Questions tagged [mesh]

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

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18
votes
2answers
2k views

DelaunayMesh in a specified closed region - creating a concave hull from a set of points

I have a list of discrete points wich I want to use as nodes for creating a 2D mesh. I used DelaunayMesh and it works fine. The problem that I have is that some elements/polygons are outside of the ...
21
votes
3answers
3k views

Removing unwanted appearance of underlying mesh

Let us first define two positive definite matrices: M1 = {{2, -6}, {4, 8}}; M2 = {{2, 3}, {4, 8}}; then set two points ...
20
votes
5answers
1k views

How to obtain the cell-adjacency graph of a mesh?

In addition to the accepted answer, see also the answer by Chip Hurst. This functionality is built in, but not documented. Given an arbitrary mesh region, how can I efficiently obtain the graph ...
23
votes
2answers
740 views

Smoothing 3D contours as post processing

Context Following this question (and great answer!), It would be nice to have a function which also smooths 3D contours plots once they have been done. There are various solutions which involve ...
22
votes
3answers
3k views

Finding a Concave Hull

I have 3D clustered data: Is there any other way to get the concave hull of 3D data points?
34
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1answer
919 views

How to perform Loop subdivision on a triangle mesh with Mathematica?

(Cross posted on Wolfram Community) Every now and then, the question pops up how a given geometric mesh (e.g. a MeshRegion) can be refined to produce a (i) finer ...
39
votes
4answers
6k views

Creating a 2D meshing algorithm in Mathematica

As what is proving to be a difficult, but entertaining task, I am attempting to adapt a 2D meshing algorithm created for MATLAB and port it to Mathematica. I understand meshing functions already exist ...
50
votes
2answers
2k views

A geometric multigrid solver for Mathematica?

Cross posted to community.wolfram.com Mathematica ships a variety of linear solvers through the interface LinearSolve[A, b, Method -> method] the most ...
29
votes
7answers
3k views

How to generate a mesh with quadrilateral elements?

I have the following code that generates a finite element mesh: ...
16
votes
3answers
1k views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
15
votes
1answer
597 views

Is it possible to re-mesh, downsample & upsample a DiscretizeRegion object?

In my project, I am importing a complex geometry from an STL file into Mathematica as a MeshRegion. I would like to edit this mesh significantly: For instance, drastically reduce or increase the ...
12
votes
3answers
971 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 ...
14
votes
1answer
1k views

Hexagonal Mesh on a 3D surface

I am new to Mathematica, and I am trying to create a 3D hexagonal mesh on a 3D surface. It is very similar to what was done in this post Create a torus with a hexagonal mesh for 3D-printing, but now ...
12
votes
3answers
2k views

Dashed mesh behind 3D object

I am trying to create a simple, almost transparent 3D sphere with a mesh that is made of solid lines if they are on the front surface (i.e. if they are directly visible) and of dashed lines if those ...
13
votes
1answer
1k views

How to create an ElementMesh of a Sphere

I want to create an ElementMesh of a "sphere". To reduce the computational effort I want to use HexahedronElement; the ...
8
votes
3answers
745 views

Polygon mesh: Compute vertex normals for smooth shading

MeshRegion has a "SmoothShading" PlotTheme which automatically computes the ...
11
votes
1answer
453 views

Boundary cells of a mesh?

This is an offspring of answering another question. Consider ...
3
votes
4answers
937 views

How to find adjacent polygons of a specific polygon in a VoronoiMesh?

I have developed some code for VoronoiMesh objects, and I am able to find the polygon with the highest number of adjacent polygons. How do I then find the indices ...
21
votes
3answers
2k views

Build a refined grid based on intersecting line

I honestly have no idea where to begin with this problem. In summary, I have a 2D coarse grid with an intersecting line. For an easy example, let's assume it's a 4x4 grid. I wish to pass through each ...
16
votes
3answers
7k views

Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
14
votes
2answers
538 views

Voronoi tessellations on meshed surfaces

Given a meshed surface, on which we can calculate geodesic distances between vertices, how can one calculate the Voronoi tessellation of a set of points located on this surface? This is somewhat ...
12
votes
2answers
643 views

Finite element mesh not resolving features

I am trying to make a finite element mesh in 2D. The features are not found by ToElementMesh. This is a shelf bracket with nails. I build the region using ...
7
votes
2answers
394 views

Mesh at Ticks positions

In a ListPlot3D[ ] I want to have the Mesh at the same positions as the ticks. For some reason this isn't default if both are ...
10
votes
1answer
685 views

Making a Voronoi diagram bounded by the convex hull

Consider the following: ...
2
votes
1answer
368 views

How does one get Mesh lines at 0 in ParametricPlot3D?

The following is in the documentation (MMA 10) under ParametricPlot3D -> Options -> Mesh : ...
20
votes
3answers
480 views

Making holes from maze generated Graphics3D

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17
votes
2answers
2k views

Estimating Principal Curvature Directions on Discrete Surfaces

I am continuing with working on implementing curvature estimations on triangulated surfaces (See: here), using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). ...
13
votes
3answers
621 views

Improve the mesh smoothing procedure

My question is inspired by this answer about meshing with quadrilateral elements. The following functions are my (naive) try of implementing the Laplacian smoothing. I find interior nodes in the mesh ...
17
votes
4answers
3k views

How to get actual triangles from DelaunayTriangulation[]?

The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
8
votes
1answer
218 views

FEM-ception: Using output of NDSolve FEM as input in another FEM problem

After having solved a Stokes flow problem in Mathematica on a subdomain RegionCapillary, I would like to solve an advection-diffusion problem on a larger domain <...
9
votes
1answer
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 ...
7
votes
1answer
924 views

Meshing the surface of a non-convex object

I would like to mesh the surface of a cloud of points that may not be completely convex, for example the points in this question. Mathematica does not provide triangulation of 3D points, but there is ...
6
votes
5answers
618 views

Colouring points in a Delaunay Mesh by the number of nearest neighbours

I apologise if this is a repeated question, but I've searched for a while and can't find anything. I'm doing some molecular dynamics simulations using Mathematica 10, and I've placed a ...
16
votes
1answer
357 views

Possible bug in RegionUnion or related functions?

Bug introduced in 11.2.0 Functions for derived geometric regions (RegionUnion and related) have been significantly updated in MMA 11.2 and now this simple example ...
14
votes
2answers
902 views

create an (almost) hexagonal mesh on an ellipsoid

EDIT I edited the question in order to take into @Kuba's comment. I want to create this figure with Mathematica (in particular an almost hexagonal mesh on an ellipsoid; thanks to @Kuba I know this ...
12
votes
1answer
436 views

Why isn't ToElementMesh figuring out what my boundary is in 3D?

Bug introduced in 10.2 or earlier, and fixed in 11.0.0 I am trying to change the element mesh for a FEA application I'm doing. I thought I understood it, when I did it in 2D. Here's my shape: ...
10
votes
3answers
699 views

Creating a Hexagonal Lattice with VoronoiMesh

I want to create a hexagonal lattice using VoronoiMesh. One can achieve that with the following code, where L=5, ...
9
votes
1answer
210 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 ...
7
votes
1answer
621 views

how to create a FEM mesh with “RegionPlot” where the sample points are a function of the position

I need to resolve the diffusion equation in a domain with circular sources (holes). I've tried defining the whole region with holes but the result is very mesh-dependent and not symmetric, so at the ...
7
votes
2answers
383 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
4
votes
3answers
1k views

Different MeshStyle for different functions

By using Plot command I want to get one curve in form of circles and other like a solid line. ...
11
votes
1answer
272 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. ...
7
votes
1answer
550 views

Making a 2D hexagonal mesh

There are a lot of answers for how to make a hexagonal mesh on a 3D surface but nothing on how to make a hexagonal mesh on a 2D surface. Can any provide code on how to do so? I am new to mathematica, ...
4
votes
1answer
244 views

How to create a neighboring list for a given triangulation and find the triangle and construct the tile?

I am new to Mathematica and I am currently in need of some help with creating a neighboring list of triangles for a given triangulation and finding the path to the triangle containing the random point ...
4
votes
1answer
70 views

Make MeshRegion/BoundaryMeshRegion work as a graphics primitive in M11

Mathematica 12 has the nice feature that MeshRegion and BoundaryMeshRegion objects render nicely when included as a primitive in ...
3
votes
4answers
289 views

Invalid region for small angles. To Element Mesh. Finite element method

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
3
votes
1answer
427 views

How to calculate a Delaunay mesh nerve?

How to calculate a Delaunay mesh nerve? A Delaunay mesh nerve is a collection of triangles that surround a single triangle called the nerve nucleus. The triangles in a Delaunay mesh nerve either have ...
2
votes
2answers
139 views

How to extrude a planar mesh to a volume slice?

Is there an easy way to extrude a planar 2D-mesh to a volume slice? ring = RegionDifference[Disk[{0, 0}, 1], Disk[{0, 0}, 1/2]]; DiscretizeRegion[ring] The ...
2
votes
1answer
138 views

Defined Mesh Coordinates are Outside of Data Range for Interpolation Function

This relates to a previous question I had about formulating an interpolation over an unstructured grid. A new issue I am running into (in this test example) is that some of the coordinates that are ...
1
vote
0answers
350 views

ContourPlot has extra mesh in PDF

When I create a contour plot it looks fine. When I copy as PDF, and paste into another document (e.g. Apple Mail, Keynote, etc.) it has an extra unwanted white mesh. This occurs even when the option ...