![]() I’m not, so below is a picture with no rules broken: Well, maybe not exactly, in this example, but that because it’s Van Gogh, and he was good enough to be allowed to break the rules. The original is at the Kroller Muller museum, and a reproduction can be seen hereĪcross those lines radiating from the vanishing point, verticals remain vertical, and horizontals remain horizontal. Anyway, I digress – I must try to stick to science…) (And note how its positioning accentuates the importance of the central figure. We are looking fairly ‘straight down the street,’ hence the use of one vanishing point. And here’s the vanishing point in Van Gogh’s Café Terrace at Night. And use two-point perspective when viewing a scene obliquely.” Now, tutorials on drawing in perspective tend to say things like “use one-point perspective when viewing a scene ‘end-on’. A vanishing point is the point on the horizon line that those railway tracks (and other parallel lines) converge at. When one-point, and when two-point perspective?įirst, some terminology: we will need a “horizon line” (does what it says on the tin). Anyway, here’s a playful take on this stuff. It’s about what happens at the eye, not in the brain, mainly because I don’t know enough about how the brain sees to write a blog post on it. This post is not about that psychological stuff. In fact if you look hard enough at the right hand part of the car figure, you might over-compensate, and persuade yourself that the red car drawing is bigger. When you looked at the photo it probably never occurred to you that the red car might be twice the size of the blue one. Your brain knows the red and blue cars are the same size, and it isn’t fooled by the effects of perspective. ![]() That all describes how big something looks optically. The sun is 400 times bigger than the moon, but also coincidentally 400 times further away, so they subtend the same angle, near enough, at your eye. This is also why the sun and moon look such similar sizes in the sky (and hence why we can get both lunar and solar eclipses). We learn examples of this at a young age. So things look smaller the further away they are, railway tracks appear to converge into the distance etc, etc. In the figure above, the red car subtends a larger angle at your eye than the blue car, because the red car is closer than the blue car. Mathematicians/scientists talk about the ‘angle the object subtends’ at your eye. How big something looks depends on the amount of your field of view it covers, which is to do with angles. You may well find this section obvious, but if we don’t get this out of the way here, there will be a conceptual jump that will annoy me. It’s about what is going on behind the scenes. I found one good source, of which more later, but that led to as many questions as answers for me…Īnyway, to address the heading of this subsection, this is NOT a tutorial on how to draw in perspective – that’s already been done by people way more qualified. Anyway, I had to try to figure things out myself, and as a consequence, this post may get more wildly speculative as it continues. To be fair, that might be down to me, rather than the videos. There are some mathematical videos on projective geometry, but I couldn’t find the answers to my questions there. ![]() They are teaching people how to draw, not explaining to people in physics why it works.Īnd I couldn’t find much on that at all. This one and this one came high up on an internet search, and for good reason I think – I really like them. There are loads of really good tutorials on how to draw in perspective. I looked it up, and found that few people had added much to the internet about this. The ‘meta-theme’ is phenomena that are special cases, or approximations, of more general phenomena, and how we tend to learn in the direction from special case to general law. The context is art, but the subject is the nature of 3D space. Now, there’s a risk that the people who normally read this blog, wanting science content, might think this is about art, and give up at this point. (I know, I know – there are other kinds, but I didn’t know that then. So I explained about one-point and two point perspective, and then realised that I couldn’t articulate how to choose between them, and why there weren’t other kinds. That was a mistake, because I am the living refutation of the encouragement “Everyone can draw.” Still, I guess the idea was that I know some physics and so must understand how 3D geometry works. Someone recently asked me how to draw in perspective.
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