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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45
votes
1answer
4k views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
22
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5answers
5k views

Plotting an implicit polar equation

Mathematica can use ContourPlot to draw implicit Cartesian equations, but doesn't seem to have a similar function to plot an implicit polar equation, for example $\...
16
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1answer
1k views

How can I define or use a new coordinate system?

I want to use the dipole coordinate system as defined in this paper: http://arxiv.org/abs/physics/0606044 I see that Mathematica can do all kinds of vector analysis using different kinds of ...
13
votes
2answers
481 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 ...
13
votes
2answers
3k views

Application of the projection matrix: Removing perspective distortion

I know that there are many posts about image treatment, but I still have trouble with this little challegene. Baisically I want to remove the perspective distorsion form this image: (source: http://...
13
votes
2answers
910 views

Coordinate system transformation problem (about Euler angle)

This question comes from the work that constructing the general cylinder by the NURBS. I have implemented the point-set $P_1,P_2,\cdots,P_n$ that in the $O-xyz$ plane, now I want to implement the ...
12
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1answer
741 views

Compose many Geometric Transformations for 3D Graphics

I'm struggling to understand what would be a good way to compose several geometrical transformations to create a single TransformationFunction to be applied to a <...
11
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1answer
2k views

ImageTransformation: polar to cartesian

I am working on something that requires the polar transformation of some images. I implemented this transformation with ImageTransformation: ...
10
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2answers
1k views

Mapping data on Archimedes' spiral

I would like to map my data on Archimedes' spiral and preserve the distance between points on the curve. The test data consists of 20 evenly spaced {x,y} ...
10
votes
1answer
231 views

Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 11.0.1 or later [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of ...
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}) \...
9
votes
3answers
1k views

Using Grad, Div, etc in polar coordinates

I'm trying to use the newish functions Grad and Div to work with a PDE with circular or spherical symmetry and getting what looks to me like a wrong result. However, I'm not sure of this--perhaps I ...
8
votes
4answers
768 views

Plotting in polar coordinates, simple implicit curves

How can I plot $\theta=\cos r$ in polar plane? Of course I know that it is different from $r=\cos \theta.$
8
votes
3answers
213 views

Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
8
votes
1answer
152 views

ImageForwardTransformation produces strange artifacts

I am trying to manipulate an image in equirectangular projection with ImageForwardTransformation. I want to change the projection's inclination to the ecliptic. For ...
7
votes
3answers
561 views

Integrate to calculate enclosed area

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve': The curve is: $r=\sin 2\theta$, $\theta \in [0, \pi]$ which I believe is already in polar form. I ...
7
votes
2answers
588 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 ...
7
votes
2answers
504 views

How can I output the coordinates of a city in coordinates of the Mercator projection?

On Mathematica version 8, I would like to use CountryData and CityData to mark Paris on a polygon map of France in the Mercator ...
7
votes
1answer
6k views

How to Make a change of variables

I have the following expresion $$\hat{M}^2=-\left[\frac{1}{\sin\beta}\frac{\partial}{\partial\beta}\sin\beta\frac{\partial}{\partial\beta}+\frac{1}{sin^2\beta}\left(\frac{\partial^2}{\partial\alpha^2}...
6
votes
2answers
1k views

How to plot a sphere with Cartesian coordinate axes?

I use this code: ContourPlot3D[x^2 + y^2 + z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}] But I can not to see the coordinate axes inside the sphere like the ...
6
votes
3answers
411 views

ListDensityPlot in Polar coordinates with a higher efficiency

I have data like this f[r,theta] and cells number are about 600*600 (uniform mesh) The original data has the property of uniform mesh for ...
6
votes
1answer
570 views

How to apply a transformation to a grid?

I would like to apply a coordinate transformation, visualised as an action on a two-dimensional grid like The particular example above is $$x^\mu \mapsto \frac{x^\mu - b^\mu x^2}{1-b\cdot x+ b^2 x^...
6
votes
0answers
249 views

Anamorphic projection onto the corner of a room

I want to use a router to carve anamorphic projections of polyhedron wireframes onto two adjacent walls of my office. Like this: In order to do this I need to transfer the positions of the vertices ...
6
votes
0answers
88 views

RegionPlot of TransformedRegion still broken in Mathematica 11? [duplicate]

This question confirms that RegionPlot of a TransformedRegion is broken in version 10. One year later, is this problem still ...
5
votes
2answers
789 views

Find a right angled triangle

If I am given 10 points in the coordinate system in the for (x,y); where x is the x-coordinate and ...
5
votes
2answers
221 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 ...
5
votes
2answers
235 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: ...
5
votes
1answer
1k views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined <...
5
votes
1answer
319 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 ...
5
votes
1answer
93 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
3answers
1k views

How to plot a parametric region representing a coordinate transformation

The Wikipedia page on Rindler coordinates shows a nice example of how a coordinate transformation can be represented in a plot. They start with two coordinates $T,X$ with $0 < X < \infty,\; -X &...
4
votes
2answers
315 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 ...
4
votes
1answer
412 views

Parametric plotting coordinate transformation

We were required, for a project, to plot surfaces of constant u, v, and z (and a sample of arbitrary 'a') of the bipolar cylindrical coordinates. (http://mathworld.wolfram.com/BipolarCoordinates.html) ...
4
votes
3answers
335 views

Translating Histogram

SeedRandom[1]; RandomVariate[NormalDistribution[], 100]; Histogram[%, Automatic, "Probability"] The above code produces a histogram like I want to translate the ...
4
votes
1answer
204 views

Change of coordinates and plots

I want to plot the following $$L(\rho) = m + \frac{c}{\rho^2}$$ That's very straightforward. ...
4
votes
1answer
369 views

Why is the range from $-\pi$ to $\pi$ in polar coordinates?

When I run this code FromPolarCoordinates /@ {{3/2, π/3}, {3/2, (5 π)/3}} Then I search the documentation of ...
4
votes
1answer
201 views

Scale Factor of Oblate Spheroidal Coordinate System

From WM 11.1 CoordinateChartsData returns the following scale factor: ...
4
votes
1answer
583 views

Convert Locator (x,y) values to Lat/Lon as per GetCoordinates on Map

I want to convert the (x,y) coordinates you get from using a locator on a map to Lat/Lon coordinates - exactly like the GetCoordinates tool does when you right click on a map. ...
4
votes
1answer
1k views

Map points on a square onto a Torus

I would like to create a 3D torus plot from a 2D graphic. This 2D original plot is a bit complex, and I haven't a clue how could transform it to a torus. The below code, from this article posted on ...
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}}]; ...
4
votes
1answer
390 views

Integration of angular distribution along cartesian axis

I am plotting an anisotropy distribution function as color coding on the surface of a unit sphere with this code: ...
3
votes
4answers
526 views

Why PolarPlot can have negative $r$?

Suppose a simple equation in Cartesian coordinate: $$ (x^2+ y^2)^{3/2} = x y $$ In polar coordinate the equation becomes $r = \cos(\theta) \sin(\theta)$. When I plot both, the one in polar coordinate ...
3
votes
2answers
98 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 ...
3
votes
3answers
402 views

How to extract coordinates {x,y,z} from Raster3D

I want to extract coordinates out of a Raster3D. It is possible to extract coordinates out of an Image3D by using ...
3
votes
1answer
111 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) ...
3
votes
2answers
244 views

Jacobian transformation [duplicate]

I would like to calculate the Jacobian transformation of the measure $dx dy$ $z = e^{x+iy}, \bar{z}=e^{x-iy}$ which should give $-2i|z|^2$. I am not sure how to do this in Mathematica. Further, I need ...
3
votes
2answers
106 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
297 views

SphericalPlot3D of an OblateSpheroid via coordinate transformation

This is an effort to reproduce an ellipse and a hyperbola of revolution from OblateSpheroidal coordinates with constant $\eta$ and $\theta$ . My approach consisted in getting a Coordinate ...
3
votes
1answer
186 views

How to guarantee the point's position is fixed in the Graphics and Image

SeedRandom[8] plot = ParametricPlot[ Evaluate@BezierFunction[temPoint = RandomReal[{-50, 50}, {5, 2}]][ t], {t, 0, 1}, AxesOrigin -> {0, 0}] We can ...
3
votes
1answer
103 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?