Talk:Spherical coordinate system

message: Previous discussions pertaining to the old article have been archived to Talk:Spherical coordinate system/Archive. --Carl (talk|contribs) 01:25, 18 September 2006 (UTC)

message: I printed out this page and the images came out as black squares.
get new images, these ones are garbage!  —Preceding unsigned comment added by 62.136.133.147 (talk) 08:26, 5 May 2008 (UTC)
replies: text: The main article would be improved considerably by changing the images to pairs of stereoptic 3D images.  216.99.219.151 (talk) 22:14, 15 June 2009 (UTC)
thread_title:  Printing 

message: This needs to be fixed, its why is there no info for spherical coordinates like they have for cylindrical, such as dV and dS:
(From cylindrical article) Line and volume elements
In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes.
The line element is dl = dr\,\mathbf{\hat r} + r\,d\theta\,\boldsymbol{\hat\theta} + dz\,\mathbf{\hat z}.
The volume element is dV = r\,dr\,d\theta\,dz.
The gradient is \nabla = \mathbf{\hat r}\frac{\partial}{\partial r} + \boldsymbol{\hat \theta}\frac{1}{r}\frac{\partial}{\partial \theta} + \mathbf{\hat z}\frac{\partial}{\partial z}.
Even mathworld has dS......
: I have added surface and volume. –Pomte 11:13, 10 April 2007 (UTC)
thread_title:  Elements 

message: I don't think this statement is correct:
The longitude is the azimuth angle shifted 180° from θ to give a domain of -180° ≤ θ ≤ 180°.
Assuming the x axis goes from the center of the Earth through the equator at 0 deg longitude, then I believe the correct wording is:
The longitude is the azimuth angle but for 180° < θ < 360°,  subtract 360° so that -180° < longitude ≤ 180°. 
Actually, it would probably be more correct to bring up East and West when talking about longitude, but in any case, saying a shift by 180 deg is wrong (unless the x axis is supposed to point through the 180 deg longitude point which I doubt) DaraParsavand 19:01, 18 January 2007 (UTC)
replies: text: You're right, it's only a shift on half the values. I think it's pointless to discern whether any shift starts at θ = 0° or θ = 90° or anywhere else, so I've left it as an east-west distinction. –Pomte 11:37, 10 April 2007 (UTC)
thread_title:  Longitude 

message: Radians should be used, not degrees.
Jarino1 18:55, 9 July 2007 (UTC)
thread_title:  Angles 

message: There seems to be a mistake in the page.
atan2 is said to return a result between pi and -pi and yet phi is said to be in the range of 0 and 2pi. What's going on here?  —Preceding unsigned comment added by 132.67.97.20 (talk) 11:30, 19 February 2009 (UTC)
replies: text: Actually it matters so that one can truly use a given coordinate system to find referenced loci, not just for uniqueness. But of course that is exactly the level of detail that someone would look to this article for, and which it fails to provide because of its over-generality. Dlw20070716 (talk) 09:05, 19 July 2011 (UTC)
thread_title:  Range of azimuth 

message: Conventional spherical coordinates as described in this article are a combination of rotations along the z and y axes. However, Euler angles are most commonly combinations of z and y rotations. Maybe someone could mention a few words about this issue? I was a bit confused by this difference. I propose to discuss this at Talk:Euler angles. Han-Kwang (t) 10:50, 4 December 2007 (UTC)
thread_title: Comparsion with [[Euler angles]]

message: φ is referred to as the azimuth and θ is referred to elevation, right?  —Preceding unsigned comment added by 131.180.34.78 (talk) 13:01, 22 May 2008 (UTC)
thread_title:  θ is referred to elevation 

message: Anonymous user 146.87.52.54 added a note to the "Geographic coordinates" section saying "There is a mistake on the 3rd equation of the formula of the cartesian coordinates!".  Would the author please clarify? (Perhaps he/she assumed that θ in the Cartesian formulas was latitude? It is actually inclination, that is, 90° minus the latitude.) --Jorge Stolfi (talk) 18:48, 24 November 2009 (UTC)
replies: text: Since geographical coordinates use latitude and not inclination, there is an obvious error to be addressed. A wikipedia author is not free to redefine the geographical coordinate system to include inclination! If it is mentioned at all, you'd better have an ironclad reference for it. Dlw20070716 (talk) 08:22, 19 July 2011 (UTC)
thread_title:  Error in Cartesian formulas? 

message: :Two comments you made still bother me:
#You insist that one "cannot use [the concept of cross product] to define the third vector in terms of the other two." Do we at least agree that any 3-D frame of reference can be represented (i.e. fixed in space) by exactly two basis vectors? Does the concept of "right angle" assume knowledge of the Cartesian coordinate system? The third basis vector in establishing such a system is simply defined as being simultaneously at right angles to the first two, with a particular handedness: you fix the system in space by only fixing two of these basis vectors; the last one follows in a predetermined way.
#*Yes, *once you choose a "right" handedness for the space*, then two orthogonal directions define a third direction orhtogonal to both, unambigously, by that "right hand" rule.  But classical Euclidean 3D geometry usually does not distingish "right handed" from "left handed".  I presume that this "hand neutrality" is a consequence of Euc.Geom. having been developed first for the plane, in contexts where the handedness is irrelevant.  Consider for example the theorem or axiom "two triangles are equal if corresponding sides are equal": it implicitly assumes that you can flip one triangle over to match it with the other triangle.  For *physical* 3D space (the one whe move in) we of course cannot "flip" a solid over, so one may assume that "right-handed" is well defined and use that to define the third axis. (But you should read Martin Gardner's discussion in The Ambidextrous Universe. And if the physical universe turns out to have the topology of a non-orientable 3D manifold, then we are in trouble again...) However, if we are choosing coordinates for some abstract 3D space (such as the state of a compressed gas), then there is no natural definition of "right-handed", and one must specify the three axes explicitly.  I suppose that there are people who define and work with "oriented Euclidean 3D space" (classical E. space plus a distinguished handedness), but that does not seem to be common. 
#:*PS. I forgot to say: yes, in Euclidean geometry the concept of "perpendicular" is defined (and almost primitive). In the plane, two lines are perpendicular if all four angles between them are congruent (and "congruent" is a primitive concept).  "Parallel" is a more primitive notion: two lines are parallel if they lie on the same plane but never meet. The existence of parallel lines is an axiom (much disputed until Lobachevski/Riemman).
#** Thanks!I guess I was confusing the definition of "frame of reference" with the definition of a "coordinate system," which requires further elaboration, such as the definition of the third basis vector (in Cartesian coordinates) even though it is based on the first two; the function that defines the third basis is what adds that third dimension. In Spherical coordinates, there are three functions of the same basis vectors defining three alternate dimensions (not basis vectors, nevertheless having the ability to uniqely define a point in space, except at the degeneracies.Toolnut (talk) 21:48, 9 December 2009 (UTC)
thread_title: Dot product, cross product, handedness; abstract and concrete

message: The fisrt three figures were recently reordered. I have partially restored their original order. The two line diagrams should come first since they illustrate the two variants of spherical coordinates (inclination vs. elevation) defined in the first paragraph.  The raytraced figure is somewhat redundant, it does not show the coordinates proper (only their isosurfaces for one point), and requires a much longer caption to make sense. 
On the other hand, I have retained the new order between the two line diagrams (with inclination before elevation), since I have also reordered the definitions of the two variants in the lead paragraph (see above). Note that swapping the two figures requires rewriting their captions. 
All the best, --Jorge Stolfi (talk) 21:30, 14 February 2010 (UTC)
thread_title:  Figure order 

message: The section "If it is necessary to define a unique set of spherical coordinates for each point..." does not appear to deal with what happens at the origin. Could someone who knows comment on any approaches or conventions there might be for this? Thanks! Gwideman (talk) 04:33, 17 March 2010 (UTC)
thread_title:  Unique spherical coordinates for origin? 

message: The range of the angles bothers me. 
0<r<
0<θ  —Preceding unsigned comment added by 168.18.148.126 (talk) 23:16, 11 August 2010 (UTC)
replies: text: Consider longitude and latitude, longitude goes from 180° east to 180° west, i.e. -π to π, or equivalently 0 to 2 *π. Latitude goes from 90° south to 90° north, i.e -π/2 to π/2. If you measure the angle from the north pole then this will be 0 to π. If they both went 0 to 2π the you would actually cover the sphere twice.--Salix (talk): 23:29, 11 August 2010 (UTC)
thread_title:  Describe to me why one of the angles has to be 0 to pie 

message: Using the stated formulas for converting cartesian to spherical coordinate returns results I believe are not consistent with dimensions or more precisely the spacial dimensions in "Dimensions".  ("The spherical coordinates (r, θ, φ) of a point can be obtained from its Cartesian coordinates (x, y, z) by the formulas .... ") 
e.g. converting (1,0,0) returns θ =π/2 and φ =π/2  , according to dimension it ought to be θ = 0. The inconsistency can well be in dimensions,  θ and φ  might adhere to a different convention with respect to their relation to x,y,y than this article.
Could somebody with knowledge please check and align if required?
Thanks, it is appreciated.
Aporio (talk) 20:50, 13 October 2010 (UTC)
thread_title:  Inconsistency with Dimensions 

message: dx=r\cos\theta\cos\phi d\theta-r\sin\theta\sin\phi d\phi
dy=r\cos\theta\sin\phi d\theta+r\sin\theta\cos\phi d\phi
then dxdy=r^{2}\cos\theta\sin\theta\left(\cos^{2}\phi-\sin^{2}\phi\right)d\theta d\phi\ne r^{2}\cos\theta\sin\theta d\theta d\phi anyone knows the reason why like this??? 
:anyway, just replace dA in one system with dA in another system. one dV with another dV. no other adjustment is required. Jackzhp (talk) 13:45, 28 March 2011 (UTC)
replies: text: It's dx\wedge dy.  See differential form.  Sławomir Biały (talk) 14:54, 28 March 2011 (UTC)
thread_title: dxdy

message: The distinguishment would be achieved by using \, \theta_{inc} (or \, \theta) and \ \theta_{el} instead of using the same \ \theta's  in this article.  Adding the description of the order of the 3D variables would be, furthermore, useful: \ (r,\ \phi,\ \theta_{el}) in a right-handed coordinate system and \ (r,\ \theta_{el},\ \phi,) in a left-handed coordinate system.
Kkddkkdd (talk) 11:07, 21 May 2011 (UTC)
thread_title: Distinguishment between inclination and elevation variables 

message: As evidenced by all the discussion above, this article has major problems, mostly because of conflicting usages by various authors and communities. That, and it has no references at all (and nobody so far seems to have noticed because of all the other problems)!
Because of all the conflicting conventions, I recommend turning it into a disambiguation-like page and redirecting to pages that better discuss specific spherical coordinate systems as they are actually used in specific systems, like geographical location, mathematics, computer graphics, etc. The page as it stands is too confusing and just plain erroneous to be useful. It would be useful to have an article that covers the conventions used in mathematics if done well, but that appears to be hopeless because of the confusion reigning therein. Dlw20070716 (talk) 07:44, 19 July 2011 (UTC)
replies: text: Agreed. This page is a mine-field of various conventions to the point of making the whole page utterly confusing. Lakhindr (talk) 18:30, 3 May 2023 (UTC)
thread_title:  This article tries to cover too much ground 

message: The spherical coordinates (r, θ, φ) of a point can be obtained from its Cartesian coordinates (x, y, z) by the formulae
:r=\sqrt{x^2+y^2+z^2}
:\theta=\cos^{-1} \left( \frac{z}{r}\right)  
:\varphi = \tan^{-1} \left( \frac{y}{x} \right)   
Wolfram disagrees with this here:
http://mathworld.wolfram.com/SphericalCoordinates.html
Images:
http://mathworld.wolfram.com/images/equations/SphericalCoordinates/Inline33.gif
http://mathworld.wolfram.com/images/equations/SphericalCoordinates/Inline36.gif
http://mathworld.wolfram.com/images/equations/SphericalCoordinates/Inline39.gif  — Preceding unsigned comment added by 129.116.33.62 (talk) 21:34, 5 September 2011 (UTC)
replies: text: -No wolfram and this article are agreeing. You just need to study up on your trigonometry to understand the relation. Cos(theta) = Adjacent Leg of triangle divided by hypotenuse of triangle. So cos(theta) = z/r and theta = cos-1(z/r)  — Preceding unsigned comment added by 99.137.50.90 (talk) 12:35, 23 October 2012 (UTC)
replies: text: Well, in our version of these formulae theta and phi are swapped compared to wolfram. But that is not incorrect, there are two common ways to define them, as explained in our article. We also explicitly state which of the definitions we use for the formulae just above them. I think that's all we can do. — HHHIPPO 17:22, 23 October 2012 (UTC)
replies: text: My apologies for not knowing the proper way to point this out to you WikiPeople, but it seems the "theta = arccos(-z/r)" equation should read "theta = arccos(z/r)", no?  — Preceding unsigned comment added by 71.237.117.249 (talk) 16:09, 28 December 2013 (UTC)
thread_title:  Incorrect Formula from Cartesian to Spherical 

message: The main topic here is the mathematical spherical coordinate system. It should not have the stuff from celestial coordinate system] and geographical coordinate system mixed into the main article. There are separate articles on those. I think it is a good idea to have a separate section on those pointing out the differences from what is done in maths but this article has become a mess by mixing them into the main article. Dmcq (talk) 20:08, 25 March 2012 (UTC)
replies: text: Agreed.  a13ean (talk) 20:13, 25 March 2012 (UTC)

text: Agreed. This main topic is distressingly confusing. Worse is the image on the right which shows the maths convention first. But it isn't the one followed up in the article. Lakhindr (talk) 17:05, 3 May 2023 (UTC)
thread_title:  Need to deal in the main with the main topic 

message: And I'm not just talking about which symbol (phi or theta) is used for which angle. For the purpose of this post, theta will be the vertical angle (the one off of the XY plane) and phi will be the horizontal angle (the one in the XY plane).
The version of spherical coordinates talked about here in Wikipedia works like this:
Theta is the angle from the z axis, and goes from 0 to pi
Phi is the angle from the x axis in the XY plane and can go from either 0 to 2pi or -pi to pi
Rho is the distance from the origin
The transformation to Cartesian coordinates, which is specified in the wiki article, is as follows.
x = rho * sin(theta) * cos(phi)
y = rho * sin(theta) * sin(phi)
z = rho * cos(theta)
However, there's a variant of the spherical coordinate system, which can actually be more practical in some applications (namely, when you don't want your vertical angle theta to be 0 on the z axis, but rather have theta be 0 on the XY plane). In this case, the definitions of the variables are as follows. 
Theta is the angle from the XY plane, and goes from -pi/2 to pi/2
Phi is the angle from the x axis in the XY plane and can go from either 0 to 2pi or -pi to pi
Rho is the distance from the origin
The transformation to Cartesian coordinates is as follows.
x = rho * cos(theta) * cos(phi)
y = rho * cos(theta) * sin(phi)
z = rho * sin(theta)
Notice that where you previously had cos(theta) you now have sin(theta), and where you previously had sin(theta) you now have cos(theta).
Benhut1 (talk) 08:10, 29 December 2016 (UTC)
replies: text: True.  This other coordinate system is mentioned in the third paragraph of the article.  It is usually called the geographical coordinate system, and is the subject of a separate article. Sławomir Biały (talk) 12:39, 29 December 2016 (UTC)
thread_title:  There's actually 2 spherical coordinate systems 

message: I added the image at right. However, I don't know if I'm measuring the angles from the correct directions. Could someone fix the caption? SharkD  ☎  21:16, 10 August 2018 (UTC)
thread_title:  Sphere image 

message: Suggestions 144.48.134.241 (talk) 17:48, 25 October 2022 (UTC)
thread_title:  Physics 

message: I may be entirely mistaken here but the φ conversion formula:
:\phi=sgn(y)\arccos\frac{x}{\sqrt{x^2+y^2}}
appears to be incorrect for y=0. While for this equation to be correct it must be sgn(0) = +1, the convention is to set sgn(0)=0. If this is actually a mistake, the formula should be modified or a comment on the re-definition of the sgn-function should be provided. 141.14.162.194 (talk) 01:37, 13 January 2023 (UTC)
thread_title:  Sign-flaw in current cartesian->spherical formula