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

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30
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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
927 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 ...
21
votes
2answers
640 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
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 ...
19
votes
3answers
2k 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, ...
16
votes
1answer
347 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 ...
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
0answers
961 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 ...
14
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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?
12
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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 ...
12
votes
1answer
500 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
751 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 ...
12
votes
1answer
156 views

How to access FEM shape functions

A couple of days ago I asked here about surface meshes and plotting on surfaces. Now I have another question: How can I access the surface or boundary element shape functions? I would like to ...
12
votes
1answer
158 views

RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
12
votes
1answer
198 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 ...
11
votes
2answers
643 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
271 views

How to mesh a region using adaptive cubic elements

Assume a list of {x,y,z} coordinates. The coordinates are arranged in a regular fashion through a fixed raster size (called ...
11
votes
2answers
182 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
269 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
416 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
215 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
1answer
517 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
662 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
650 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
387 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
131 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
8
votes
2answers
292 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 ...
8
votes
2answers
169 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
660 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
150 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:" ...
8
votes
1answer
403 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 ...
8
votes
0answers
79 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 and persists through 10.4.1 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
8
votes
0answers
281 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 ...
7
votes
3answers
366 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
4answers
478 views

Change appearance of ConvexHullMesh

I'm struggling to understand the behaviour of ConvexHullMesh (or rather the non-behaviour). I have a polynom p ...
7
votes
1answer
317 views

Eliminate an unexpected mesh line

What is the source of the vertical mesh (ring) in this figure and how does one eliminate it? ...
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
690 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
178 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
295 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
172 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
3answers
215 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 ...
6
votes
2answers
242 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
687 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
511 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
244 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 ...