# Questions tagged [mesh]

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

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### Adaptive Meshrefinement NDSolve&FiniteElements

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
1answer
41 views

### Draw Lines on 3D Plot at certain coordinate

Following this example, I though it would be as easy as this: ...
1answer
114 views

### Nonatomic expression expected at position 1 in First[None]

This is a follow-up question to an earlier question:Solving a system of PDEs on a piecewise polynomial domain. I tried to solve the system of equations from one of my previous post with the different ...
3answers
515 views

### Compare FEM mesh with the mesh created within Mathematica

This is a follow-up question to an earlier question: Make uniform mesh with quad elements Question: How to solve system of equations with NDsolve on the mesh created in Ansys in order to compare it ...
3answers
560 views

### Computing the surface area and volume of molecules

Here is a somewhat difficult problem I've had for a long while. Space-filling models of molecules can be easily generated by ChemicalData[], ...
1answer
74 views

### BoundaryDiscretizeRegion Plots does not work with ParametricPlot3D

I am trying wit this data ...
3answers
458 views

### Nearly equally spaced 3D-mesh

How to mesh a volume (3D region) with nearly equaly spaced vertices? Example: Disk with radius 50 and height 15 ...
1answer
130 views

### Unable to use ElementMarker in DirichletCondition with structured quad mesh

I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error: ...
2answers
84 views

### Blunt edges of an octahedron by Region

Why does the octahedron constructed by the following code have blunt edges ? Region[ImplicitRegion[Abs[x] + Abs[y] + Abs[z] <= 1, {x, y, z}]] How to improve it?...
2answers
244 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 ...
1answer
248 views

### Mesh a hollow cylinder

Questions seems to be simple answerde, but in Mathemtica v11.0.1 I didn't find a solution ...
1answer
163 views

### control FEM grid size for 1D regions

I need to manage the mesh size for finite element method solution to a differential equation, where properties change over two regions. This is for one dimension. I created a boundary mesh of three ...
1answer
107 views

### RegionUnion works but RegionIntersection does not

I am trying to create an Alberti's window figure as described in this question, in which a (three-dimensional) polyhedron (e.g., dodecahedron) is projected onto a (two-dimensional) plane. I realized ...
1answer
97 views

### Unwanted mesh line in spherical plot

I am trying to create a spherical colour plot on which the mesh will rotate with manipulating the \phi1 variable. I read this solution and gave it a try with the following code: ...
0answers
87 views

### Combining MeshRegions of generated 3D shapes and RandomPolygons

I am interested in generating 3D a joint BoundaryMeshRegion or a MeshRegion from different shapes and polygons. This works for <...
2answers
346 views

### Make uniform mesh with quad elements

I have the following code that generates a finite element mesh with triangular elements which by using command ToQuadMesh I convert to the quadrilateral elements, but I am not able to make the uniform ...
2answers
245 views

### How to sample numerically a function using a mesh-grid function in 3D?

I am working on a problem where I want to sample a scalar function f[x,y,z]. The problem is how to obtain a mesh-grid in 3D (A grid of points in x,y, and z). In order to study this function. Of ...
0answers
118 views

### Calculate the intersection points of a line and a parametrically defined 3D surface

Thanks to Henrik Schumacher for advice to simplify the sample code: I would be grateful for any pointers on the following issue. A line from an external point intersects the surface at 2 points (...
1answer
141 views

### How to solve wave equation with finite elements when material properties vary continuously over a region

I am solving the one-dimensional wave equation over regions where the bulk modulus (and thus the wave speed) vary continuously over a region. The current version seems to assume that the material ...
2answers
149 views

### How to refine a linear FEM mesh in three regions?

I am trying to solve the one-dimensional wave equation with a frequency dependent source function over three intervals with varying velocity. I need to refine the mesh over the low velocity regions ...
2answers
237 views

### Automatic solution to label boundary elements with BoundaryMarkerFunction

Preparations Mathematica 11.3, Windows. Let us say I have a rectangular region with 10 little holes inside. Their coordinates are given by positionList. The ...
0answers
87 views

### Non-convex hull mesh from 3d points [duplicate]

I am trying to create a 3d mesh object from list of points, but the only options I see in Mathematica are ConvexHullMesh and ...
1answer
107 views

### Signed cell adjacency matrices (boundary operators)

In How to obtain the cell-adjacency graph of a mesh? there are some great answers that show how to obtain the cell adjacency matrix of a mesh. How would one generalize these to incorporate the ...
2answers
163 views

### Adjacent faces in a discrete mesh

I have a MeshRegion R and I want to extract all pairs of adjacent faces efficiently. The way that I've been computing this is demonstrated below: ...
3answers
170 views

### RegionMember does not work with RandomPolyhedron or Polyhedron object

According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function ...
2answers
235 views

### Extracting points from 3D plot that lie along an arbitrarily oriented line

Starting from i.e. the following 3d plot: d = RandomReal[1, {100, 3}]; ListPlot3D[d] Is it possible to extract points that lay along an arbitrarily oriented line,...
1answer
127 views

### Set maximum space between elements in 3D mesh

A region in 3D space has been discretized to obtain a list of points. The resulting ListPointPlot3D plot is: I will like to obtain a mesh from these points, but ...
1answer
57 views

### Extra Lines in 3D ConvexHullMesh

I would like to make a picture of a truncated octahedron using ConvexHullMesh as follows: ...
1answer
188 views

### Given a cell in a Voronoi diagram, which point did it come from? [duplicate]

Given a set of points pts = Table[{RandomReal[], RandomReal[]}, {i, 1, 10}]; and their Voronoi diagram ...
1answer
206 views

### Mesh quality error with interpolation of table

I am trying to interpolate a table of the following form. {{x1,y1,z1},{x2,y2,z2}...} Where z depends on x and y, and x ranges from 0.01 to 1 in steps of 0.01, ...
1answer
146 views

### Find surrounding vertices (simplexes) of a given point for DelaunayMesh

Generating a Delaunay triangulation of some random points: pts = RandomReal[{-1, 1}, {50, 2}]; dm = DelaunayMesh[pts]; HighlightMesh[dm, Style[0, Black]] gives [...
0answers
89 views

### Create a tube from a section of a sphere using mesh

How does one make a meshed tube starting from a section of a sphere and later edit the tube's section parametrically.
1answer
100 views

### Difficulty in specifying mesh refinement

I am trying to give a region within a 3D volume a finer mesh than the rest of the volume. My problem is more complicated but here is a minimum working example. I define a 3D cuboid and try and have a ...
1answer
73 views

### Mesh mixes up markers in multiple curves

Following is my code: ...
2answers
318 views

### Node numbering and element numbering for a mesh

I want to create a mesh with the following The rows and columns control. For example, a mesh of 6 by 3. But the code shown below has no control over rows and columns. Instead, it has some ...
1answer
120 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 ...
1answer
58 views

### RandomPoint returns compiler errors on RegionIntersection of two Meshs?

Consider the intersection of two ConvexHullMesh's, m1 and m2. ...
1answer
146 views

### How to draw individual mesh lines in ArrayPlot

Consider the following ArrayPlot. ...
1answer
132 views

### Creating a mesh from a very thin layer

I have the following code which works just fine: ...
2answers
167 views

### Holes in ElementMesh with ToElementMesh of ImplicitRegion

I am trying to plot a function in a region below a level curve of the function and within a cell. I have been doing this by calculating an ElementMesh using ...
2answers
888 views

### Catmull-Clark and Doo-Sabin Subdivision Implementations

I want to work on subdivision surfaces. Unfortunately, I don’t have any source code to start with. I need some Mathematica codes for applying Catmull-Clark and Doo-Sabin methods. I would like to ...
1answer
180 views

### Meshing control of NDEigensystem

I have to solve an Eigenvalue problem originating from the Electrodynamics. It is a 2-D problem with a rectangular region. More specifically, there is a hole on a rectangle made by magnetic material. ...
1answer
92 views

### Is there a way to automatically use triangular elements in ToElementMesh [closed]

I have some simple code to generate a mesh over a rectangle. ...
1answer
228 views

### Converting .STL from Shell to Solid for stress analysis of wing

I'm new to Mathematica as this is the first class I've had to used it in my undergrad time as an aerospace engineer. Anyway, I have run into a problem that I can't figure out. I have created .STL's of ...
1answer
132 views

### Finding the tangents of the function in each mesh

I have a 2D graphic which contains a table of curves within a circular region. ...
1answer
95 views

### Mesh cell count for Voronoi mesh too low

I was trying to solve this question out of interest and thought perhaps creating a Voronoi mesh, cropping it to a circle, and colouring the mesh cells might work. However, if I ask ...
1answer
50 views

### Uneven distribution of nodes by ToElementMesh[]

We are using FEM package to generate mesh in a circular sector. Somehow mesh becomes dense in upper right corner. Is there any way to circumvent this uneven distribution? ...
1answer
115 views

### VoronoiMesh with custom distance function

I'm failing at reading the documentation. Is there a way to specify the distance function used by VoronoiMesh? As a stripped down example say I have a rank-1 lattice such as: ...
2answers
244 views

### ToElementMesh of Region with Hole

When I try to mesh the following region it fails. Why? Is there a workaround? ...
2answers
705 views

### Meshing the cow

As a simple example for applying stl-files I took "cow" out of MMA example data. I'm able to discretize the Graphic without problems ...