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

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29
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4answers
4k 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 ...
22
votes
2answers
900 views

How can the {x,y,z} points that fall on the outer boundary of a set of values be selected and smoothly surfaced?

For a given set of x,y,z values, that may, or may not form a uniform shape, how can the center of the data cloud be found, and the surface points be located and a solid smooth surface created from ...
20
votes
3answers
1k 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 ...
20
votes
2answers
566 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
19
votes
3answers
1k 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 ...
16
votes
4answers
2k 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, ...
15
votes
3answers
3k 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: ...
15
votes
1answer
288 views

Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
14
votes
3answers
2k views

Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
14
votes
0answers
879 views

Using TetGen in Mathematica to get 3D Voronoi diagram

In this post, the use of TetGen for 3D Voronoi tesselation has been briefly discussed. However there is still no info about the use of TetGen to generate a 3D Voronoi diagram. The TetGen documentation ...
12
votes
1answer
422 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
2answers
632 views

How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
11
votes
2answers
609 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 ...
11
votes
2answers
159 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
11
votes
1answer
240 views

How to specify PDE Boundary condition on Bspline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a ...
10
votes
2answers
361 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 ...
10
votes
2answers
181 views

VoronoiMesh without edges

How can I remove the edges of a VoronoiMesh? I would like to display only the closed cells not touching the border of the image. This is my binarized source image (imgbw): I am doing this: ...
10
votes
3answers
1k 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 ...
10
votes
1answer
471 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: ...
10
votes
1answer
121 views

how to enforce a symmetric solution with fem?

I'm solving the laplace equation in a domain with holes, and I need to compute the integral of the gradient on the boundary of these holes. For that I define a mesh and solve the laplace equation ...
10
votes
1answer
621 views

How do I place a texture on an irregular 3D model?

I'm trying to reproduce a textured head in Mathematica, and I'm using a kind of 'net' of a head which contains all the features on the face. The texture looks like this: which is supposed to look ...
9
votes
4answers
1k views

Triangular mesh of random points on a sphere

My employer with a new logo (shown below). I do not have information on how this was created (as it was done by an outside company), though I'm fairly sure it was not done in any formal mathematical ...
9
votes
4answers
541 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 ...
9
votes
2answers
379 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} ]
8
votes
3answers
1k views

Custom mesh in ListPlot3D

I have the following data: ...
8
votes
2answers
158 views

Mesh Problems with MatrixPlot

I've come across some weird behavior in 10.1 when trying to use Mesh with MatrixPlot. In the example below, when specifying Mesh, I only get one line along the X axis at 100 instead of lines at {100, ...
8
votes
2answers
629 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 ...
8
votes
1answer
148 views

ParametricPlot MeshStyle bug in v10?

Bug introduced in 10.0.1 or earlier and fixed in 10.0.2.0 Original Post The documentation gives the following code and says "Use a red mesh in the x direction and a blue mesh in the y direction:" ...
7
votes
3answers
343 views

Converting Mesh in Density Plots to a Graph

Consider the following line of code: ...
7
votes
2answers
3k 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 ...
7
votes
2answers
1k views

How can I mesh a solid cylinder with triangular or tetrahedral elements

I need to plot triangular mesh on a cylinder. However the function Cylinder doesn't have a mesh option. By using ...
7
votes
2answers
664 views

Finding concave hull for separated small clusters

Data : data3D = Import[file, "VertexData"]; Graphics3D[Point[data3D]] How to find concave polygon for separated small clusters.
7
votes
2answers
136 views

How do I get ConvexHullMesh to return polygons instead of triangle as surface mesh?

I would need to identify the types of regular polygons forming the surface of a convex hull of 3D points. If I e.g. take the following example of a regular polyhedron ...
7
votes
2answers
289 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 ...
7
votes
2answers
169 views

Poor/wrong sampling in 1D DiscretizeRegion of splines?

Bug introduced in 10.1 and persisting through 10.2 or later Context In relation to this question I have would like to use splines to define a ...
6
votes
1answer
302 views

Eliminate an unexpected mesh line

What is the source of the vertical mesh (ring) in this figure and how does one eliminate it? ...
6
votes
2answers
218 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 ...
6
votes
2answers
631 views

How to show wireframes on imported Object / Mesh (.obj file)

I've managed to import a Wavefront (.obj) file and store it in a variable like so: ...
6
votes
2answers
451 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 ...
6
votes
1answer
187 views

What are some useful (or hidden) properties of MeshRegion?

There is quite a bit of powerful functionality built in to MeshRegion, but it seems to be lacking in some areas. For example: extracting a list of edges that live ...
6
votes
1answer
305 views

How do I get a MeshRegion from an obj file, or from Geometry3D

How do I read in an obj file as a MeshRegion so I can e.g. compute its area? If I just import the object and try Area[O] it ...
6
votes
1answer
280 views
6
votes
1answer
378 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
1answer
1k 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 ...
6
votes
2answers
82 views

How to scale values for ColorFunction in SliceContourPlot3D?

Trying to help out in the question, Finite Elements 3D, I came across this behavior of SliceContourPlot3D: ...
6
votes
1answer
162 views

Long running ToElementMesh with very “large” domains

This is fixed in version 10.3. I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. ...
6
votes
1answer
196 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 ...
6
votes
1answer
371 views

ListContourPlot3D doesn't use all points

Edited thanks to @Kuba: In the following example, ListContourPlot3D accepts an array of points spaced at intervals 0.1 apart throughout the volume, but seems to choose an arbitrary number of points ...
6
votes
0answers
101 views

Possible Bug with Options in DelaunayMesh

Update: It turns out after some testing, none of the Options work in DelaunayMesh when 3D point sets are involved. Original ...
5
votes
3answers
142 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 ...