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

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4
votes
2answers
508 views

Different MeshStyle for different functions

By using Plot command I want to get one curve in form if circles and other like a solid line. ...
1
vote
2answers
282 views

Time-dependent mesh deformation

I want to display the result of a deformation with a mesh, but I solved the deformation with a time dependency. So I have two functions: uxsol[t,x,y] and ...
10
votes
2answers
418 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 ...
0
votes
0answers
29 views

How can I efficiently select certain mesh elements based on measurement criteria?

I am trying to do some mesh cleaning based on element size, but I'm having a hard time seeing how to best use the MeshRegion data structure to accomplish it without ...
0
votes
0answers
43 views

Ordering of MeshCoordinates in MeshRegion and associated BoundaryMeshRegion

When generating a MeshRegion from a BoundaryMeshRegion and vice versa it would be advantageous if the two types of objects were ...
2
votes
1answer
106 views
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:" ...
5
votes
3answers
169 views

Simple triangular meshes of primitive shapes

I'd like to generate triangular meshes or a cylinder and sphere primitives as part of a lattice meshing program I am writing to experiment with Mathematica. Consider the following snippet: ...
2
votes
3answers
938 views

How to generate 2D FEM mesh in Mathematica?

To generate 3D mesh TetGen can be easily used. Are there similar functions (or a way to use TetGen) to generate 2d mesh? I know that such functionality can be easily implemented but I would like to ...
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: ...
30
votes
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 ...
2
votes
1answer
74 views

Extract arguments from MeshRegion created by STL import

I've been trying to extract points and polygons from a MeshRegion expression created by importing an STL file. At first I thought I could use a simple ReplaceAll as shown below: ...
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, ...
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 ...
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 ...
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? ...
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
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
135 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
2
votes
1answer
282 views

Distinguishing left from right adjacent triangles in triangle mesh [closed]

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between 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 ringsā€¦ Starting with: ...
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 ...
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 ...
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: ...
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 ...
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 ...
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 ...
4
votes
1answer
310 views

ArrayPlot copied to PDF shows blurred mesh [duplicate]

Certain (but not all) images displayed in ArrayPlot, and then copied to PDF, show what appear to be fuzzy mesh lines in white areas. An example is shown below. I ...
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? ...