2-point #perspective question: how do I draw a box to the right of the right vanishing point? #MastoArt #drawing #asktodon
@peterdrake shooting from the hip— if you take all the guiding lines and vanishing points and reflect them about the vertical line through your central vanishing point, you get a third point on the horizon (off-page) and a new set of guiding lines. Objects to the right of the central vanishing would seem to need to be aligned with the guides that go towards the right hand off page point.
Does that make any sense?
@bfjvii Yes. I think that would be approaching 5-point perspective, but with the top and bottom VPs infinitely far away.
https://www.creativebloq.com/how-to/draw-5-point-perspective
@peterdrake Here's an animation I just put together in GIMP from a decent quality photo, not a fisheye lens or anything. Note that each line in 3D space is parallel to the others of the same colour, but orthogonal to those of different colours. But in 2D space, all the lines of a particular colour converge to a single point - even the vertical ones.
@khird Yes, that looks like standard 3-point perspective.
My understanding is:
- Looking down? 3-point with the 3rd VP well below the horizon, as in your photo.
- Looking up? 3-point with the 3rd VP well above the horizon.
- Neither? 2-point (or possibly 1-point, if one set of lines is parallel to a line from the viewer straight toward the center of the page).
@peterdrake Yes, that’s correct. It looks like uploading the image broke the animation, but imagine that it overlays another set of lines highlighting the dark square building along the right-hand edge, near the bottom (which is past the right-hand vanishing point, similar to the box in your drawing). The green lines corresponding to the 3D-vertical edges are nowhere near 2D-vertical, which is why the building doesn’t look too distorted.
More broadly, imagine you’re in the centre of an octahedron with its vertices at the cardinal directions (or whatever alignment corresponds to your drawing, if the boxes aren’t oriented with their faces normal to NESW/UD). If the ray from your viewpoint through the centre of your image plane would intersect the octahedron at:
@peterdrake I tried working through the trig to figure out where to place the third point. I assumed you could measure the distances ℓ₁ and ℓ₂ from the image centre to the existing vanishing points, and the perpendicular distance 𝓱 from the image centre to the horizon passing through both points.
The method I came up with requires you to first calculate 𝓭², which is the square of the distance from the observer to the image plane:
𝓭² = √[(ℓ₁² - 𝓱²)(ℓ₂² - 𝓱²)] - 𝓱²
Then you simply divide by the distance to the horizon to calculate the distance from the image centre to the third vanishing point:
ℓ₃ = 𝓭²/𝓱
I don’t know how I could test this rigourously, but it gives sensible results at a couple key cases:
@khird Here's a 3-point attempt. I always have trouble pointing rays at an imaginary vanishing point well beyond the page.
@peterdrake Nice! I extended the lines out further to see how you did. The blue lines, of course, are very good, the red ones have some variation, and the green ones are similar to the red but have worse outliers. If the extremes were improved a little bit I think it'd be quite good. The lower right corner is the only one I could tell looked wonky without the help of the extended lines.
@khird Wouldn't the lower right corner look even weirder if it was aimed properly?
Also, any advice on getting those lines aimed precisely at the vanishing point a meter away from the paper?
@peterdrake I think it’d look less weird - to me, the angle between the two rightmost “verticals” is too large for my brain to accept that they’re parallel in 3D-space.
I don’t know what an artist’s advice would be, but from a geometry point of view:
The advantage to doing it this way is that once you’ve constructed the first arc, you can move the paper around as much as you’d like without worrying about keeping track of the vanishing point, because all the future work is relative to marks already on the page.
Of course you could come up with another way of constructing that first arc. If you have an angle θ cut out of something rigid or marked on something you can trace, then:
@khird I'll try a few variations in coming days.
@peterdrake I expect it'd look better - at that point everything ought to be lined up. Maybe try tracing that drawing onto another sheet, but offset vertically so it's like you describe? I'm trying to imagine it, and I think my brain is happier with the shape of the box when I picture it down near the bottom edge.