# Questions tagged [coordinate-transformation]

Questions relating changing coordinate systems of numerical points and analytical expression including vector fields and vector analysis.

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101 views

### How to solve for Transpose[X] A X = B

I need to find a transformation matrix of the metric tensor but I don't know how to solve for X from Transpose[X]*A*X=B
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### Cannot remove ragged edges of TransformedRegion plot

I am working with two mappings of a region in the complex plane and I can't eliminate the ragged edges of the region in the second map and do not see anyway to add points to make the perimeter smooth ...
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### Point manipulations to list form

I tend to do a lot of code the manual way, which doesn't work out for bigger data sets. I wanted to know if there were in built functions to do the following; ...
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### TransformedRegion with Circular Sectors

Here is a circular sector: Disk[{0, 0}, 1, {-\[Pi]/6, \[Pi]/6}] I'd like to reflect that about a vertical line. I could use ...
53 views

### Error with StateSpaceTransform: the rule based transformation must be of length 2

I would like to perform a change of variables on the following dynamics system: ...
52 views

### General coordinate transfomation

I am looking for a (free) package or snippet that makes the transformation of tensors between spacetimes easy. What do you suggest?
69 views

### Plot Using User-defined Coordinates

Suppose instead of using Cartesian coordinate $\vec{x}=(1, 0)$ and $\vec{y}=(0, 1)$, I want to define new coordiates $\vec{a} = (1,0)$ and $\vec{b} = (\frac{1}{2},\frac{\sqrt{3}}{2} )$. And when I ...
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### Does Laplacian use first argument “theta” for polar angle or azimuthal angle?

Only example I could find in the help for Laplacian is this My question is, is $\theta$ meant to be the polar or the azimuthal angle? Using $\theta$ for polar is ...
155 views

### Converting from UPS(x, y) to geodetic latitude/longitude

I'm trying to create a program which converts latitude/longitude (wgs84) to UPS (Universal Polar stereographic) coordinates, and then UPS(x, y) to WGS 84. I mean Given UPS(x, y), be able to compute ...
101 views

### ArrayPlot in polar coordinates?

I have a 2-D array ($360 \times 512$). The 360 rows represents the azimuthal angle from (0° to 359°) and the 512 columns are radial segments. This is the ArrayPlot...
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### Where to find order of arguments for default functions

Lets take for example the Laplacian. So I want to apply it in spherical coordinates, so I go the the associated documentation page (https://reference.wolfram.com/language/ref/Laplacian.html?view=all) ...
212 views

### Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
116 views

### VectorDensityPlot, [closed]

I'm trying to plot the following function for two different values of variable m. However, it seems the second figure never appears. Weirdly, I noticed that real numbers are being attributed to ...
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### Integrating Hamilton's equations for the Schwarzschild metric

Part 1 I am trying to integrate Hamiltons equations for the Schwarzschild geometry using NDSolve, these equations must all be integrated simultaneously and are nice ODE's. A similar task is done in ...
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### Surface integral in different coordinate systems

Say I have a vector field that is expressed in cylindrical coordinates. Now, I want to integrate this field over a sylinder with radius $R$ and height $Z$. Now I sigh, and start with making my surface ...
216 views

### Removing anomalous points from data

I have two sets of 2d-data points which can be transformed in each other by using a certain transformation function. The problem is that in both data sets there are points which do not have ...
92 views

### Transform a field with derivatives

Given a function of Cartesian coordinates $(x, y)$ in $g(x, y) = \frac{d}{dx}f(x, y)-y\frac{d}{dy}f(x, y)$, I want to transform this expression to polar coordinates $(r,\phi)$. I saw a solution using ...
585 views

### Calculating the volume of a sphere after switching to spherical coordinates?

I used the code in the second answer on this page to switch from Cartesian to Spherical coordinates and integrate a function over the sphere. I would like to use this code to calculate the volume of a ...
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### Linear mapping to fit points to subset of other points

I have some set of points making a specific pattern. I want to find a linear mapping (dilations + translations) to find a similar pattern in a second larger set of points. I want to find the best (or ...
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### Representing 3D vectors, manipulating them, and identifying symmetry operations [closed]

I am sure this is relatively straightforward, but I feel like I am missing some basic knowledge to let me find the answer. I have a list of 3D vectors not (necessarily) originating at the origin. ...
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### ScalingFunctions produces a warning on ListDensityPlot

Using ScalingFunctions in a ListDensityPlot produces a warning "An unknown option name has been used." Yet, the code still seems ...
235 views

### Plotting a function $\psi(\rho,\theta,\phi)$ in spherical coordinates

If I want to plot the function $\qquad \psi(\rho,\theta,\phi)=\frac{1}{8}\left(\frac{1}{\pi}\right)^{1/2}\rho e^{-\rho/2}sin(\theta)e^{-i\phi}$, for which I wrote the code ...
73 views

### Convert RotationMatrix to RotationTransform

Is it possible to convert RotationMatrix to RotationTransform ? I guess it should exist a function to do this Thank you for ...
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### Is there a way to establish an angle distribution coordinates with Mathematica? [closed]

Can I use Mathematica to plot an angle distribution like the images shown below, where the angle stands for an axis and the length along the radius stands for another axis?
158 views

### How can I transform a density plot into a stream plot?

I have a table with three columns: x, y and z, where z is a function of x and y. Right now, I have a ListDensityPlot of z (below). Is it possible to plot a stream plot of this data, so that arrows go ...
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### With equation of vector fields which are in cylindrical polar coordinates, how to plot 3-D vector field? [closed]

I have the equation of vector fields which are in cylindrical polar coordinates. How do I plot 3-D vector field? I never used Mathematica. Edit2: ...
537 views

### ContourPlot3D in spherical coordinates

Is it possible to define/code a new plot in 3D directly using Spherical coordinates imagined to be somewhat like: ...
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### How to reflect from an ellipse while solving a system of differential equations?

While solving a system of differential equations to plot trajectories, we can use NDSolve and WhenEvent like shown here. I am trying to solve this for a system of equations (Hamiltons Equations) for ...
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### How to update a coordinate of an existing graph object and how to check its value?

I have a graph g1 as below:- g1 = Graph[{1 -> 2, 2 -> 3, 3 -> 1}, VertexCoordinates -> {{0, 0}, {0, 1}, {1, 0}}]; ...
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### How to find the parametric equation of the von Mises yield function?

The von Mises yield function is given by: $\Phi(\sigma_1,\sigma_2)=\sqrt{\sigma_{1}^{2} +\sigma_{2}^{2}-\sigma_{1} \sigma_{2}} - \sigma_y$ were $\sigma_1$ and $\sigma_2$ are the principal ...
474 views

### How to plot a rotated ellipse using ParametricPlot?

I'm plotting the von Mises yield surface using CountourPlot and ParametricPlot. With ...
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### Sphere Point Picking in Cartesian coordinates [closed]

I have a vector $\vec{A}(x, y, z)$. Now I want to rotate the vector randomly (x by ϕ, y by ...
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### Define a new coordinate chart and do algebra/calculus in it

I've stumbled across a very nasty problem: define a toroidal coordinate chart and calculate Laplacian in it. As I'm going through it manually, I wonder if this can't be made in Mathematica. Sure, MMA ...
120 views

### how plot this region in spherical coordinates

how plot this region $S=[1,2] \times[0, \dfrac{\pi}{2}] \times[0, \dfrac{\pi}{2}]$ in spherical coordinates? Under the commands command, {{ParametricPlot3D[FromSphericalCoordinates[{{{1,[{0, Pi},...
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### Plotting a function in a toroidal domain

Consider a function in cylindrical coordinates given by $\Psi(\rho,\theta,z)$. I want to plot this function in a domain which is toroidal(assume the necessary geometric parameters of the toroid). What ...
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### How to do nonlinear substitution?

Suppose, I have an expression. For example: $$\cos^5(\phi) \sin^3(\theta)$$ And I want to change variables to $(x, y, z)$, knowing that the new variables are related to $\theta$ and $\phi$, via ...
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### Offset plot in Mathematica

I have a figure obtained from ParametricPlot, which is relatively costly to obtain. For example: I would like to offset the picture in terms of a parameter, for ...
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### Change of variables in a linear differential operator

Suppose I start with a differential operator in two variables x1 and x2 as follows: ...
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### Change of coordinates and plots

I want to plot the following $$L(\rho) = m + \frac{c}{\rho^2}$$ That's very straightforward. ...
646 views

### Does Mathematica 11 have spherical coordinate unit vectors?

I have a spherical vector wave for an electric field: e[r_, θ_, ϕ_, t_] := (Sin[θ]/r) [Cos[r - t] - Sin[r - t]/r] which points in the ϕ direction. In mathematics,...