# Questions tagged [discretization]

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### Enclosing ParametricPlot3D to create a solid volume

I'm creating a 3D parametric hourglass shape that I hope to fill, making the center solid to use as a 3D volume, because I can't set parameters to it in COMSOL for simulations right now. I know that a ...
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### DiscretizeRegion fails on a simple implicit region

No matter what option I set to DiscretizeRegion it fails on the region (missing second line). What else can be done? ...
• 18.7k
117 views

### How to get finer discretization of 3D polytope?

For some purposes I need detailed mesh models of 2D and 3D shapes. No problem with 2D, so for Rectangle[] we get for example ...
• 1,699
204 views

### Get interior of mesh region

I really like the functionality of Mathematica for mesh-based regions, and have enough understanding of it. But this problem bothers me. There is a similar question, but the functionality used now ...
• 1,699
103 views

### How to build the following region?

Consider a 3D figure defined by the dependence $\Delta x(z),\Delta y(z)$. One example is a pyramidal frustum, for which $\Delta x, \Delta y$ are linear functions of $z$, and $z$ lies inside the ...
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52 views

### Express the double integral in terms of the function values at discrete nodes

Consider the following integral: $$\mathcal{I}[p_{1},t] = \int \limits_{0}^{p_{1}}dp_{2}\int \limits_{0}^{p_{2}}dp_{3} \ \text{integrand}$$ where ...
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162 views

### Accuracy of numerical solutions provided by pdetoode

I am interested in solving the following differential equation using pdetoode (you can find pdetoode here). ...
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1 vote
75 views

### A non-degenerate region error in DiscretizeRegion

Consider the following region: ...
• 5,827
1 vote
49 views

### 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 ...
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### How to generate a random point inside this region/discretize it?

Consider the following region: ...
• 5,827
1 vote
64 views

### How do discretize the following region?

Consider the following region: ...
• 5,827
1 vote
155 views

### 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 ...
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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 ...
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### BoundaryDiscretizeGraphics for exotic unicode glyphs

This code works BoundaryDiscretizeGraphics[Text@"\[WolframLanguageLogoCircle]\[WolframLanguageLogo]", _Text] But for more exotic characters, it produces ...
• 3,956
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### Coarse mesh of a sphere

I try to mesh a sphere (examplary) in different qualities, using MaxCellMeasure: ...
• 54.1k
1 vote
143 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 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 ...
• 2,335
311 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 ...
• 553
210 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
100 views

Consider an integral $$I[f_{n},T]=\int \limits_{0}^{\infty} dE_{n}F(f_{n}(E_{n}),E_{n},T)+\int\limits_{0}^{\infty} dE_{n}\int_{\mathcal{F}(E_{n})}dE_{n}^{'}G(f_{n}(E_{n}),f_{n}(E_{n}^{'}),E_{n},E_{n}^... • 5,827 4 votes 1 answer 185 views ### How to improve the solution of the following differential equation? Consider a PDE$$ \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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432 views

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 ...
• 479
1 vote
186 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): ...
• 1,027
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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 ...
• 1,070
1 vote
71 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 ...
• 1,070
138 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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416 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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### 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 ...
• 525
276 views

### Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
174 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 ...
• 207
114 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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276 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
90 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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161 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. ...
• 2,279
110 views

### Discretize Graphics3D with Scale and Rotate?

How can I discretize a Graphics3D object that makes use of Scale and Rotate? When I try <...
• 272k
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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 ...
233 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 ...
• 583
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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'...
161 views

### Randomly distributed circles inside an annulus

With the following code: ...
• 4,824
169 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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### 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 ...
280 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 ...
341 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 ...
158 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 ...
108 views

### Unexpected DiscretizeGraphics behaviour

One way to generate an annulus is by using ChartElementData: ...
263 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 ...
• 4,452
200 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: ...
• 4,452
48 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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### 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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