Questions tagged [mesh]

Questions on the use and creation of meshes including the use of MeshRegion, ElementMesh, and TetGenLink.

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1answer
95 views

Mass Transport FEM Using Quad Mesh

This question is a follow-up to my previous question and an attempt to implement @Tim Laska's excellent approach of setting up an anisotropic quad mesh. I'm solving a similar problem to @Tim Laska's ...
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0answers
79 views

Why is there no heat being transfered in my program?

I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
5
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2answers
167 views

How to fill in interior in a mesh region

Say I have a mesh region which encloses a region. How do I get a mesh region where this region is filled? Take for example the meshregion below: ...
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0answers
40 views

obtain the analytics region from mesh or vtk file

Is it possible to obtain the region inequalities from a mesh file (vtk-file). On gmsh I build a Sphere, and with Mathematica I would like to obtain the analytics region function, that's is possible?. ...
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1answer
81 views

ToElementMesh Error/General meshing strategies

I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
5
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1answer
153 views

Improving mesh and NDSolve solution convergence

I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
5
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2answers
228 views

Mesh Generation help

I am having trouble generating a mesh of a rectangle inside another rectangle. I have been following the steps on this article: https://reference.wolfram.com/language/PDEModels/tutorial/HeatTransfer/...
5
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3answers
251 views

How to discretize a parametric polar surface ensuring the correct periodicity of the mesh

I am trying to discretize a polar surface using a combination of ParametricPlot3D and DiscretizeGraphics. Unfortunately, the ...
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0answers
46 views

Why does ConvexHullMesh give inconsistent output stuctures?

I know much of the stuff in ConvexHullMesh needs some TLC convexhullmesh-inconsistency But, can anyone see why this would produce inconsistent output: Case 1 (expected behavior): ...
5
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1answer
92 views

ConvexHullMesh inconsistency

I am seeing an inconsistency in ConvexHullMesh that I don't understand. Here is Rhull = ConvexHullMesh[pts8] where the $8$ ...
2
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2answers
50 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 ...
4
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1answer
69 views

Strange behaviour in ToElementMesh

Why would that not work: ...
9
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1answer
290 views

Help to create a 2D mesh generator (FEM)

I'm working in a finite element mesh generator. I built this function which generates an 8 node mesh (polynomials of order 2) without any interior node: ...
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1answer
39 views

How can I specify the output mesh resolution for ListPlot3D?

I am using a grayscale image to generate a 3D topology, with the help of ListPlot3D. However, the output mesh resolution is far too high for my purposes. I need to ...
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1answer
36 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 ...
4
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1answer
44 views

VoronoiMesh with boundary edges removed

I would like to create a Voronoi diagram without the boundary edges highlighted. This code gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}] ...
4
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1answer
106 views

Drawing a “realistic” VoronoiMesh

Consider a set of points generated via Lloyd's relaxation algorithm ...
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0answers
27 views

Extract data from ConvexHullMesh [closed]

I have a ConvexHullMesh and want to extract the bounding points. I am familiar with using Cases to extract data from plots but ...
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0answers
44 views

Why BoundingRegion Fails in such cases

When I was playing this answer of tube, function TubePolygons used in my question. ...
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1answer
62 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 ...
2
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1answer
99 views

Finding lower boundary of a 3D object in list format

I have the following point list and would like to find the points located in the lower boundary of the 3D object (It is part of a body torso). https://pastebin.com/L12n0Gfr I am using the following ...
3
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0answers
49 views

Unfold/develop a RevolutionPlot3D mesh onto a 2D plane?

I'm making my own blimp out of emergency blankets (Mylar), and I want it to have a NACA0025 airfoil shape. I'm new to Mathematica, but I still managed to create the shape I wanted with ...
14
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3answers
212 views

Ordering Problem With VoronoiMesh

Imagine I want to model 2D cells moving in a tissue. Consider, as an example, Lloyd's relaxation algorithm. Using VoronoiMesh I'm able to mimic some cell movement. ...
4
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1answer
83 views

Capturing mesh information

Mesh information Using the helpful tips from Triangular mesh of random points on a sphere, it's easy to generate solids: ...
14
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2answers
456 views

How to make a structured mesh with a hole and extrude it

I am trying to use the FEMAddOns package to make a structured mesh with a hole and then extrude it. As a warm up example this worked nicely. ...
4
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1answer
127 views

MeshRefinementFunction analogue for ToElementMesh

MeshRefinementFunction according to the documentation is an option for DiscretizeRegion. Is there an analogue for ...
5
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1answer
52 views

How to create a 1D mesh from a curved line (with ToElementMesh)

I want to create an element mesh from an arc $x=Rcos(\varphi), y=Rsin(\varphi)$, with $R=100, \varphi \in [0,\pi/4]$ which looks like this: ...
6
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2answers
207 views

Computing volume of intersection of two regions

I am trying to compute the volume of intersection of the following two regions: ...
7
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1answer
181 views

Convert ConvexHull to Inequality

I have the following convex hull. P0={0,0,0}; P1={1,0,0}; P2={0,1,0}; P3={0,0,1}; ConvexHullMesh[{P0,P1,P2,P3}] Now I want the region algebraically as equality ...
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0answers
62 views

Surface area of a list of points

I would like to know how I can get the area of the following point list. I am using the following script to make a mesh region and then find the area. However, the area is much larger than the value ...
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1answer
57 views

RegionResize works improperly with different digital accuracy

The data is copied from the output cell of my original data. ...
9
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3answers
510 views

How to determine if a point is within a concave 3D polyhedron?

Generally, if you have a 3D polyhedron and wanted to check if a point was within it, you would use something like a ConvexHullMesh to create a region, which you can ...
1
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1answer
60 views

How to efficiently animate changing mesh on a fixed 3D plot?

Say I'd like to visualise a height function of a torus by animating a plane going upwards, and highlighting the intersection via Mesh/...
9
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1answer
128 views

Why do some PlotThemes not work with Mesh as expected? What can be done about it?

While updating my answer for (189038) I noted that some PlotThemes do not work with Mesh in a meaningful way: ...
4
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1answer
104 views

How to draw surface with four space curves as boundaries

How to draw a surface with four space curves as boundaries of the surface? ...
4
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1answer
95 views

MeshTools package: can one translate 3d meshes in order to then merge them?

I have created a 3d region for Laplace's eqn ...
11
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4answers
589 views

Area/Volume of a 2D/3D object as it is filled up with water

How could I get the volume of water on a region as it is filled up with water from below? Assume gravity points in some appropriate downward axis like -y (or -z in 3D) so the water fills upward from ...
6
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1answer
106 views

RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver

I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf This method inspired by random-walks and ray-tracing ...
3
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0answers
36 views

DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
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0answers
82 views

Periodic Voronoi Mesh in a box

Is it possible to generate a periodic Voronoi Mesh inside a rectangular domain? I would also like to obtain the coordinates of each cell separately so that I can perform further operations on each ...
2
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0answers
47 views

Removing polygons from exported RegionPlot

I have the following code that runs a RegionPlot ...
0
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1answer
58 views

How to find out the number of nodes in the interval of mesh [closed]

I have a mesh created for the femur. I need to apply a total load of 800 N in the range 480 < z < 500. To do this, I need to know the number of nodes in this interval in order to apply Force to ...
7
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2answers
360 views

How to add 'border' to Voronoi diagram

Suppose I have a set of points pts, from which I generate a Voronoi diagram VD: ...
3
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2answers
109 views

FEM 2D mesh with inclusion

I want to create a FEM mesh with an inclusion, but I want to define the coordinates of the edge nodes manually, since I need the nodes for a problem that requires periodic boundary conditions. The ...
0
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0answers
19 views

modify the elements numbers of a mesh file

I have loaded the mesh of simulation on Mathematica: geo = Import["geometry.vtk"]; The elements of geo are: ...
0
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0answers
38 views

How can I convert such a model into a BoundaryMeshRegion

The obj file is here As you see, I cannot import such a house model into Mathematica with BoundaryMeshRegion Option. Import[objFile, "BoundaryMeshRegion"] So my ...
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0answers
31 views

How to find intersection of higher dimensional convex hull?

I have often used ConvexHullMesh to obtain a convex hull for 2-d and 3-d points. But when I try to find it for 4-D points I encounter error even for simple cases. <...
1
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1answer
58 views

Represent a Concave Mesh Volume

I programmatically generate a shape, where the top surface is defined by a series of polygons. I generate all the points of the polygon. ...
3
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2answers
117 views

Finding mesh elements within a given region

I write a code that generates the following mesh. I would like to find out the elements that completely lie within a certain circular region inside this meshed area. How do I do that? The code that I ...
3
votes
1answer
43 views

Euler Characteristic of MengerMesh

When I ask Mathematica to give me the Euler characteristic of MengerMesh[1, 3], it returns 16. It seems to me the 1-step Menger sponge has genus 5 and should ...

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