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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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How to transform a tensor (for example, the second order identity tensor) or matrix from cartesian coordinates to cylindrical coordinates?

First, I believe the unit tensor is a diagonal tensor with diagonal elements of 1, regardless of whether it is in Cartesian coordinates or cylindrical coordinates. Then, I wanted to verify this using ...
xinxin guo's user avatar
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4 votes
0 answers
69 views

Memory leak of coordinate transformation functions with symbolic evaluation

Some functions like ToPolarCoordinates seems not to manage memory usage properly. As is compared to Norm: ...
Ming's user avatar
  • 91
4 votes
0 answers
72 views

Interpreting the coordinates in a shapefile

I am trying to interpret the coordinates in the shapefile downloadable from here (Dataset 1). We can extract coordinates like so: ...
Szabolcs's user avatar
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2 votes
1 answer
111 views

How to visualise a rotated cuboid as an output of its rotation matrix and original dimensions, using Graphics3D?

I'm new to Mathematica, and I'm trying to figure out how to visualise a rotated cuboid as an output of its rotation matrix and original dimensions using Graphics3D. ...
Richard Casey's user avatar
1 vote
1 answer
83 views

Metric tensor coordinate transformation with off-diagonal components

I know there is already an answer for this type of question given here: Computing the metric tensor under a coordinate transformation but the answer is not satisfactory as it is not clear to me how I ...
MathZilla's user avatar
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2 votes
1 answer
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How to create a vector as a tensor object for different euclidean bases?

The components of a tensor are always displayed with respect to one or multiple basis vectors. For a tensor of rank 1, a vector, in 3D-euclidean space, we resort to three orthonormal basis vectors. ...
ango4's user avatar
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0 answers
97 views

Linear RGB to Stockman-Sharpe LMS conversion

I'm working on a psychophysical project that aims to emulate LMS cone responses accurately. My final goal is to transform linear RGB coordinates to physiologically relevant LMS responses (Stockman ...
Vyso's user avatar
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13 votes
1 answer
327 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
2 votes
0 answers
77 views

Defining my own set of orthogonal curvilinear coordinates

I want to use Vector Analysis functions (Grad, Div,Curl etc) with the following set of simple Toroidal coordinates $(r, \theta, \phi)$: $x = (R+r \cos\theta)\sin\phi$, $y = (R+r \cos\theta)\cos\phi$, $...
Javier Chico's user avatar
3 votes
3 answers
349 views

How to plot polar coordinates?

I'm trying to plot polar coordinates, that is to plot surfaces of constant parameters $r$ and $\theta$. Which are related to the cartesian ones by $$ x = r \sin \theta\\ y = r \cos \theta $$ One way ...
Nitaa a's user avatar
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4 votes
2 answers
209 views

Fill ParametricPlot3D into 3D solid shape

i have data point and transform it with matrix and plot with ParametricPlot3D and look like this my goals is to fill this and get the centroid with ...
葉柏樂's user avatar
  • 157
4 votes
1 answer
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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
0 votes
2 answers
144 views

Convert Cauchy Riemann equations from cartesian to polar coordinates

We know that the Cauchy Riemann equations in cartesian coordinates are: $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y} \quad$ , $\quad \frac{\partial u}{\partial y}=-\frac{\partial v}{\...
lotus2019's user avatar
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3 votes
3 answers
252 views

Create a new graph based on a manipulated circle

I make a circle based on CirclePoints. From this list of points I take a part and rotate the coördinaties. Then I join the rotated part with the rest of the circelPoints. For example ...
Michiel van Mens's user avatar
1 vote
1 answer
65 views

Transform a plot/graphics from one coordinates to another? [closed]

I wonder if it is possible to transform plot/graphics from one coordinate system to another in Mathematica. To be more specific we can consider some plot in $(r,\...
Nitaa a's user avatar
  • 770
23 votes
2 answers
998 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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3 votes
0 answers
60 views

How to transform the default coordinate when set up the mesh with FEM method?

I want to establish the electromagnetic field of the motor based on the finite element method, because the governing equations are different in different regions, so we need to first build the shape ...
fhrl's user avatar
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0 answers
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Functions for translating a vector from one coordinate system to another

I have a vector $\vec{H}$ with components in Cartesian coordinate system $(x,y,z)$: $\vec{H}=(0,0,H)$. I would like to obtain coordinate of this vector in Spherical coordinate system $(r,\theta,\phi)$....
Mam Mam's user avatar
  • 1,863
0 votes
1 answer
282 views

Spherical coordinates Earth science convention

Earth science often uses a different convention for spherical coordinates than the spherical coordinates Mathematica defines by "Spherical". "Spherical" uses (radius, colatitude, ...
jeff's user avatar
  • 51
2 votes
2 answers
114 views

Cannot work out a simple operation on coordinates

I am trying to substract a value, 172 from the x-value of a system of coordinates. I try: ...
Superunknown's user avatar
2 votes
1 answer
236 views

How to get an analytic function out of a set of points?

I have the given set of points: ...
Superunknown's user avatar
0 votes
0 answers
41 views

Coordinate tool in mathematica fails to arrange the points in a preferred order

I am trying to extract the coordinates from a plot directly by using the Coordinate tool in Mathematica. I show this in figure below. The problem is that the arrangement of the coordinates does not ...
Superunknown's user avatar
4 votes
2 answers
126 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
1 vote
1 answer
223 views

How to use VectorPlot3D to visualize a solution of Navier-Stokes equations in cylindrical coordinates?

I try to solve axially symmetric Navier-Stokes equations in cylindrical coordinates. I have successfuly solved the equations, but I have troubles when I try to plot the solution, as VectorPlot3D does ...
lemurman's user avatar
  • 412
2 votes
2 answers
124 views

Is it possible to change the coordinates / basis to an arbitrary choice?

I know Mathematica can change the coordinate system with the command ''CoordinateTransform''.For example, you can change the coordinates of an $(x,y,z)$ vector in cartesian coordinates like this. <...
Javieer Picazo's user avatar
2 votes
1 answer
153 views

Is it possible to use non-orthogonal 2D axes for plots in Mathematica?

I want to plot uni-variate functions using 2D plots but I want to be able to change the angle between the axes so that they are not perpendicular. Is this possible? I have looked through all the ...
John's user avatar
  • 19
0 votes
0 answers
160 views

How to find the image of a matrix by a transformation in Mathematica

I have searched for image of a matrix, but I just get graphics-related results here. So I try to make a new post: Let m2={{4,-9},{4,-8}} Express the image $x\...
Superunknown's user avatar
2 votes
2 answers
457 views

How to compute Basis-transformation matrix

I have the given matrix {{-1, 4}, {5, -3}} which is is the simplest representation of the two bases: $$\mathscr{B}=[b_1,b_2]$$ and $$\mathscr{C}=[c_1,c_2]$$ where $...
Superunknown's user avatar
3 votes
3 answers
228 views

Transforming the axes of a Contour Plot

I have contours of the following function $$\Psi(\nu,\mu) = -\frac{1}{4} e^{-2 \mu} \cos{2 \nu} - \frac{1}{2} \mu$$ in terms of $(\nu,\mu)$: I need to obtain the contours for $\Psi$ in terms of a ...
Arnav Das's user avatar
3 votes
2 answers
192 views

How can we get coordinates of 3D vector with respect to a specific plane?

I have three vectors that are lying down in the 111 plane ...
MMA13's user avatar
  • 4,732
4 votes
1 answer
291 views

How is a 3D plot drawn in 2D from an arbitrary viewpoint?

I am working on a project that involves SciDraw. The SciDraw software is great for making high quality plots, but it is not compatible with any 3D plots. I need to add some relatively simple 3D plots -...
Lucas Marden's user avatar
2 votes
1 answer
429 views

Changing from cartesian to polar

I want to change the following integral to the polar form $$\int_{y=0}^a \int_y^{\sqrt{1-y^2}}(x^2+y^2) dx dy,\ a>0$$ in Mathematica.I would be highly obliged for any help
AgnostMystic's user avatar
0 votes
0 answers
102 views

Spherical Polar Coordinates VectorPlot3D

I understand the VectorPlot3D function allows you to plot a 3D vector ${Vx,Vy,Vz}$ as a function of $x,y,z$. Is there a function that allows you to plot in ...
Physics_cool's user avatar
-2 votes
1 answer
107 views

help me to clarify the transformation of the functions by using Mathematica

help me to clarify the transformation of the functions by using Mathematica
Hala's user avatar
  • 5
3 votes
2 answers
165 views

Plotting a family of 2D curves of a surface of revolution using spherical coordinates

I am trying to plot the family of curves $V = constant$ from the following surface of revolution expressed in spherical coordinates $(r,\theta,\phi)$ with $\phi = constant$:$$ V = \frac{2 r\sin\theta}...
Bobster's user avatar
  • 143
0 votes
1 answer
243 views

How to project a 2D region from one plane to another?

I have one of a general set of 2D regions (Disk, Rectangle, Polygon, etc.), as well as 3D origin points and normal vectors defining two reference planes/coordinate systems. I want to find a series of ...
CacophonyofVoices's user avatar
1 vote
0 answers
196 views

How to convert a PDE from cartesian to spherical coordinates?

I am investigating solutions to $\Delta u - x\cdot \nabla u=0$ in $\mathbb{R}^n$ and I would like to convert this equation from cartesian to spherical coordinates in mathematica. How should I go about ...
Student's user avatar
  • 113
0 votes
0 answers
48 views

Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way

Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
Diffusion's user avatar
  • 101
3 votes
1 answer
83 views

Help converting Cartesian to Spherical Symbolically [closed]

I am attempting to use Mathematica for basic coordinate conversion symbolically but I am struggling to get it working. In the example below I am trying to convert from cartesian to spherical. Any help ...
SedTempeste's user avatar
0 votes
1 answer
335 views

Solution this problem to illustrate the conformal mapping [duplicate]

Find the mapping of circle using confirmal mapping ( joukowski tansformation method) Assume w= z+1/z 〖z=re〗^iθ = 〖r(cosθ+isinθ)〗^1 ( a Circle with radius r and center (0,0))
Y Oui's user avatar
  • 17
2 votes
2 answers
513 views

Coordinate Transformation

I'm trying to define a module (in Mathematica) that receives a point $\mathbf{p}(\mathbf{x})\in\mathbb{R}^n$ (expressed in the coordinate system $\mathbf{x}$) and a coordinate transformation $\bar{\...
Amit Zach's user avatar
  • 123
-1 votes
1 answer
106 views

Please help me insert this example into Mathematica to illustrate the transformation

Please help me insert this example into Mathematica to illustrate the transformation
misoon's user avatar
  • 3
5 votes
2 answers
254 views

Sorting Cartesian coordinates

Here is the problem: I create a coordinate list as follows: ...
Jocelyn Minini's user avatar
1 vote
1 answer
206 views

Does have Mathematica a built-in function for write Dirac delta in spherical coordinate?

It has been appeared $\delta(\mathbf r_1 -\mathbf r_2)$ in one of my integrals which I have to calculate. The differentials of the integral are $dr_1d\theta_1d\phi_1 dr_2d\theta_2d\phi_2$ So I need to ...
Wisdom's user avatar
  • 1,268
0 votes
0 answers
102 views

Finding transformation matrix for a coordinate transform

I have a matrix in two different bases. Suppose they are called $g_{\mu \nu}$ in one basis and $\eta_{ab}$ in the other basis. If the transformation between the bases is represented by $T_{\mu}^{\text{...
newtothis's user avatar
1 vote
2 answers
182 views

Add gaussian noise to 2D Point

I implemented a program for a camera calibration in Mathematica with with prototypical data to see if my calibration works. Here I converted 3D object coordinates into 2D sensor coordinates. I have ...
Sabine Schleise's user avatar
0 votes
1 answer
287 views

How to plot a function $\Psi (r, \theta, 0) $ and its **rot** in polar coordinates? [closed]

The function is: $\boldsymbol{\Psi}(\rho, \theta, 0)=-\left(2+\frac{8}{\rho}\right) \operatorname{Sin} \theta \boldsymbol{e}_{\boldsymbol{\theta}}+\left(2 \rho-\frac{8}{\rho}\right) \operatorname{Cos} ...
Dayzk's user avatar
  • 147
1 vote
1 answer
242 views

Converting system of ODE from polar to rectangular coordinates

I am trying to convert the following system of equations from polar coordinates to rectangular coordinates. (A,phi)->(u,v) ...
qahtah's user avatar
  • 1,396
2 votes
1 answer
603 views

How to find a transformation matrix between two set of operators?

The following set of operators $P_1,P_2,P_3,P_4$ and $Q_1,Q_2,Q_3,Q_4$ are related as $P_i=\sum_j w_{ij} Q_j$. How can I find the matrix $W=[w_{ij}]$? ...
Zubin's user avatar
  • 425
1 vote
1 answer
605 views

How to represent polar coordinates in a easy way?

I've been using the TI-NSpire CX Cas calculator to solve some electronic problems that work a lot with polar coordinates, in this calculator representing these exercises is very easy, as shown below. ...
Guillermo Rojas's user avatar

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