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# Questions tagged [mesh]

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

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645 views

### Converting Mesh in DensityPlot to a Graph

Consider the following line of code: ...
1k views

### How discretize a region placing vertices on a specific non-uniform grid

Given a generic region, for example: Ω = ImplicitRegion[ 2 x^2 + 3 y^2 + 2 x y - 2 <= 0 ∧ x^2 + y^2 > .1, {x, y}]; and a non-uniform grid, for ...
811 views

### FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...
865 views

### representation of custom deformation on a meshgrid

I am trying to represent 2D deformations on a rectangular grid. In Mathematica 10, there is a method to solve the elastic differential equations and then represent the deformation as presented here: ...
435 views

### Boundary cells of a mesh?

This is an offspring of answering another question. Consider ...
1k views

### Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
268 views

### Inaccurate (non-smooth) boundary of the mesh generated by ToElementMesh

I try to generate a mesh over a region, which has a wavy boundary at its bottom and needs very fine mesh around the bottom. However, the generated mesh boundary is not as smooth as the specified one. ...
760 views

### Making good meshes

I have been looking at how to make meshes and how to control the size of the boundary elements and the interior elements. A relevent question may be found here. I can see how to do this for regions ...
385 views

### How to wrap a crumpled paper over a surface?

My initial question was about the making of a crumpled paper. After reading this article suggested by J.M. and little more browsing (kind of random walk you do on a Saturday) I thought about expanding ...
890 views

### Lloyd relaxation on VoronoiMesh

How can we apply Lloyd's relaxation algorithm to a VoronoiMesh? Thanks. UPDATE Thanks a lot KennyColnago for your answer. Based on Simon Woods suggestion of ...
1k views

### Change appearance of ConvexHullMesh

I'm struggling to understand the behaviour of ConvexHullMesh (or rather the non-behaviour). I have a polygon p ...
368 views

### Interior of discretized region

I have some domain of interest: r = 0.3; dom = ImplicitRegion[(x - 1/2)^2 + (y - 1/2)^2 >= r^2, {{x, 0, 1}, {y, 0, 1}}]; Now I can extract mesh of the whole ...
189 views

### How to return the coordinates of the respective 3 vertexes of a DelaunayMesh's face?

I have a set of points pts1 and a point redPts as below:- ...
625 views

### Making a Voronoi diagram bounded by the convex hull

Consider the following: ...
1k views

### How to use Mathematica to turn a picture into low poly style?

I want to use Mathematica to turn a picture into low poly style. That is, to make the following conversion: Bill to Bill low poly(Using Image Triangulator App). I think the biggest difficulty is how ...
146 views

### ToElementMesh of Region with Hole

When I try to mesh the following region it fails. Why? Is there a workaround? ...
318 views

### Orientation of boundary domain normals

Bug introduced in 11.2.0 or earlier, and fixed in 11.3.0 I would like to use BoundaryNormals provided by the ElementMesh object. To demonstrate my problem I will take my favorite domain: ...
394 views

### AceFEM: Conversion of triangular to quadrilateral mesh

I am using AceFEM command SMTTriangularToQuad to convert 2D triangular mesh (created by Mathematica) to unstructured quadrilateral mesh. This mesh has internal "...
195 views

### Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 11.1 Update: It turns out after some testing, none of the Options work in ...
338 views

### Catmull-Clark and Doo-Sabin Subdivision Implementations

I want to work on subdivision surfaces. Unfortunately, I don’t have any source code to start with. I need some Mathematica codes for applying Catmull-Clark and Doo-Sabin methods. I would like to ...
701 views

### Removing cells from Voronoi mesh if they exceed a certain area or circumference

I start with the example in Finding the perimeter, area and number of sides of a Voronoi cell with RunnyKine's answer: ...
2k views

### Custom mesh in ListPlot3D

I have the following data: ...
408 views

### Eliminate an unexpected mesh line

What is the source of the vertical mesh (ring) in this figure and how does one eliminate it? ...
346 views

### How to smoothen a surface given as a mesh?

I am trying to "smoothen" meshes. For example, if starting from a cuboid, I would like something similar to a rounded cuboid. There are many ways to smoothen a surface, but I am not going to give a ...
349 views

### Picking mesh elements that are not on the border of the mesh

As an example, let's say I use a set of random points to create a Voronoi mesh pts = RandomReal[{-1, 1}, {100, 2}]; VoronoiMesh[pts, {-1, 1}] and get something ...
350 views

### 3D internal subregion

I'm trying to follow the documentation for Element Mesh Generation, but somehow I cannot understand it correctly. Here is a simplified version of my real problem. I'm trying to simulate the ...
501 views

### Small circles at mesh nodes

How to show the (16 X 4) mesh intersection points by a tiny red dots? ParametricPlot[v { Cos[u], Sin[u]}, {u, 0, 2 Pi},{v,1,3}, Mesh-> {15,3} ]
423 views

### Mesh Problems with MatrixPlot

Bug introduced in 10.1 or earlier and persisting through 11.3.0 or later I've come across some weird behavior in 10.1 when trying to use Mesh with MatrixPlot. In the example below, when specifying ...
173 views

### Distinguish between inner and outer boundary in MeshRegion

For example, this is a 2D MeshRegion with one (or more) holes in it: ...
1k views

### How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
326 views

### Computing volume from node coordinates on the surface of a non-convex solid

I have a question regarding computation of volume of an irregular shape. I have looked around Mathematica -StackExchange but I could not find a solution which suits me the best. Problem Description: I ...
1k views

### Smoothing out data points in a ListDensityPlot

I stumbled upon this problem when I was trying to make some nice smooth ListDensityPlots of my numerical data. In short, my problem is that I let Mathematica plot two copies of basically the exact ...
229 views

### Problem when using the MeshRefinementFunction option of FEM`ToElementMesh

I'm trying to solve Stokes equation in the following domain The border of the inner half circle where I define a certain boundary condition different from zero and where I am interested in obtaining ...
867 views

### Function Interpolation with Automatic / Algorithmic Values Mesh

I have an underlying function f(x,y,z) that is computationally intensive, but is smooth and continuous. I'm needing to find the function values along a line in xyz. Currently, I'm calculating f at ...
198 views

### Use a symmetric mesh in ListDensityPlot

I am trying to produce a ListDensityPlot but I am having issues with aliasing. The problem arises from the way that Mathematica is breaking up the mesh into ...
835 views

### Export generated mesh

Say I have generated a mesh using ToElementMesh, following one of the examples here: http://reference.wolfram.com/language/FEMDocumentation/ref/ToElementMesh.html ...
2k views

### Construct a simple mesh or tetrahedral mesh from 3D image surface

I have a 3D Y-Shape hollow tube, not so good surface. Import["http://dl.dropbox.com/u/68983831/tube02.vtk", "Graphics3D"] I tried to use following vertex data ...
247 views

### Shell elements in FEM

I was wondering how to find the modes of a shell (i.e., a structure with one dimension [the thickness] smaller than the two others). Consider for instance the following ...
156 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 <...
157 views

### Control color of edges in ListPlot

I have a list of 2D points I want to plot with ListPlot. I want the edges connecting these points to have certain colors. So in addition to setting the ...
144 views

### Defining a MeshRegion from a list of points and Polygons with duplicate points does not work in 10.4

Bug introduced in 10.4.0 and fixed in 11.0 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
254 views

### How to label vertices on a mesh with user defined values?

I am trying to write a code to estimate geometric properties (i.e. Mean Curvature, Gaussian Curvature, Principle Curvatures) on a triangulated mesh. I would like to save the calculated data as a set ...
386 views

### Generate mesh from picture

It is probably a stupid question, but I can't figure out how to generate a mesh from picture like this ...
672 views

### Polygon mesh: Compute vertex normals for smooth shading

MeshRegion has a "SmoothShading" PlotTheme which automatically computes the ...
369 views

### Triangulate a surface given as a MeshRegion

Suppose I have a surface given as a MeshRegion. Example: ...
432 views

### Discretizing regions with pointy boundaries

I'm trying to discretize a region with "pointy" boundaries to study dielectric breaking on electrodes with pointy surfaces. So far I've tried 3 types of boundaries, but the meshing functions stall ...
5k views

### Delaunay Triangulation for 3D Surface Data

I want to do a Delaunay triangulation on scattered 3D surface data. Mathematica itself does it only for 2D through the command DelaunayTriangulation[], which gives ...
211 views

### Make uniform mesh with quad elements

I have the following code that generates a finite element mesh with triangular elements which by using command ToQuadMesh I convert to the quadrilateral elements, but I am not able to make the uniform ...