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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33 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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0answers
29 views

How does a satellite calculate a vector's intercept/path with Earth? [migrated]

Let's say you have a satellite at altitude h, and you know the position of this satellite above earth in latitude and longitude. You detect a signal with the satellite and want to know where on the ...
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2answers
52 views

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 ...
2
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2answers
100 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 ...
2
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2answers
87 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...
3
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1answer
103 views

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) ...
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3answers
187 views

Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
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2answers
109 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 ...
5
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1answer
255 views

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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0answers
34 views

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 ...
5
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2answers
172 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 ...
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0answers
68 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 ...
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2answers
538 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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1answer
94 views

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 ...
1
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1answer
49 views

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. ...
1
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1answer
35 views

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 ...
2
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2answers
148 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 ...
2
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1answer
64 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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1answer
97 views

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?
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0answers
47 views

How to use Absolute Coordinates to define Graphics3D Rotation Compositions

When composing multiple rotations of an object inside Graphics3D, each rotation is applied in that object's local coordinate system. For example in this code (modified from Is it possible to ...
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1answer
102 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 ...
0
votes
1answer
69 views

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: ...
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1answer
365 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: ...
5
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1answer
79 views

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 ...
4
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1answer
34 views

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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1answer
172 views

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 ...
2
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1answer
251 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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1answer
206 views

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 ...
2
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0answers
60 views

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 ...
0
votes
1answer
93 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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vote
1answer
140 views

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 ...
4
votes
2answers
313 views

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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1answer
205 views

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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0answers
90 views

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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1answer
179 views

Change of coordinates and plots

I want to plot the following $$L(\rho) = m + \frac{c}{\rho^2}$$ That's very straightforward. ...
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2answers
498 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,...
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0answers
137 views

Duffy Coordinate Transformation

I'm having trouble with with Duffy Coordinate Transformation routine within Mathematica. I'm able to use NIntegrate`DuffyCoordinatesIntegrand command correctly as indicated in the manual (link) for ...
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2answers
240 views

How to determine roll pitch and yaw/Euler angles from approximately orthogonal matrix?

I have a collection of rigid bodies, each comprising ~100 particles. Each body is defined by a list of points corresponding to the coordinates of its constituent particles. The rigid bodies are ...
13
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2answers
459 views

Extracting data from analog screen photograph

I'm using an analog profilometer from the 1970s and need a way to digitize the data and the only way is through a photograph. I've searched but all I could find was how to extract data from computer ...
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1answer
95 views

Animating the transformation of a probability support

I'm trying to visualize how a transformation changes the support of a pdf. My problem is as follows: Let X and Y be random variables with a joint pdf defined on the support ...
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0answers
53 views

Help generate useful solutions with Solve

I have the Equations for converting between cartesian and spherical polar coordinates eqns = {u*Sin[v]*Cos[w], u*Sin[v]*Sin[w], u*Cos[v]} == {x, y, z}; when I ...
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1answer
214 views

Vector analysis in curvilinear coordinates

It is known that vector calculus in 3D takes quite a simple form when one uses orthonormal curvilinear coordinates (check out, for example, here, in section "Differentiation"). Is there any ...
3
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0answers
87 views

Solving PDEs over a region in different co-ordinate system?

Since Mathematica 10 there's been an option to solve PDEs over a region which I'm currently playing around with to solve Poisson-like PDEs in cartesian coordinates. By changing the region from a disk ...
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1answer
130 views

Legendre Transform Taking Too Long

I am trying to perform Legendre transform on $x^2 \ln(1+x^{\frac{1}{3}}+x^{\frac{2}{3}})$ using this. ...
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1answer
372 views

Plotting vector field in cylindrical co-ordinates

I am trying to plot the following. Let $\Gamma^\top \Gamma=1$, and $e_3=\{0,0,1\}$ (unit vector along Z-axis). I am trying to plot $\dot \Gamma=e_3\times \Gamma$. Tried the following: $\Gamma =\{\...
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2answers
211 views

ImageTransformation and corresponding points

I have identified a list of corresponding points on two different images manually. I have found the geometrical transformation between such sets of points using ...
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1answer
153 views

Extracting scaling factor and rotation angle from TransformationFunction

I have successfully transformed two 2D data sets (data1, data2) by using ...
2
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1answer
135 views

Transforming a Bézier Curve by a Complex Function

I have a method to plot a rectangular region and then plot the lattice transformation by some complex function $f[z]$. ...
2
votes
1answer
397 views

Transforming the parametric equations of a curve into an implicit equation in Cartesian coordinates

I have a parametric curve defined by x = 2 Sin[t] + Sin[3 t] y = 2 Cos[t] - Cos[3 t] How can I eliminate t so get a single ...
4
votes
1answer
158 views

Scale Factor of Oblate Spheroidal Coordinate System

From WM 11.1 CoordinateChartsData returns the following scale factor: ...