Talk:Cylindrical coordinate system

Direction

The article doesn't show the directions of ρ, φ, z vectors. —Preceding unsigned comment added by 187.58.12.119 (talk) 13:39, 14 June 2010 (UTC)[reply]

It's kind of astonishing that this comment has been here for more than a decade and no one has made an attempt to add the meanings of the symbols

{\boldsymbol {\hat {\rho }}},{\boldsymbol {\hat {\varphi }}},\mathbf {\hat {z}}

to the article :(. JBL (talk) 01:06, 29 November 2022 (UTC)[reply]

Physics convention

This needs a discussion regarding the alternate convention used by physicsts: rho and phi instead of r and theta. [Unsigned comment by User:Starwed on 2006-02-0 T10:44:46]

Done, I hope. --Jorge Stolfi (talk) 22:36, 2 August 2009 (UTC)[reply]

Line element

The line element equation looks wrong. Shouldn't it be $ds^{2}=dr^{2}+r^{2}d\theta ^{2}+dz^{2}$ ? [Unsigned comment by Special:Contributions/139.184.30.16 on 2006-10-31 11:31:06]

The line element is given in vector form; when you calculate the magnitude of it you indeed get the expression above. [Unsigned comment by Special:Contributions/65.110.29.238 on 2007-02-28 08:02:28]

ISO notation

I have adapted the notation to the standard ISO notation (ρ,φ,z). I think the article should be expanded to include the relation with spherical coordinates, while the parts about cylindrical harmonics perhaps should go to an independent article. Gonfer (talk) 17:17, 2 February 2008 (UTC)[reply]

I agree with everything you mention above. PAR (talk) 23:05, 2 February 2008 (UTC)[reply]

Done, I believe. --Jorge Stolfi (talk) 22:36, 2 August 2009 (UTC)[reply]

Too many images

There are now *three* images illustrating the concept. Methinks that is too much. It would not be proper for me to vote on my own contribution; but, of the other two, I would rather remove the animated gif. Animated images in general are not good: they force the reader to stop reading in order to look at them, and keep "pulling the eye" even after the reader has looked at them. Metinks that an animated image should be displayed only when the reader explicitly asks to see it, e.g. by clicking on a wikilink or external link. All the best, --Jorge Stolfi (talk) 22:36, 2 August 2009 (UTC)[reply]

I agree. The animation on this page does not say anything that requires animation. On the other hand, in some ways it is the best of the three, showing the three coordinate surfaces clearly. (But it lacks a prominently visible bead in the intersection between the three surfaces.) The second image has too many colors, transparencies, reflections and what not. The three perpendicular axes do not really belong in an illustration of cylindrical coordinates. With so much clutter it is hard to see what it shows. The first image is not bad, (none are terribly bad), but it would be an advantage if it could 1) show why this coordinate system is called cylindrical - where is the cylinder? and 2) correspond more closely to the terms in the text, especially the lead. Now that I have rewritten it, I wish the drawing would show the reference plane more prominently. To nit pick a little, both the first and second drawings pretend to show points at specific coordinates, but the units are poorly marked along the axes, or not at all, making it a mystery why the point is said to have rho=4. How do you see that? Cacadril (talk) 03:09, 15 February 2010 (UTC)[reply]

Textbook Mismatch

My textbook (Calculus Early Transcendentals, 5e by James Stewart [Published through Thomson|Brooks/Cole]) tells me that the cylindrical coordinates are (r, θ, z) and spherical coordinates are (ρ, θ, φ). Was there an update to the standards and this wiki page is up to date, OR is the book right? --Charles Timko —Preceding unsigned comment added by 128.211.207.28 (talk) 03:48, 28 October 2009 (UTC)[reply]

The naming of the coordinates (in any system) is arbitrary and is often determined by the application. (In a 2D Cartesian plot, for example, the coordinates may be (t,P) where t is time and P is pressure.) There are standards but they are not mandatory, so usage does vary. Authors generally have a dilemma when choosing their notation: either invent the notation that seems most logical (or elegant, or convenient) for each text, or follow the tradition of the field (or some official standard), to make reading easier for those who are used to it. Unfortunately, in the specific case of angular coordinate systems (2D polar, 3D spherical, or 3D cylindrical), the tradition is not very specific. It is common to use r or ρ for the two radial coordinates (spatial or planar); but authors vary about which is which --- especially if they are using only one coordinate system in the text. Similarly, it is traditional to use θ and φ for the angular coordinates (azimuth, elevation, or inclination); but again authors do not agree on which is which. So, in conclusion, the page is correct, and your textbook is correct too. The only iron rule is: always define your notation upfront! All the best, --Jorge Stolfi (talk) 03:26, 19 November 2009 (UTC)[reply]

A mistake?

In conversions: I think it should be arcsin(y/x) instead of y/ρ but I am no professional
--91.113.28.31 (talk) 23:11, 18 November 2009 (UTC)[reply]

Basically, it is either arcsin(y/ρ) or arctan(y/x). However, both formulas only return angles in -90 to +90 so one must test for the signs of x and y and handle two separate cases. The arcsin formula is slightly better because it avoids division by zero when x = 0. But, as the page explains, neither formula is good for programming: one should use instead the atan2(y,x) function, provided by most decent languages. All the best, --Jorge Stolfi (talk) 03:43, 19 November 2009 (UTC)[reply]

I didn't mean arcsin or arctan but x instead of ρ --81.217.4.39 (talk) 11:26, 19 November 2009 (UTC)[reply]

That is what I understood. It is /x if you use arctan, but /ρ if you use arcsin. (But in either case you need to test signs and handle two cases.) --Jorge Stolfi (talk) 15:02, 19 November 2009 (UTC)[reply]

In the Coordinate system conversions section, part Cartesian coordinates, the second defining line of φ should read "arcsin(y/ρ), if x == 0". Otherwise, the reader will never reach the third line when reading from top-to-bottom. :-)--81.217.17.35 (talk) 12:23, 29 June 2022 (UTC)[reply]
Fixed There was a mixture of two formulas. I have also fixed other errors. D.Lazard (talk) 14:18, 29 June 2022 (UTC)[reply]

Use accessible language in the lead

I just rewrote the lead to make it more accessible. Encyclopedia articles are supposed to be legible for the non-specialized reader; they shall explain computing concepts for the doctor, medical terms for the musician. Who looks up "cylindrical coordinates" shall not have to look up "orthogonal projection" and figure out what it computes to when applied to a point and a plane. There should be a hierarchy of concepts where the complex ones are explained in terms of simpler ones. "Orthogonal projection" is admittedly a more fundamental concept in some ways than "cylindrical coordinates", but not sufficiently so that it should be made a prerequisite, especially when it is not necessary. —Preceding unsigned comment added by Cacadril (talk • contribs) 02:51, 15 February 2010 (UTC)[reply]

Hm, I am not sure that the rewrite was entirely an improvement. As Einstein is supposed to have said, "make it as simple as possible, but no simpler".

The definition in the lead section needs to be accessible only to those readers who can make some use from it. On the other hand, the definition in the lead *must* be correct and precise, for the sake of readers who come here seeking for such a thing. There is no excuse for giving an incorrect or partial definition.

While I agree that the term "perpendicular projection" should be used instead of "orthogonal", I doubt that a reader who cannot understand this concept will understand spherical coordinates, no matter how the definition is worded. The previous definition connected to polar coordinates; so readers who knew the latter would immediately understand cylindrical coordinates, and readers who didn't had better read that article first anyway.

The new lead says that the azimuth is a direction, relative to another direction. That is inaccurate because the azimuth is an angle (a number), not a direction (a vector): and the very purpose of any coordinate system is to replace geometric notions by numbers. Also the new definition fails to say that the reference direction is parallel to the reference plane; if the reader does not know that beforehand, and assumes that the reference direction is arbitrary, he will not understand the lead. Also, while the explanation on the sign of Z sounds clearer than "signed distance", it doesn't really explain it because it does not tell which side is positive.

All the best, --Jorge Stolfi (talk) 04:50, 15 February 2010 (UTC)[reply]

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ISO convention update

The article mentions ISO 31-11:1992, but it has been revised in 2019 in ISO 80000-2:2019.

This standard still defines (ρ, φ, z) for coordinates in item n° 2-16.2 and indicates it's an update for item 11-12.2 from ISO 31.

It adds in remark that it uses an orthonormal right-handed system, again like previously.

So we could directly note ISO 80000-2 in the article instead of ISO 31-11 I guess. --Dereckson (talk) 15:17, 21 January 2022 (UTC)[reply]