting the channel!
Why not use a measuring line
Measuring lines get us the distances in space, but getting that vertical measurement can be the tricky one.
Quick question: Won’t the 45degree VP always be in centre of the two VP since it’s half of 90degrees?
Good question. It will only if the corner of the box is aligned perfectly perpendicular to the horizon line. However the box can be rotated at any angle to the horizon so the corner of the box favors one vanishing point more than another. My previous video touches on that a bit. Hope that makes sense.
m.ua-cam.com/video/XYrAkcEs6GQ/v-deo.html
@1:52
@@DrawshStudio okay so looking back at the example in this video, the SP seems to favour left VP so is that why 45degree travels from left to right?
Because the line needs to go from corner to corner through the box at the station point. If you went through the other corners it would take you outside of the vanishing points and would not work.
Those two lines conecting to both sides of each vanishing points seems to come out of nowhere or arbitrary.
What is CONE OF VISION (CoV)?
Drawing range?
Thanks for the Interest in my videos. If you find my perspective playlist you will see a series of videos that cover the cone of vision and more :)
Dachte erst: "brauch ich eigentlich nicht, kenne ich ja schon... " nun bin ich erschlagen.😅
Glad it made an impact on you, thanks for the comment!
whar if the vanishing point is off the page?
That’s a relative question, because how big is a page? If it’s a small page, then your picture plane is small, and your vanishing point will be outside of your page. The farther away the vanishing points are the more “normal” perspective looks, so we may need to add paper on the sides or is a large desk (or file).
but how did you derive this? What assumptions does this rely upon?
It is a method I learned, it relies on the assumptions that these series of steps are correct.
@@DrawshStudio Did you learn it from scott robertson's how to draw book?
❤🔥
🙏
@0:52 how did you come up with these lines? I'm confused.
Thanks for watching the video. Those lines you asked about are drawn wherever you choose, as long as you then use the 45 degree line to create the back of the tile.
Hope that helps :)
@@DrawshStudio ok. I kept stopping the video and rewatching it . But now I realize that I should have kept watching as it is explained shortly after my question. Thanks for the response.
Your welcome.
Have no idea why, but this box is not looking equally sized to me :(
It’s because it is in perspective, and depending on where the vanishing points are will make it look more or less perfect. But that is why we need systems like this to help us build correctly despite how the vanishing points make something look.
How do I use this while drawing during urban sketching.
Thanks for the comment. If you mean sketching outside on location, I wouldn’t probably bother with this. I would just free hand perspective based on what I saw.
But if you mean how to use this to draw a city, then you could start with a perfect cube in the foreground as a way to build a grid and creat a scale, the. Build the city around it using the techniques in the video.
@@DrawshStudio off to your web site for more basics. I indeed like to sketch outdoors. The more I do it the more I find I don’t have a theory based knowledge to guide me.
Drawing outdoors is wonderful. This perfect cube method is more about creating absolute accuracy, which is often difficult in a outdoor setting. This is best practiced in you studio space or at home. When you get a feel for it, you can “rough” the idea out by hand and be much more accurate in your quick sketches. Good drawing!!
There is more useful and easy to use measuring system with measuring points and lines
That’s great, there are usually a few different methods to achieve something in perspective :)
I don't understand the method used to Calculate the Height of the Cube and why it works/is correct... All the Steps Used seem Arbitrary...
Similar to some problems in math, it may seem arbitrary but it gets the correct answer. This too is like that, these specific (complex) steps will create a perfect cube :)
@@DrawshStudio I would rather not just take it on faith though... Could you please explain it?
While i support an evidence based understanding, I’m not sure how to explain it further than the video does. Using the 45 degree line creates a perfect tile, then going back to the station point creates lines based on where the “viewer” is standing. This then creates a scenario where lines connect to give us the height of the cube. I don’t know how to put into words the reason it IS correct.
@@DrawshStudio That is Unfortunate... I don't really understand how the "tile" has equal X and Z Edges, but it seems to be Reasonable I suppose? It makes some kind of Logical Sense...
However, the lines that are used to ultimately derive the Y Edge Length of the Cube seem less Reasonable/Logical for some reason... I have no idea what kind of math is being used there, and how the Lines are all Related to one another...
Thanks for being Honest though... I'm reminded that it's never wrong to admit when one doesn't know something...
How to draw a perfect cube in 3 point perspective
Thanks I will add that to future topics.
Me exploto la cabeza :'v
I hope that’s a good thing 😂
I've listened to this over a dozen tines. I'm not getting this.
Perspective is tough.
This is interesting. Thank you! However, I find myself wondering why anyone would actually use a method like this in practice nowadays for making art or architectural drawings or mechanical drawings or whatever. It is quite impractical in a sketchbook or even on a drawing board since you need to define points far off of your paper or canvas. This is super impractical if you need vanishing points and station points way outside the edges of a big canvas! And we have computers and free 3D apps like Blender now that allow us to mock up shapes in 3D, keeping accuracy no matter how various objects are rotated in space.
What if you have a bunch of cubes at random orientations? That would be a nightmare to try to draw using methods like this! You need different horizons for each cube and different station points. With something like Blender, it is trivial, and so, so much more powerful and flexible. You don't need to do everything in the 3D app. If you want, you can just create boxes with grids and maybe ellipses where needed to use as a guide layer for use in a 2D painting app. Or you could print it out or project it onto a canvas.
This kind of approach seems like it was useful in the time before modern tools. Of course, it's great if you just have a fascination with the math and geometry. But I can't see why I would ever actually use this for drawing or painting. Maybe some would be impressed that you didn't use a computer, thinking using a computer is cheating, or somehow not artistic. But some might also consider using a straight edge or such engineering approaches as this, or any tools or aids at all, to be cheating or not in keeping with some romantic notion of what it means to be doing something in a proper artistic manner.
It seems to me that using a 3D app, you can focus more on composing your scene, and you can be much more free with it, and even change perspective after arranging your objects if it gives a better composition. You aren't limited to what you know how to construct perfectly using such perspective techniques. I suspect that with old perspective techniques, there is a tendency to restrict everything to certain orientations that work with a single horizon line, and so on. There is a fear of rotating objects to certain orientations in space. And things must remain more simple.
Or if you want a perfect cube as a standard for other parts of a scene drawn with the usual pair of vanishing points, you could just render a single cube as you like and determine the vanishing points from its faces by projecting lines until they intersect. Or if you just do a really rough mockup with cubes and boxes, you can use rulers to find the vanishing points, centers, and whatnot, for various faces.
Furthermore, in a 3D app, you can simulate light and shadow to as detailed a degree as you like. How to cast shadows accurately using the old methods, especially with multiple light sources, especially when those light sources are at inconvenient locations? With a scene of any complexity, these old methods would turn your drawing or painting into a very time-consuming engineering project.
Sure, there is a learning curve with 3D apps, but there is also a learning curve with such methods as this. You could learn how to create and arrange boxes and do basic boolean operations and setup a camera and render a scene in Blender in an afternoon.
Maybe I missing some reason to do it this way. I am curious about your thoughts!
Also, as for needing to learn Blender, just open it and you already have a perfect cube in perspective! Middle-click and drag in the viewport and you can change your perspective. You also have a floor grid. You don't even have to mess with a camera or rendering if all you need is this for a guide. Just take a screenshot!
Thanks for the in depth question, I definitely have a few thoughts regarding your view point.
First, this is a pretty technical bit of perspective knowledge that would only need to be applied if accuracy were necessary. In most cases, eyeballing perspective with tools or even freehand (with some prior knowledge) is fine. Whether we like it or not, perspective is a complex process where most of the time vanishing points will be off the page and will take some serious effort and skill to learn.
You talk a lot about using 3D apps like blender to do this type of problem solving for you. But it is not every artists dream to use 3D software. Many artists enjoy having the deep knowledge of these processes as well as the ability to execute them without needing 3D software. These are time honored skills, starting in the Renaissance, that many people value and practice with joy not tedium.
To the question of practicality, it depends on what your agenda is. It is only impractical if your needs make it so. Many artists, like those in the entertainment field, do work from sketch up, blender, or similar programs to mock up perspective quickly and build on. There is no problem with this, especially if your goal is rapid visualization of concepts. However, most of these artists still have a very solid understanding perspective and how to make it work for their scene.
But I think there is a problematic underlying view in the idea that a computer will solve perspective, rendering, etc. for us. The computer and 3D software are merely another tool. It shouldn’t replace training and understanding craft. While I love that we have many tools and ways to solve to problems, to assume there is no longer a need for an artist to have the knowledge and skills to create from their imagination has the potential to limit an artist in their work and career. Artists who have knowledge, skill, and are versatile in their tools have to potential to make better work and be more hire-able in their field.
@@DrawshStudio Thank you for your thoughtful answer!
My pleasure :)
Hnnnnghhhh.....
Took me a few watches to fully understand, but aaagh. Perspective is so difficult. ;u; You explained it as simply as possible though.
I'm also trying to learn to use Blender.
Yeah, these deep perspective things get really technical and depend on following lots of steps that seem unrelated until the end. Stick with it :) good luck with blender!