Questions tagged [coordinate-transformation]
Questions relating changing coordinate systems of numerical points and analytical expression including vector fields and vector analysis.
210
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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 ...
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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).
...
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votes
2
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87
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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}{\...
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3
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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
...
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1
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58
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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,\...
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281
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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 ...
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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 ...
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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 $(r,\theta,\phi)$....
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160
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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, ...
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2
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111
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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:
...
- 561
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1
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132
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0
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0
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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 ...
- 561
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2
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124
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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 ...
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51
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Polar to Cartesian coordinate transformations [duplicate]
I'm trying to plot the energy boundary function EBminus[r, \theta, LL, S, BB] using Polar to Cartesian coordinate transformations. The plot should be a closed curve....
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1
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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 ...
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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.
<...
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1
answer
122
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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 ...
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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\...
- 561
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2
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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 $...
- 561
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votes
3
answers
209
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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 ...
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168
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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
...
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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 -...
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1
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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
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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 ...
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1
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98
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help me to clarify the transformation of the functions by using Mathematica
help me to clarify the transformation of the functions by using Mathematica
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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 $\phi = constant$:$$ V = \frac{2 r\sin\theta}...
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169
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How to project a 2D region from one plane to another?
I have one of a general set of 2D regions (Disk, Rectangle, Polygon, etc.), as well as 3D origin points and normal vectors defining two reference planes/coordinate systems. I want to find a series of ...
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0
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136
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How to convert a PDE from cartesian to spherical coordinates?
I am investigating solutions to $\Delta u - x\cdot \nabla u=0$ in $\mathbb{R}^n$ and I would like to convert this equation from cartesian to spherical coordinates in mathematica. How should I go about ...
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Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way
Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
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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 ...
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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))
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2
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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{\...
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Please help me insert this example into Mathematica to illustrate the transformation
Please help me insert this example into Mathematica to illustrate the transformation
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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 ...
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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{...
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2
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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 ...
0
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1
answer
224
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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} ...
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1
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184
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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)
...
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2
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1
answer
417
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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 $W=[w_{ij}]$?
...
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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.
...
4
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1
answer
160
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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:
...
1
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1
answer
293
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How to Form Rigid Body Transformation Matrices?
We have two line segments specified by a pair of points $(b_1,t_1)$, and $(b_2,t_2)$. We want to find the transformation between the two line segments. Define a unit vector $z_1$ from $b_1$ and ...
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556
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0
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0
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72
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Different results from polar and cartesian forms of a function?
I am trying to write up and study the given function:
by the following Mathematica input (with N=5 and not infinity)
...
- 561
3
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1
answer
125
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Find centre of spiral similarity of two lines
I am trying to find a formula for the centre of spiral similarity (see here) of two lines, lineAB and lineCD. My problem comes ...
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How to troubleshoot TransformedField functionality in Mathematica?
I list up this method to transform a complex function to Cartestian form, which can be used on virtually any function:
such as:
...
- 561
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4
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296
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Coordinate transformation can this be done with AffineTransform?
Looking for alternatives or improvements for accomplishing the following:
Given the position of points A, B, and C in both the x-y and u-v planes, determine transformation functions to map values ...
- 1,027
3
votes
2
answers
322
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Plot eigenfunctions w/ looped boundary conditions on a torus
How we can show results (eigenfunctions) obtained in this post on the surface of a torus, not on a square?
https://www.wolfram.com/language/11/differential-eigensystems/investigate-a-laplace-equation-...
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Transformation of Differential Operators
I would like to gain some knowledge about how to transform differential operators to different coordinate systems using Mathematica. I know that the Laplacian ...
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