Klye @khird@qoto.org
Mod
Joined Sep 2018
@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:
- In the correct two-point perspective case, the horizon passes through the image centre, so 𝓱 = 0. The first formula gives the formula 𝓭 = √[ℓ₁ℓ₂] for altitude of a triangle, and the second one blows up as the third vanishing point goes to infinity.
- In the correct one-point perspective case, the line connecting the vanishing point to the centre of the image is perpendicular to the horizon, so ℓ₁ = 𝓱 and ℓ₂ = ∞; consequently, the distance is indeterminate. This corresponds to an extra degree of freedom, as the observer can move directly toward or away from the vanishing point without changing its position on the image plane.
- If ℓ₁ = ℓ₂ = 2𝓱, then ℓ₁ = ℓ₂ = ℓ₃. This corresponds to a pseudo-isometric orientation; all the vanishing points lie at 120° intervals on a circle surrounding the image centre.
@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:
- a face, it's three-point perspective with the vanishing points at the three corners of the triangular face.
- an edge, it's two-point perspective with the vanishing points at the endpoints of the line segment defining the edge.
- a vertex, it's one-point perspective with the vanishing point at the vertex.
@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.
@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.
@sabbatical Plexiglass is a trademark for acrylic - it's the same thing!
Polycarbonate's a different thing, but I think the forum post that made that claim is wrong.
@mitch one syllable, but the vowel's a diphthong. Same as my name!
@ShadSterling Oh yeah! definitely a cognitive speed bump when I come across that usage. At one point BLM was the same thing - historically for Bureau of Land Management; for a time in the mid-2010s it was more common to abbreviate the Black Lives Matter slogan to the same acronym.
This is on the right track.
The problem is that your vertical lines (that is, representing vertical edges in 3D space) are all parallel on your 2D image plane.
This means that your image plane is itself vertical. But your viewpoint is above the horizon, and the horizon is above the midpoint of the page. This implies that your image plane is oblique relative to the direction of observation (red line on my diagram) instead of normal to it (green line). That's the difference between a two- and three-point perspective, and the cause of the distortion you see.
The solution is to also draw the vertical dimension with perspective. Because your direction of observation is slightly downward, the third vanishing point should be directly below the midpoint of the image, and probably at quite a distance (it would be infinitely far away only if you were looking perfectly horizontally, which is when your verticals should come out parallel).
I think that with some trig you could work out the proper distance as a function of the coordinates, relative to the centre of the page, of the two existing vanishing points.
@ShadSterling Point of Contact is how I would normally expand it. Proof of Concept is new to me though. What would you use that acronym to represent?
@sabbatical That sounds like an epoxy - they want you to mix two components and apply with a syringe. The point of a solvent weld is that it just dissolves a bit of plastic from each face, creating a thin layer of liquid plastic-in-solvent solution between the two pieces, and then as the solvent evaporates, the plastic remains, leaving it as one continuous piece. Were I in your shoes, I'd just get a can of acetone from the local Rona/Lowes/Home Depot and give that a shot - but your dollar, your decision.
No matter what you use, you'll have to get the two faces lined up as exactly as you can to maximize the surface area in contact (viscous products are more forgiving in this regard, but you have two perfectly mated halves of the fracture, so that's probably more hassle than it's worth). Then you'll need to clamp them together without flexing the join. I think the clamping will be the hard part, because it's a curved surface without anything to easily line them up against.
@sabbatical Hm yeah that looks to be in shear if I understand the orientation correctly. You can still try solvent welding it but you might benefit from coming up with a way to clamp things firmly in place while the weld sets.
@sabbatical Thanks! I'm the son of two chemists, and I broke my fair share of plastic toys as a kid. My dad would use the repairs as an opportunity to teach me.
@sabbatical Wikipedia says acrylic, not polycarbonate - and I tend to think that's likelier, just because it's a quarter century old and it looks way too clean for lexan (look at how hazy old Nalgene bottles etc. get), plus lexan is notably shatter-resistant, and the evidence suggests that's not true of the article you have.
If it is lexan, you probably need something more exotic like dichloromethane, which both is harder to source and demands MUCH more attention to safe practices regarding inhalation, skin contact, etc.
@sabbatical Worth a shot. Looking at the picture I think the fracture will mostly be under compressive stress when the computer's upright; that is to say, the weight of the machine will tend to press the two faces of each fracture together rather than pulling them apart. Can't say from that pic whether that looks to be true of the monitor as well.
It might not be invisible but I'd guess it'd be structurally adequate.
@sabbatical per Wikipedia, it's made of plexiglass, so you can just get a tin of acetone from the hardware store. That's good news; some plastics require nastier or harder-to-source solvents.
@sabbatical Depending on what kind of plastic it is, I think you'd have better luck solvent-welding it than epoxying it.
Could someone kindly explain what the advantage is, from the employer's perspective, of locking out workers who have given notice of an imminent strike? Or, from the union's perspective, why this is a problem and worth complaining about? I understand that in general, a lockout is a way to put pressure on the labour force by denying them the opportunity to earn, but in such a case, the workers already announced their intention to forgo that opportunity.
For example, here's an airline doing this: https://www.westjet.com/en-ca/news/2023/the-westjet-group-issues-lockout-notice-in-response-to-alpa-s-st
And here's a port authority doing it (and then rescinding the lockout when the strike was disallowed by the regulator) :
https://www.portvancouver.com/about-us/information-updates/port-of-vancouver-operations-update-58/
@pganssle Here are fiction recommendations based on what I enjoyed when I was in that age range. Both are starts to longer series in case they're well received.
Relativistic effects are used in Ender's Game to allow characters to age at different rates, and it was my assigned summer reading for freshman year at my all-boys high school, so that's my recommendation for your nephew.
Sabriel has a competent female protagonist, but her enemies are so powerful that she has to outthink them more than outfight them. I read it in sixth grade, so that's my recommendation for your niece.
For nonfiction you could consider Randall Munroe's books (Thing Explainer, What If?, and How To) for your nephew. I don't have much idea here for your niece, so I'll offer the Golden Compass as a second fiction choice for her.
@garyackerman I think this derives from the educational presentation of science as detective work. In fiction, the sleuth finds clues, but not enough to publicly accuse a suspect, and declares, "I've got a *theory*, but I need more proof!" As a scientist, I try to set a good example by preferring the word "hypothesis" in these contexts.
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