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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SixJSymbol not triangular in basis transformation
The basis transformation is given by
$$\left| J^{P}, jd \right\rangle = \sum_ {S} (-1)^{J + L + Sd + Sq}\sqrt {(2 S + 1) (2 jd + 1)}\, \biggl\{\begin {array} {ccc} L & Sq & J \\ S & Sd &...
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Are there contributed Mathematica programs which yield the normal form and Lyapunov coefficients of an ODE at a bifurcation point, in dimens 3 or more
Despite the very numerous times this computation (see for example normal forms and Lyapunov exponents in Guckenheimer and P. Holmes.Nonlinear Oscillations, Dynamical Systems, and Bifurcations of
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Help me figure out how to solve the gravitational lens equations [migrated]
I want to simulate gravitational lensing. In the article LENSINGGW: a PYTHON package for lensing of gravitational waves there is this fragment [page 3]:
My research: As far as I understand, this is a ...
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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 ...
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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:
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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:
...
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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. ...
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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 ...
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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.
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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 ...
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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 ...
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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$, $...
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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 ...
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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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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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