Questions tagged [discretization]
The discretization tag has no usage guidance.
62
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How can I discretize four long and complex functions with Mathematica?
I am looking for a procedure with Mathematica where one can discretize a function in a specific interval to a set of multidimensional vectors. In this way, we can possibly ease the calculation time ...
- 561
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115
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How to generate a random point inside this region/discretize it?
Consider the following region:
...
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58
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124
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Proper way to discretize a parametric spline surface
Given that I have a triangular mesh model defined in obj format (1590 vertices and 300 faces), I reconstruct it to a single B-spline surface.
Now I want to export ...
- 119
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Discretizing Geographics
I am in need of boundary regions for cities. A previous question shows that it is possible to discretize CountryData:
...
- 19.6k
2
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100
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Ternary: TernaryListPlot and DiscretizeRegion - Formatting and Error Messages
I am trying to illustrate regions based on conditions in a ternary. I got help with a ternary template and I would like to include the regions now.
Template
...
- 307
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51
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BoundaryDiscretizeGraphics for exotic unicode glyphs
This code works
BoundaryDiscretizeGraphics[Text@"\[WolframLanguageLogoCircle]\[WolframLanguageLogo]", _Text]
But for more exotic characters, it produces ...
- 3,797
7
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285
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Coarse mesh of a sphere
I try to mesh a sphere (examplary) in different qualities, using MaxCellMeasure:
...
- 47.2k
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130
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Compute area enclosed in a curve on a surface
Let's consider a 2D smooth surface embedded in 3D shown in the figure below. The corresponding metric tensor in Cartesian coordinates is
\begin{equation}
h = \biggr(\matrix{1 + \frac{A^2\pi^2}{4} \sin^...
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Are there commands other than ListPlot3D for plotting 3D points, where one coordinate ls either 0 or 1, and the other two lie in [0,1]?
I have a set of 3D points, the first coordinate of which, say, is confined to the values 0 and 1, while the other two can assume values within the unit interval [0,1]. ListPlot3D shows a continuous ...
- 2,315
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282
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Calculate surface normals at the boundary of a Graphics3D object
How do I go about calculating and plotting the surface normals at the boundary of a Graphics3D object?
For example, consider this custom-defined ...
- 473
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MeshRefinementFunction on 2D surfaces embedded in 3D
DiscretizeRegion doesn't seem to run the supplied MeshRefinementFunction when meshing a 2D surface in 3D.
For example:
...
- 443
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Discretization of the following integral: an optimal way
Consider an integral
$$
I[f_{n},T]=\int \limits_{0}^{\infty} dE_{n}F(f_{n}(E_{n}),E_{n},T)+\int\limits_{0}^{\infty} dE_{n}\int_{\mathcal{F}(E_{n})}dE_{n}^{'}G(f_{n}(E_{n}),f_{n}(E_{n}^{'}),E_{n},E_{n}^...
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How to improve the solution of the following differential equation?
Consider a PDE
$$
\tag 1 \frac{\partial f_{n}}{\partial t}- \frac{1}{2t}E\frac{\partial f_{n}}{\partial E} = 0
$$
I choose the initial condition $f_{n}(E, t_{0}) = e^{-E/T_{0}}$, where $T_{0}$ is some ...
- 4,982
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391
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Create graded mesh
I want to create graded mesh inside a cube, with finer mesh in the left half and a coarser mesh in the right half. My plan was to partition the cube with a 2D plane and then generate boundary mesh ...
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165
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How do I properly define and work with region unions?
Suppose I have two regions defined by two hexahedrons (slightly adapted from this question):
...
- 1,017
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244
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How to discretize the boundary of two regions?
Problem
How to discretize a surface constructed with multiple components?
Unsuccessful attempts include combining the objects top and ...
- 1,010
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Unable to affect mesh regions with DiscretizeGraphics
Problem
On the sphere, it is easy to control the resolution of the mesh in DiscretizeGraphics using the MaxCellMeasure ...
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122
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Mesh Refinement for interpolation of f[x,y] fails for all but the simplest f
I would like to interpolate a function, f[x,y,z], on a mesh of the unit cube, starting with a coarse tetrahedral mesh and refining tetrahedra as needed to reduce the interpolation error below a ...
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403
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Computing volume of intersection of two regions
I am trying to compute the volume of intersection of the following two regions:
...
- 193
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4
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559
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What is the best way to parse differential equations and boundary conditions to a custom function?
I have written a method to turn systems of linear differential equations into matrix equations (discretisation). This handles boundary conditions using the row replacement method.
At the moment, I ...
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262
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Why can't an annulus be mapped as a rectangle
The following code is used to map an annulus to a rectangle:
...
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170
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Discretizing a (kinked) line and showing how the points were determined [closed]
Suppose I have a (kinked) line, for example
2-x==y && x< 1
3-2x == y && 1.5>=x>= 1
I want to take this kinked line and represent ...
- 207
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105
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How to discritize a function domain (break xy-plane to a grid/mesh of squares with vertex values for evaluation)? [closed]
I wrote a code using MATLAB to discritize a function's 2D domain into squares/rectangles, whose vertex data (x,y) I can use to evaluate the function at. Then I sum these values over all vertices to ...
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259
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Discretisation of region intersection in 3D
If I try to discretise the intersection (BoundaryDiscretizeRegion), of a shell in a cuboid, some of the regions (that are found with RegionIntersection) are lost in the discretising process. I tried ...
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Errors from NDSolve [closed]
I'm trying to solve a system of PDEs with periodic boundary conditions using NDSolve. This works if I don't specify an initial condition (but is uninteresting, ...
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Is there a way to automatically use triangular elements in ToElementMesh [closed]
I have some simple code to generate a mesh over a rectangle.
...
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Discretize Graphics3D with Scale and Rotate?
How can I discretize a Graphics3D object that makes use of Scale and Rotate? When I try <...
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154
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(Updated) How do I fix a Discretization error?
I am attempting to model a cross section problem from Calculus II using the general slicing method. Below is the working code to generate the "slices" of the defined problem; however, I would like to ...
4
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2
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232
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Generating a grid such that the elements in each row add up to one
I'd like to generate a grid such that each element is a dimension $d$ vector ($\vec v$) of non negative components that add up to one. I could use the approach in this post and then choose among the ...
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106
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Perpendicular chord lengths from the boundary points of an arbitary 2D shape
Let's generate an arbitrary convex domain with smooth boundaries:
Graphics[BSplineCurve[{{1, 4}, {5, 3}, {9, 4}, {5, 5}, {8, 7}},
SplineClosed -> True]]
I'...
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153
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Creating Voronoi Mesh Region Bounded by Convex Hull (Possible problem with DiscretizeGraphics)
I want to create a MeshRegion that is VoronoiMesh bounded by the associated ConvexHullMesh. I followed the procedure in the answer for this post, but the resulting MeshRegion is very wrong.
This is ...
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741
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DiscretizeRegion was unable to discretize the region ImplicitRegion
I'm trying to model a 3D die with ImplicitRegion[] in order to find out its center of mass. However, when I apply ...
- 740
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259
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Converting 3D graphics primitives to 3D image data
My goal is to produce a 3D dataset, from a scene of simple transformed shapes. The idea is that this data serves as a ground truth for some tomographic reconstruction problems. (For this, it is ...
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337
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using a custom method to discretize functions with 3 variables to be used in NDSolve
I was using the pdetoode function that @xzczd made:
Dynamic Euler–Bernoulli beam equation
But it only works for functions with 2 variables, I was wondering if it ...
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157
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DiscretizeGraphics on a RegionDifference not returning a MeshRegion
I want to take region difference of a sub-mesh of a Delaunay Mesh and a discretized ImplicitRegion. However, Mathematica does not recognize the return as a MeshRegion. Moreover, Discretizing the ...
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103
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Unexpected DiscretizeGraphics behaviour
One way to generate an annulus is by using ChartElementData:
...
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244
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Collision between a point and a square
Suppose we have a point of time laws:
xP[t_] := 0.40 + 0.51 t;
yP[t_] := 0.41 + 0.42 t;
and a square with side:
L := 2.01
...
- 4,412
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198
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RegionPlot of DiscretizeRegion of ImplicitRegion
Writing:
A = ImplicitRegion[Max[Abs[x - 1 + 2 y], Abs[y - 1 - 2 x]] == 1, {x, y}];
RegionPlot[DiscretizeRegion[A]]
I get:
while writing:
...
- 4,412
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48
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Loops and guesses
I have to solve a system of equations in the following way: I first guess a value for a variable, let's call it y, calculate another variable ...
- 383
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2
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366
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How to discretize parametric curves for FEM analysis
I would like to know if there is anything available in order to
discretize a 3D curve given by parametric equations in order to apply
FEM analysis, e.g. to solve the wave equation on a thin wire ...
- 353
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137
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Discretize a Graphics3D object over a given 3D lattice
Is there a way to discretize a Graphics3D object using a regular lattice with a given lattice spacing. For example:
...
- 137
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1
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315
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A simple way to discretize a linear region
I have a few hundred linear regions of dimensions 0, 1, 2 and 3 embedded in $R^3$ that I need to discretise. DiscretizeRegion does a good job with most of them, but ...
- 5,404
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216
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Problem with ToBoundaryMesh
Bug introduced in 11.1.0 and fixed in 11.2.0
I have a problem that occurs in ToBoundaryMesh in Mathematica version 11.1, whereas in 11.0 it worked fine. I defined <...
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How to get a larger triangle when we discretize a sphere?
In order to solve this problem,I want to get larger triangles (Of course less amount). But I don't know how to do this. I have tried MaxCellMeasure and ...
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Traverse "curve" on a grid from a given cell
I've got a binary grid which is mostly zero but contains a bunch of 1-cell wide lines (e.g. obtained from a ridge extraction). You can obtain an example input from the following line:
...
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Problems with sampling
Let $t\ge 0$ and let $f_{s}(t)$ be the sampled version of $f(t)$.
If $$f(t)=\begin{cases}\int_{0}^{t}\exp\left(-\frac{1}{1-s^{2}}\right)\,ds,&|s|<1,
\\ 0,&\text{otherwise}.\end{cases}$$
I ...
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Issue with discretizing two arbitrary regions
Description
This is in relation to this question. I am trying to derive this conical figure yet I seem to get an error with this code. I would be happy if someone could point out how to solve this ...
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