Wikipedia:Reference desk/Archives/Science/2024 November 2

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November 2

Is there a name for 0.001 miles?

I need to work on a software that works in units of one one-thousandth of a mile internally. Is there a name for such a unit? --193.83.24.42 (talk) 00:35, 2 November 2024 (UTC)

American silliness? HiLo48 (talk) 00:45, 2 November 2024 (UTC)

As opposed to French silliness, such as the met-ray. ←Baseball Bugs ^{What's up, Doc?} carrots→ 02:09, 2 November 2024 (UTC)

The Roman mile was by definition a thousand paces (milia passuum). catslash (talk) 01:24, 2 November 2024 (UTC)

Actually, that's 1000 double steps, a bit under 1500m. --Stephan Schulz (talk) 22:40, 7 November 2024 (UTC)

The obvious millimile gets a little use. (The author there can't redefine span (unit) so easily though.) I also found it in a more modern book about chemistry, where it seems to be part of a quiz designed to test the reader's understanding of units: Which length is longer, a millimile or a decameter? but archive.org has stopped showing snippet views of in-copyright books. Millimole tends to pollute search results, which is perhaps why a chemist would be inspired to invoke millimiles.  Card Zero  (talk) 01:46, 2 November 2024 (UTC)

See pace (unit). When I worked as a surveyor, we often used this informal unit and with practice it became 99% accurate, good enough for most purposes. Shantavira|^{feed me} 09:21, 2 November 2024 (UTC)

There is an existing more accurate unit, used by the railways, known as the "link". Your unit is 8 links. The link is divided decimally and contains 7.92 inches. Your unit is therefore (7.92 x 8) = 63.36 inches. Before metrication, Ordnance Survey maps were scaled at 1 inch to a mile. The scale was therefore 1/63 360. 2A00:23D0:FFC:3901:90DF:CC65:72B0:11FF (talk) 14:51, 2 November 2024 (UTC)

Can I determine distance from size of a photographed object

If a photograph contains an object of known real size, can I use that to determine how far it was from the camera or other device that took the picture? Also, would this question fit better here or on the math reference desk? Primal Groudon (talk) 16:18, 2 November 2024 (UTC)

For one thing, you would have to know the type of lens. A wide-angle or fisheye lens makes things look farther away than they actually are. ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:55, 2 November 2024 (UTC)

Even with a pinhole camera you couldn't, unless you know the distance inside the camera between the pinhole and the photographic plate or film. Define four variables:

• h_ext is the real size of the object;
• d_ext is the distance between the pinhole and the object;
• h_int is the size of the object's image;
• d_int is the distance between the pinhole and the photographic plate or film.

Then h_ext : d_ext = h_int : d_int.

If you have the values of three of these variables, you can determine that of the fourth. With simple fixed lenses, this also gives a reasonable estimate.

To determine the value of d_int, you don't have to look inside the camera. Just take a picture of an object of known size at a known distance and measure h_int. You can now calculate d_int.  --Lambiam 20:16, 2 November 2024 (UTC)

Empirical calibration is surely the best approach, but if your camera has a zoom, then you will need to ensure the same level of zoom is used for the measurement and the calibration. You can do this by checking the 35 mm-equivalent focal length in the exif meta-data in the jpeg files. catslash (talk) 23:49, 2 November 2024 (UTC)

Lambiam, what if the object is a building of known dimensions? If you can see 3 corners couldn't you solve for the relative position of the camera? Or do you need 4 points? fiveby(zero) 04:32, 9 November 2024 (UTC)

In general, we have a projective transformation that projects a 3D point $(x,y,z)$ in real space to a 2D point $(\xi ,\eta )$ on the film by a transformation of the form

$\xi ={\frac {d+ex+fy+gz}{1+ax+by+cz}},~~\eta ={\frac {h+ix+jy+kz}{1+ax+by+cz}}.$

Let $y$ denote the vertical coordinate in the 3D space and $\xi$ the horizontal coordinate on the film. Then, assuming the camera is not tilted, the value of $\xi$ is invariant under changes of $y$ while $x$ and $z$ remain constant, which implies that $f=b=0.$ Let furthermore $x$ denote the horizontal coordinate parallel to the film in the camera. Then the value of $\eta$ is invariant under changes of $x$ while $y$ and $z$ remain constant, which implies that $i=a=0.$ Every point in the straight line of sight from the camera, as well as in the vertical plane through that line, has the same value for $x$, and its image on the film is on a vertical line with constant $\xi .$ We can set both equal to $0,$ which implies that $d=g=0.$ The third 3D coordinate $z$ denotes the horizontal coordinate in the direction of sight of the camera. We can set $\eta =0$ for the height of the horizon on the film. This means that $\eta \to 0$ as $z\to \infty ,$ which implies $k=0.$ Finally, at a constant distance $z,$ real-world squares remain squares on the image, so we know that $e=j.$ A judicious choice of coordinates has led to the simpler projective transformation

$\xi ={\frac {ex}{1+cz}},~~\eta ={\frac {h+ey}{1+cz}}.$

Three unknown coefficients still remain: $c,e,h.$ Relating a real-world point with known coordinates $(x,y,z)$ to a point on the film with known coordinates $(\xi ,\eta )$ gives you two equations, so if my reasoning is correct, in general doing this for two points should suffice. It becomes more complicated if you don't know the coordinates of real-world points but only the distances between them.  --Lambiam 07:34, 9 November 2024 (UTC)

Furthermore, putting

$\lambda ={\frac {e}{c}},~~z_{0}=-{\frac {1}{c}},y_{0}=-{\frac {h}{e}},$

we can rewrite the transformation as

$\xi =\lambda {\frac {x}{z-z_{0}}},~~\eta =\lambda {\frac {y-y_{0}}{z-z_{0}}}.$

Fixing the value of $y$ for the ground level as being zero, $y_{0}$ should be the eye height of the camera, which is presumably easily measured, eliminating one more unknown. This might suggest just one real-world point $(x,y,z)$ needs to be related to an image point $(\xi ,\eta ),$ but the equations you get are not independent, since, if the values of $\xi ,\eta$ and $y$ are known, the value of $x$ can be computed without measuring it, using $x={\frac {\xi (y-y_{0})}{\eta }}.$.  --Lambiam 12:18, 9 November 2024 (UTC)

Here is a scenario, if you have an uncropped picture of the White House and you know the Camera Model and the Fixed Len used. You can buy the Camera and Len and take the same Picture at vairous distance of the White House until the your picture matches up to the target Picture. Then you can estimate the distance. 2001:8003:429D:4100:5CCA:727C:C447:3877 (talk) 22:07, 3 November 2024 (UTC)

There are two factors that change the size of an object in a photo when you fix the lens and zoom. One is the distance to the object. The other is the scaling of the photo itself. If I print a photo as 4x6 it will be much smaller than the same photo printed on 8x10. To measure distance, you really need another photo with known distance from the same camera with same lens and same zoom so you can measure the width of an object of known size on the size of the photo you printed. Then, you know the scaling factor to work out the distance to an object in another photo. Another option is to have two (or more) objects of known size at different distances where you know the distances between them. When in the same photo, you can use the sizes of the objects and the known distance between them to estimate the distance to the camera. 12.116.29.106 (talk) 18:26, 5 November 2024 (UTC)

Projective Geometry can help if you know the length of something in a picture and the shape of something, e.g. a square on the ground. NadVolum (talk) 18:47, 5 November 2024 (UTC)

Magenta vs. purple

How come mixing blue and red with equal gets magenta in modern color theory but a bluer purple (more violet-like) in RYB color theory?? Georgia guy (talk) 16:36, 2 November 2024 (UTC)

No colour theory is perfect, but, more importantly, it is ill-defined what it means to "mix" colours. Different physical procedures will also give different outcomes.  --Lambiam 20:20, 2 November 2024 (UTC)

it depends! Red in RYB is something "not (subtracting) blue" and blue is somewhat "not (subtracting) red". So the red takes the role of the blue in the other system and vice versa. If you constructed a special "blue pigment" with some green in it and a special red pigment with some orange in it, you would mix either the pigments and have a tone between magenta and purple or you would mix the reflected light from both pigments, and have a more bright version of exactly the same tone. I don't know if you can make the brightness the same too. So it doesn't have to be a different colour, but that only works with purple because of the complementarity. Generally the colours in both systems are very differently mixed. 176.2.70.177 (talk) 20:48, 2 November 2024 (UTC)

Reading Subtractive color and Additive color might help. Klbrain (talk) 01:08, 11 November 2024 (UTC)