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

Update Finally in v13.1 the function DSolveChangeVariables is introduced, try it out! DChange in the answer below is still a ...
xzczd's user avatar
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24 votes
5 answers
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 $\...
one-more-minute's user avatar
22 votes
2 answers
967 views

How to find the conformal mapping between two regions

As the Riemann Mapping Theorem, if both regions are simply connected regions, there must be a unique one-conformal mapping such that the points between the two regions correspond one-to-one. Can we ...
yode's user avatar
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17 votes
1 answer
2k 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 ...
jvriesem's user avatar
  • 417
16 votes
2 answers
6k 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://...
henry's user avatar
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14 votes
2 answers
613 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 ...
dVilhena's user avatar
  • 143
13 votes
3 answers
1k 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 ...
xyz's user avatar
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13 votes
1 answer
1k 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 <...
rhermans's user avatar
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13 votes
1 answer
319 views

Lens on a map. Realistic imitation of magnifying glass on images with text and other small features

UPDATE: Code from this post was used for video generation here: Cinematically moving a lens over images: magnifying glass effect in videos I am trying to create a magnifying glass effect for images ...
Vitaliy Kaurov's user avatar
13 votes
1 answer
3k views

ImageTransformation: polar to cartesian

I am working on something that requires the polar transformation of some images. I implemented this transformation with ImageTransformation: ...
paw's user avatar
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11 votes
5 answers
6k 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}) \...
Conor's user avatar
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11 votes
2 answers
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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} ...
shrx's user avatar
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10 votes
3 answers
720 views

Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
rpa's user avatar
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10 votes
3 answers
2k 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 ...
Leon Avery's user avatar
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10 votes
1 answer
277 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 ...
Oleksandr R.'s user avatar
9 votes
4 answers
1k 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 $r=\cos \theta.$
Nimbigli's user avatar
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9 votes
1 answer
422 views

Better replacement rules to perform this change of variables?

In cosmology, it is common to work with both a normal (a.k.a. “cosmic”) time variable t and a “conformal” time variable τ, which ...
thecommexokid's user avatar
9 votes
1 answer
192 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 ...
shrx's user avatar
  • 7,807
8 votes
2 answers
2k 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 ...
user37694's user avatar
  • 423
8 votes
3 answers
689 views

Tensor transformation

Consider the following tensor in coordinate basis $T=T^{\mu}_{\nu\lambda} \partial_{\mu}\otimes dx^\nu \otimes dx^\lambda$ in two dimensions with coordinates $x^1 = x$ and $x^2 = y$. We take $T^{\mu}...
fasdgr's user avatar
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8 votes
2 answers
651 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 ...
Andrew's user avatar
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8 votes
1 answer
11k 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}...
shadraws's user avatar
  • 139
8 votes
1 answer
735 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 ...
user61882's user avatar
  • 349
7 votes
3 answers
816 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 ...
alfredo's user avatar
  • 71
7 votes
2 answers
793 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 ...
sonicboom's user avatar
  • 183
7 votes
2 answers
1k views

Cylindrical coordinates in FEM

I am trying to solve the Stokes equation for fluid flow in a 3d cylinder. All boundaries are no-slip, apart from the top boundary, which enforces flow in the x-direction. My problem is that I can't ...
Oscillon's user avatar
  • 1,231
6 votes
3 answers
493 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 ...
Longfei Zhang's user avatar
6 votes
2 answers
7k views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
José D.'s user avatar
  • 1,135
6 votes
1 answer
953 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^2}....
Anne O'Nyme's user avatar
6 votes
1 answer
2k 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 ...
pnz1337's user avatar
  • 609
6 votes
0 answers
365 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 ...
geordie's user avatar
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6 votes
0 answers
93 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 ...
qwr's user avatar
  • 413
5 votes
2 answers
857 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 ...
coderzz's user avatar
  • 61
5 votes
2 answers
557 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 ...
mrz's user avatar
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5 votes
2 answers
932 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) ...
ShinyPebble's user avatar
5 votes
2 answers
251 views

Sorting Cartesian coordinates

Here is the problem: I create a coordinate list as follows: ...
Jocelyn Minini's user avatar
5 votes
1 answer
2k 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 <...
Shakil Ahmed Rafi's user avatar
5 votes
2 answers
586 views

On orthographic projection

Writing: ...
Monster's user avatar
  • 335
5 votes
2 answers
370 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: ...
Quark Soup's user avatar
  • 1,610
5 votes
1 answer
659 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. ...
Gordon Coale's user avatar
  • 2,341
5 votes
1 answer
188 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 ...
Nishchal Dwivedi's user avatar
4 votes
3 answers
2k 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 &...
sjdh's user avatar
  • 7,757
4 votes
3 answers
182 views

Is there an intuitive and rational way to automatically convert ranges into coordinates?

I'm tired of typing and deciphering coordinates of the corners rectangles, and I'm wondering if anyone has found a better way. A rectangle can simply be described by two lists ...
Niel Malan's user avatar
4 votes
2 answers
332 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 ...
Janusz Przewocki's user avatar
4 votes
3 answers
403 views

Translating Histogram

SeedRandom[1]; RandomVariate[NormalDistribution[], 100]; Histogram[%, Automatic, "Probability"] The above code produces a histogram like I want to ...
user13892's user avatar
  • 9,363
4 votes
1 answer
112 views

How to create a pin cushion (or barrel) distortion from the square function on Cartesian coordinate?

I want to make a distorted square shape in 2D data set from a rectangular function. Here is my code to draw a square shape(Field length : 10, Square length: 5, Data num : 101). ...
Taeshin Kim's user avatar
4 votes
2 answers
125 views

Repeated offset of line along vector and output of point tour

I would like to make a number of copies of a line along a vector (with a specified spacing) and then output a list of points at each end of the line sequenced in a back-and-forth tour. Any help is ...
Young's user avatar
  • 7,495
4 votes
1 answer
188 views

TransformedField on Tensor

I was trying to use the TransformedField function to Transform the Metric Tensor $ds^2 = dx^2 + dy^2 + dz^2$ into Spherical coordinates. So i use: ...
The Mastermage's user avatar
4 votes
1 answer
526 views

Change of coordinates and plots

I want to plot the following $$L(\rho) = m + \frac{c}{\rho^2}$$ That's very straightforward. ...
user avatar
4 votes
1 answer
753 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 ...
yode's user avatar
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