Questions tagged [discretization]

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6 votes
2 answers
233 views

Coarse mesh of a sphere

I try to mesh a sphere (examplary) in different qualities, using MaxCellMeasure: ...
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1 vote
1 answer
116 views

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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0 votes
1 answer
63 views

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 ...
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3 votes
2 answers
200 views

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 ...
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  • 473
7 votes
1 answer
191 views

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: ...
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1 vote
0 answers
52 views

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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  • 4,038
4 votes
1 answer
135 views

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 ...
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  • 4,038
2 votes
1 answer
284 views

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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  • 459
1 vote
1 answer
132 views

How do I properly define and work with region unions?

Suppose I have two regions defined by two hexahedrons (slightly adapted from this question): ...
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  • 967
5 votes
2 answers
158 views

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 ...
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  • 956
1 vote
1 answer
63 views

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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  • 956
0 votes
1 answer
90 views

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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  • 35
8 votes
2 answers
351 views

Computing volume of intersection of two regions

I am trying to compute the volume of intersection of the following two regions: ...
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6 votes
4 answers
506 views

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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  • 453
4 votes
2 answers
241 views

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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3 votes
1 answer
154 views

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 ...
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  • 207
0 votes
1 answer
87 views

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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8 votes
3 answers
232 views

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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1 vote
1 answer
84 views

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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  • 11
3 votes
1 answer
118 views

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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  • 2,075
2 votes
1 answer
78 views

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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  • 265k
0 votes
1 answer
135 views

(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 ...
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4 votes
2 answers
227 views

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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  • 543
2 votes
1 answer
85 views

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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5 votes
1 answer
138 views

Randomly distributed circles inside an annulus

With the following code: ...
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  • 4,734
4 votes
1 answer
127 views

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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  • 43
4 votes
1 answer
583 views

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 ...
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  • 710
5 votes
1 answer
224 views

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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3 votes
1 answer
319 views

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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2 votes
0 answers
139 views

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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3 votes
1 answer
100 views

Unexpected DiscretizeGraphics behaviour

One way to generate an annulus is by using ChartElementData: ...
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3 votes
1 answer
224 views

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 ...
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  • 4,281
2 votes
1 answer
187 views

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: ...
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  • 4,281
0 votes
1 answer
41 views

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 ...
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  • 383
3 votes
2 answers
343 views

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 ...
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0 votes
1 answer
129 views

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: ...
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2 votes
1 answer
272 views

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 ...
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  • 5,374
9 votes
1 answer
205 views

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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  • 232
5 votes
1 answer
249 views

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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  • 24.5k
6 votes
3 answers
247 views

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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  • 8,574
0 votes
0 answers
85 views

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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0 votes
1 answer
157 views

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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  • 5,719
0 votes
1 answer
290 views

Beginner Simulating Gaussian Process with Correlation

I have no little experience with algorithms. I would like to learn how to simulate a real valued Gaussian process with correlation (e.g., exponentially correlated $\Gamma(t)=e^{-\vert t \vert/2}).$ ...
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5 votes
4 answers
276 views

Discretize chart in a given interval

Using the following code: plot = Plot[Sin[x], {x, -Pi, Pi}]; points = Cases[plot // Normal, Line[{x__}] -> x, Infinity]; ListPlot[points] I get: Question: Is ...
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  • 4,281
1 vote
1 answer
107 views

Unexpected behavior of DiscretizeGraphics

As this code,we can visualize the "Test text" Graphics[Text[Style["Test text",20],{0,0}],Axes->True,AxesOrigin->{0,0}] I try to use <...
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  • 24.5k
2 votes
2 answers
472 views

How to apply `DiscretizeGraphics` to a tube? [duplicate]

I want to export the numerical solution of the Chan-Lee oscillator as an STL file so that I could print it out. But when I expanded the curve into a tube, ...
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  • 1,801
12 votes
3 answers
431 views

How to generate grid points on boundary of $[-1,1]^d$ for arbitrary dimension $d$ and specified resolution?

This must be a trivial thing, but I was not able to find a function for it in Mathematica. How do you efficiently create a grid with constant but specific resolution $r$ in all directions on the ...
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6 votes
1 answer
1k views

Finding NonlinearModelFit of multiple data sets with the same parameters and in two dimensions

I have multiple sets of data (between 3 and 6 depending on the cases) dependent of space, time, and some parameters. The data are the response of a harmonic oscillator under a non-trigonometrical ...
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9 votes
1 answer
184 views

DiscretizeRegion fails for a triangular region

Bug introduced in 10.2.0 or earlier and fixed in 11.0.0 I define an implicit region like ...
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  • 409
3 votes
1 answer
119 views

How to turn a Graphics primitive into a list of data?

I tried something small first, to get a feeling about this. So I defined a Rectangle[], placed it in a corner of ...
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  • 975