Talk:List of common coordinate transformations

Notation Conventions
We should try to follow CONVENTIONS FOR SPHERICAL COORDINATES. It is very possible that I have broken compatibility. --MarSch 15:06, 30 April 2006 (UTC)


 * Unfortunately it is useless because it does not mention the formulas it is proposing. Anyone know of a not useless proposal? --MarSch 15:14, 30 April 2006 (UTC)

Since there is no universal convention for spherical coord's, all articles using them must include a diagram showing the convention used in the article.


 * Yes, you appear to have broken compatibility. The paragraph "3-Dimensional" defines the angles with theta in the x-y plane, but the equations in the "from spherical coordinates" has theta measured away from the Z axis, as in the spherical coordinates article.

Roger wilco (talk) 04:00, 22 February 2009 (UTC)


 * I have changed the title of this proposal to be a bit more informative. Feel free to revert back if it was unneeded. As for the conventions, I highly suggest we follow "ISO 80000-2 Part 2: Mathematical signs and symbols to be used in the natural sciences and technology". It specifies that, for spherical coordinates, $$ \phi $$ is the angle within the x-y plane and $$\theta $$ being off of the z axis. I do suggest that we try and follow that ISO standard throughout the entire article for consistency with other Wikipedia articles that, for the most part, also follow this standard. Having a diagram similar to the Spherical coordinate system article is a good idea. Potchama (talk) 22:27, 18 July 2018 (UTC)

Intrinsic coordinates
I'm changing some of the wording to fix links to Intrinsic coordinates which has been moved to Intrinsic equation. The link now points to Cesàro equation because that's what was actually being converted. The titles of sections converting to Intrinsic coordinates (now Cesàro equation) have been reworded because really there is no such thing. To get the Cesàro equation you must find the arc length and the curvature in terms of the parameter and then eliminate the parameter. Often the arc length is given as an integral which can't be expressed in closed form and the curvature is a complicated expression, so eliminating the parameter is pretty much out of the question. There are a few, rare curves where this can be done, but not enough to justify a claim that there is some sort of conversion formula.--RDBury (talk) 14:07, 13 July 2008 (UTC)

Simplified equations
I suggest the addition of some of the following simplified equations for finding the T and Curvature vectors using Cartesian coordinates: T(t) = r'(t)/|r'(t)| and k= |T'(t)|/|r'(t) —Preceding unsigned comment added by 130.127.255.224 (talk) 20:31, 12 April 2009 (UTC)

To cylindrical coordinates From Cartesian coordinates
The current equation for $$\theta$$ contains an undefined $$u_0(\cdot)$$ operator:


 * $$\theta=\arctan\frac{y}{x} + \pi u_0(-x) \, \operatorname{sgn} y $$

I guess that this is supposed to be the indicator function $$u_0(a)=\mathbf{1}_{a\geq0}(a)$$, but it is not clear and would be a bit confusing (IMO) even with standard notation. Either $$u_0$$ should be clearly defined, or the equation from Cylindrical coordinates should be used:
 * $$\theta =

\begin{cases} 0 & \mbox{if } x = 0 \mbox{ and } y = 0\\ \arcsin(\frac{y}{r}) & \mbox{if } x \geq 0 \\ -\arcsin(\frac{y}{r}) + \pi & \mbox{if } x < 0\\ \end{cases} $$

I like the piecewise definition, myself, and it makes equations on both pages consistent.

--Quantum7 00:11, 14 August 2013 (UTC)
 * I've gone ahead and changed the article to use the second function. --Quantum7 18:03, 19 August 2013 (UTC)

There seems to be an error in the Jacobian matrix, can someone please double check? --2001:610:1908:1400:F064:913E:C253:DEB3 (talk) 15:17, 23 September 2013 (UTC) Currently on the page:

\frac{\partial(r, \theta, h)}{\partial(x, y, z)} = \begin{pmatrix} \frac{x}{\sqrt{x^2+y^2}}&\frac{y}{\sqrt{x^2+y^2}}&0\\ \frac{-y}{\sqrt{x^2+y^2}}&\frac{x}{\sqrt{x^2+y^2}}&0\\ 0&0&1 \end{pmatrix} $$

What I calculate with Mathematica (and what seems to give the right Jacobian determinant, since this must be 1/r)

\frac{\partial(r, \theta, h)}{\partial(x, y, z)} = \begin{pmatrix} \frac{x}{\sqrt{x^2+y^2}}&\frac{y}{\sqrt{x^2+y^2}}&0\\ \frac{-y}{x^2+y^2}&\frac{x}{x^2+y^2}&0\\ 0&0&1 \end{pmatrix} $$ -- 2001:610:1908:1400:F064:913E:C253:DEB3 (talk) 15:17, 23 September 2013 (UTC)

To spherical coordinates From Cartesian coordinates
$$ \begin{pmatrix} \frac{\partial(\rho, \theta, \phi)}{\partial(x, y, z)} = ... \end{pmatrix} $$ I think the matrix is wrong in some places by a factor of $$\rho$$. Specificly, the 3rd column, second row caused me great grief. Also, why not give the transformation in terms of the unit vectors instead of $$\rho, \theta, \phi$$ (or as well)? 130.237.45.198 (talk) 15:06, 17 March 2014 (UTC)

The matrix is correct: specifically for the element you asked for, you can use this Wolfram|Alpha query: http://www.wolframalpha.com/input/?i=derivative+of+arctan%28sqrt%28x%5E2%2By%5E2%29%2Fz%29+with+respect+to+z. You can verify the rest of the elements in the same way.

130.237.45.198 (talk) 15:06, 17 March 2014 (UTC)

Type of Spherical Coordinates Used
The page for the [Spherical coordinate system] indicates that there are two primary methods of notating spherical coordinates. One where theta and phi represent the polar and azimuthal angles respectively, and another where they are reversed (azimuthal and polar respectively). Do we know which system of notation the conversions on this page are using? This is important as the conversions will result in incorrect values if the wrong notation is used. FrankCarroll (talk) 13:38, 18 August 2014 (UTC)

Never mind ... I found the paragraph talking about it! FrankCarroll (talk) 13:39, 18 August 2014 (UTC)

Assessment comment
Substituted at 18:27, 17 July 2016 (UTC)

There's actually 2 spherical coordinate systems
The one 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)

Benhut1 (talk) 03:08, 29 December 2016 (UTC)