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

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2
votes
2answers
83 views

mesh vertex coloring

So I created a mesh like this: mesh2 = ToElementMesh[FullRegion[2], {{1, 10}, {1, 10}}, MaxCellMeasure -> 1.]; and want to plot it, coloring the squares: ...
7
votes
2answers
179 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 ...
0
votes
1answer
98 views

How to add Polygons (using existing Lines and Points) to MeshRegion?

I have a MeshRegion N with Points and Lines, but without Polygons. That means that MeshCells[N, 2] returns ...
21
votes
2answers
647 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
5
votes
1answer
70 views

Efficient way to get adjacency information from MeshRegion

What is the most efficient way to get adjacency information from a MeshRegion, i.e. some efficient representation of which vertex is connected to which other one? ...
6
votes
3answers
223 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 ...
3
votes
1answer
125 views

Repeated interpolation for 3D unstructured grid -> Optimization

Trying to perform mesh-to-mesh 3D interpolation on unstructured grid. Mesh size is about 200k nodes. Painful thing that interpolation shoud be repeated ~1000 times (different thermal map) on the same ...
2
votes
2answers
103 views

Problem about ListPlot

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2
votes
0answers
83 views

ListPlot3D: generating mesh lines at hard-coded locations [closed]

I am plotting a surface specified with a set of {x,y,z} coordinates with ListPlot3D. This data set surface does not extend ...
0
votes
1answer
185 views

Improving NDSolve computation speed for 3D stationary PDE

Continuing my last question, I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). The analytical solution for this equation is ...
11
votes
2answers
183 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 ...
3
votes
1answer
134 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
0
votes
0answers
123 views

How to get an element mesh from a region?

I've been exploring a new 3D solid commonly called the "Chestahedron" (7 faces of equal area). I wanted to find the centroid, so turned to Mathematica and found it!:) Other things of interest turned ...
4
votes
1answer
175 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
3
votes
3answers
123 views

List connectivity of points in discretized mesh

I'm trying to automate the extraction of the points and a compatible connectivity list for meshes created using the DiscretizeRegion or similar method. If I create ...
3
votes
2answers
317 views

Generating Meshes with Conforming Boundaries for FEM

I would like to solve a PDE on an annulus with some boundary condition that relates the inner circle to the outer circle. (For example, periodicity along radial lines). If I use a finite element ...
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 ...
11
votes
1answer
270 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 ...
8
votes
2answers
297 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 ...
6
votes
0answers
135 views

Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 10.4 Update: It turns out after some testing, none of the Options work in ...
0
votes
1answer
93 views

Boundary discretize region of ellipsoid returns a three dimensional region

I need to integrate a rather complicated function on an ellipsoidal surface, specifically a prolate spheroid surface. Im using the mathematica 10 feature of discretize the regions in mesh and pass ...
3
votes
1answer
175 views

Surface Area of a Region inside a Region

I need to find the surface area of a region which is within another region. The regions I'm working with are fairly complex and so I'm looking for a general solution, but I'll use a cylinder and ...
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, ...
2
votes
2answers
205 views

Extracting points from the MeshFunctions of Plot3D

I am trying to extract the points from the mesh lines of a 3D plot. (Not my actual function.) ...
3
votes
1answer
228 views

Transforming a region obtained with RegionPlot

I have a region r0, obtained from an interpolated function, with the use of RegionPlot. Let's call this function under the ...
2
votes
1answer
136 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
8
votes
0answers
289 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 ...
11
votes
2answers
218 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: ...
4
votes
1answer
121 views

ConvexHullMesh sometimes excludes valid points from convex hull

I have a sequence of polytopes that I am trying to visualize, and I find that ConvexHullMesh sometimes excludes points from the convex hull, and it does so inconsistently. In particular, notice these ...
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 ...
1
vote
1answer
279 views

Generating a boundary mesh from a list of points

I have a list of points from which I am trying to generate a mesh: ...
4
votes
0answers
247 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
16
votes
1answer
352 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 ...
3
votes
1answer
49 views

Disassambling a boundary mesh into pieces and building it back again fails. Why?

I have just a misunderstanding of a sort. What I want is (1) to build a boundary mesh, (2) then to disassemble it into a list of the boundary points, and (3) to further assemble it back starting from ...
2
votes
1answer
107 views

ToElementMesh[]

Could you please help with the following: ...
0
votes
0answers
120 views

RegionPlot3D of MeshRegion with VertexColor-like behavior

I regularly use the VertexColors option with GraphicsComplex[] to render images of objects with certain attributes at the ...
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? ...
4
votes
1answer
105 views

Problem with MeshOrderAlteration to create a 2nd order ElementMesh

After working on this 2D domain, I'm trying to reproduce the same ideas to create a mesh of a sphere composed of QuadElement, instead of more simple and common ...
1
vote
1answer
325 views

Create hexagonal mesh on 3D Parametric Plot and 3D spheres?

I am looking to put a cool geometric mesh on this object. I came across this question that explained how to put a hexagonal mesh on a parametric equation but I have a series of geometric objects of ...
5
votes
1answer
238 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
3
votes
1answer
174 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
0
votes
0answers
156 views

NDSolve: basic settings for PDEs

I am trying to learn how to solve PDEs in Mathematica in order to deal with relatively simple problems without needing to formulate weak formulations in FreeFem++, which is rather time consuming for ...
12
votes
1answer
503 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 ...
1
vote
0answers
153 views

Draw mesh edge / map a graph to a mesh [closed]

I am doing a "force density" method to generate a mesh under certain load. The original mesh is like this: Then, I generate a IncidenceMatrix from the graph for further matrix transformation and ...
4
votes
2answers
489 views

How to generate mesh and calculate volume of 3d object?

I saw a couple of posts dicretizing the graphic and generate DelaunayMesh to get volume of 3D object. The issue I'm having is that DelaunayMesh creates a bigger solid covering the original one, ...
4
votes
2answers
292 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
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 ...
2
votes
1answer
207 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 ...
3
votes
1answer
201 views

Meshing of a cube

I want to mesh a cube and what I use is ToElementMesh[Cuboid[ {-1, -1, -1}, {1, 1, 1}]]. This creates a regular grid of the cube. Is there a way to specify that ...
6
votes
1answer
167 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. ...