Questions tagged [coordinate-transformation]

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

Filter by
Sorted by
Tagged with
2
votes
1answer
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
2
votes
1answer
68 views

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 ...
0
votes
3answers
54 views

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; ...
1
vote
1answer
96 views
1
vote
1answer
39 views

Polynomial transformation coefficients

Given a 3D polynomial of degree $m$ and coefficients $a_{ijk}^0$, $$p(x_0, y_0, x_0) = \sum_{i,j,k}^{m} a_{ijk}^0 x_0^i y_0^j z_0^k, \quad i + j + k \le m,$$ I want to make the transformation: $$x_0 =...
1
vote
0answers
24 views

Coordinate transformation of a table of multi-variable function values

I've created a table in Mathematica for a function dependent on r and phi of the form ...
5
votes
2answers
234 views

How do I get actual values from a Jacobian matrix?

I have a Jacobian function: D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] It gives me a matrix with the formulas I need for my transposition matrix: ...
0
votes
0answers
53 views

Distance matrix inside a neural net

So what I would like to do is to create a NetGraph that takes in an $n\times 3$ (with $n$ varying in length) list of 3D coordinates as an input and creates an $n \times n$ distance matrix or an $\frac{...
2
votes
1answer
65 views

Hammer projection to rectangular

This might be more of a mathematical problem than a Mathematica'l one, but still, maybe you'd help me. I want to write a function that would produce a rectangular image from an image with Hammer ...
3
votes
1answer
88 views

Convert a point in the Radon Space to a line

I need a function point2line to convert a point in the Radon Transform Space to a straight line. But I don't know the algorithm inside mathematica, I don't know ...
9
votes
5answers
1k views

Polar contour plot in Mathematica?

I am following a text on fluid mechanics with MAPLE examples. I want to do the following ContourPlot in Mathematica in Polar coordinates: $$ (r^2-\frac{a^3}{r}) \...
0
votes
0answers
33 views

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 ...
1
vote
1answer
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: ...
0
votes
0answers
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?
1
vote
1answer
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 ...
3
votes
2answers
91 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
votes
2answers
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 ...
3
votes
2answers
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...
3
votes
1answer
110 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) ...
8
votes
3answers
212 views

Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
1
vote
2answers
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 ...
5
votes
1answer
313 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 ...
0
votes
0answers
70 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
votes
2answers
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 ...
0
votes
0answers
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 ...
7
votes
2answers
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 ...
2
votes
1answer
97 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
vote
1answer
58 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
vote
1answer
47 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
votes
2answers
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 ...
2
votes
1answer
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 ...
3
votes
1answer
102 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?
1
vote
1answer
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 ...
0
votes
1answer
101 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: ...
2
votes
1answer
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: ...
5
votes
1answer
90 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
votes
1answer
38 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}}]; ...
1
vote
1answer
427 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
votes
1answer
474 views

How to plot a rotated ellipse using `ParametricPlot`?

I'm plotting the von Mises yield surface using CountourPlot and ParametricPlot. With ...
0
votes
1answer
249 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
votes
0answers
62 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
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},...
1
vote
1answer
171 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
314 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 ...
1
vote
1answer
278 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 ...
1
vote
0answers
97 views

Change of variables in a linear differential operator

Suppose I start with a differential operator in two variables x1 and x2 as follows: ...
4
votes
1answer
202 views

Change of coordinates and plots

I want to plot the following $$L(\rho) = m + \frac{c}{\rho^2}$$ That's very straightforward. ...
2
votes
2answers
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,...
1
vote
0answers
172 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 ...
1
vote
2answers
319 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 ...