Questions tagged [mesh]

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

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6
votes
2answers
202 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,...
6
votes
3answers
132 views

Sometimes Region can't build right region

During my work with NDSolveFEM I found strange behavior of function Region. ...
6
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2answers
165 views

Inconsistent mesh generation from BoundaryDiscretizeRegion and ToBoundaryMesh at creases

I'm trying to use BoundaryDiscretizeRegion and/or ToBoundaryMesh to generate polygonal models for 3d printing, but I'm having ...
6
votes
2answers
308 views

Automatically generating boundary meshes for region intersections

I am trying to solve a PDE having different coefficients in different regions. I have been having trouble getting Mathematica to do it automatically, so I have gone down the route of creating my own ...
6
votes
2answers
260 views

Assigning Element Markers to 3D FEM Mesh

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. ...
6
votes
1answer
139 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
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1answer
367 views
6
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1answer
158 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 ...
6
votes
2answers
291 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
2answers
95 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 ...
6
votes
3answers
319 views

Trouble with discrete MeshRegions: Integrating over plane slices

I would like to slice a discrete 3D region with a plane, and integrate some field over the resulting 2D region (embedded in 3D). Let me be clear: I do not mean analytical regions (the kind you could ...
6
votes
1answer
191 views

ConvexHullMesh fails with small numbers

When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ...
6
votes
1answer
194 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
80 views

How to specify the text size of a vertex index in a 3D mesh using Labeled

My code takes a list of {x, y, z} vertices and displays a convex hull with each vertex labeled by its index in the list. Here is a minimal working example of the ...
6
votes
1answer
150 views

Investigating mesh suitability

Trying to get a good mesh often requires significant work. For the finite element package we can have first and second order elements. Thus this suggests we need fine good quality meshes rather than ...
6
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0answers
328 views

How to increase boundary mesh quality?

Update: I tracked down the current issue to errors generated by numerically integrating over the boundary mesh. What's the proper way to integrate a function over the boundary of an implicit region? ...
5
votes
3answers
268 views

How to create “Volumemesh” from closed “surfacemesh”?

Given a surface region (MesgRegion netz2D), for example ...
5
votes
2answers
165 views

How to upsample a (non-boundary) mesh region

I have a simple 2D triangle mesh embedded in a 3D space; note that it is not a BoundaryMeshRegion, but it is a MeshRegion. What ...
5
votes
2answers
255 views

color voronoi cell based on area

According to mrz's question: Color code Voronoi cell areas depending on number of vertices, he colored voronoi cell by number of corners corresponding to a Voronoi cell. My question is how to ...
5
votes
3answers
152 views

Unexpected behavior of ListPlot3D

This question surfaced when I was working on this question Given zVals = {{1, 1, 1, 1}, {1, 2, 1, 2}, {1, 1, 3, 1}, {1, 2, 1, 4}}; and ...
5
votes
1answer
576 views

How to generate certain number of random points in a convex hull mesh?

I am a newbie to Mathematica. I have some 2D point data, and I generated a ConvexHullMesh from it. Now, I want to generate a certain number of random points within ...
5
votes
2answers
138 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: ...
5
votes
2answers
189 views

How to extract parts of this expression

If you look up ImageMesh, it shows how to extract a BoundaryMeshRegion from an image mask. http://reference.wolfram.com/language/ref/ImageMesh.html ...
5
votes
2answers
143 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 ...
5
votes
2answers
133 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 ...
5
votes
1answer
174 views

How to specify a mesh in plotting options [closed]

I have a very simple question: Imagine I have solved a PDE on a mesh and want to display the solution on the same element mesh that was passed to NDSolve. I have ...
5
votes
1answer
71 views

How to not show line mesh elements

Let's say I make a mesh from a collection of random points: SeedRandom[1234] points = RandomReal[1, {20, 2}]; mesh = VoronoiMesh[points] For the purposes of my ...
5
votes
1answer
218 views

How to create meshes with multiple regions from 2D images?

I would like to import 2D images to Mathematica and to use them to create meshed regions which can then be used for FEM. I create the images in Adobe illustrator so can either import a vector based ...
5
votes
3answers
593 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: ...
5
votes
1answer
357 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 ...
5
votes
1answer
545 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 ...
5
votes
1answer
142 views

Area of an Annulus (MeshTools<>NIntegrate)

In a very simple example I try to describe an annulus using MeshTools package mesh2D = AnnulusMesh[{0, 0}, { 1 , 2 }, {-Pi, Pi}, {36, 10}]; The area given ...
5
votes
1answer
147 views

How to find the index of a facet of a boundary mesh region closest to a given point?

Using the RegionNearest[] function, it is possible to calculate the point, $p_{mesh}$, on a mesh region that is nearest to some input point, $p_{input}$. My ...
5
votes
2answers
143 views

Union of a List of ConvexHullMesh

How can I create a Union of a List of several ConvexHullMesh? My List is of variable length and the containing BoundaryMeshRegions may overlap. I want to create ...
5
votes
1answer
760 views

How do you refine the elements of a 3D mesh?

Response to Answer below. Original Question: I am trying to refine a 3D mesh in a certain region. This seems relevant but does not work for me. I start by making the region which consists of a box ...
5
votes
2answers
1k 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, ...
5
votes
1answer
96 views

How to set a NeumannValue on a given ElementMarker on the boundary of a mesh?

How can one apply a NeumannValue on an ElementMarker on the boundary of an ElementMesh for a ...
5
votes
1answer
143 views

Finding a Voronoi nerve

I have a Voronoi mesh and I need to find a "nerve" which is all the polygons that have common edges with a specific single polygon (a nucleus). Which Mathematica functions can I use?
5
votes
3answers
710 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 ...
5
votes
1answer
65 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 ...
5
votes
1answer
76 views

How to define element size with ToBoundaryMesh?

I am trying to make a mesh for finite element analysis with shell elements: I have to define 2D finite elements in 3D space. My code is: ...
5
votes
1answer
238 views

Simplify BoundaryMeshRegion

I have a point cloud as X,Y,Z-coordinates which form a parallelepiped (with most data points inside the solid) that is rotated in space by some unknown amount and would like to find the 8 corners of ...
5
votes
1answer
301 views

Efficient generation of a 3D mesh to solve a diffusion PDE

I'm new to FEM and trying to figure out what is the most efficient way of generating a mesh and solving an equation. As a warm-up to the particular problem I'm interested in, I want to calculate the ...
5
votes
1answer
176 views

Are the triangles in DelaunayMesh oriented ccw?

MeshCells[R, 2] returns the triangles from R=DelaunayMesh[pts], where pts is a list of 2D ...
5
votes
1answer
49 views

RandomPoint returns compiler errors on RegionIntersection of two Meshs?

Consider the intersection of two ConvexHullMesh's, m1 and m2. ...
5
votes
1answer
139 views

Analyzing MethodOfLines

In this example the wave equation ...
5
votes
1answer
69 views

Is this a bug of BoundingRegion?

...
5
votes
1answer
226 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 ...
5
votes
0answers
222 views

Volume Deformation

I want to do a volume deformation based on Bezier volumes. For example, if I have a triangle mesh, then I want to deform the mesh into a weird shape like the example image attached here. Can anyone ...
5
votes
0answers
638 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 ...