# Questions tagged [mesh]

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

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### VoronoiMesh with boundary edges removed

I would like to create a Voronoi diagram without the boundary edges highlighted. This code gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}] ...
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### Drawing a “realistic” VoronoiMesh

Consider a set of points generated via Lloyd's relaxation algorithm ...
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### Extract data from ConvexHullMesh [closed]

I have a ConvexHullMesh and want to extract the bounding points. I am familiar with using Cases to extract data from plots but ...
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### Why BoundingRegion Fails in such cases

When I was playing this answer of tube, function TubePolygons used in my question. ...
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### Mesh Refinement for interpolation of f[x,y] fails for all but the simplest f

I would like to interpolate a function, f[x,y,z], on a mesh of the unit cube, starting with a coarse tetrahedral mesh and refining tetrahedra as needed to reduce the interpolation error below a ...
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### Finding lower boundary of a 3D object in list format

I have the following point list and would like to find the points located in the lower boundary of the 3D object (It is part of a body torso). https://pastebin.com/L12n0Gfr I am using the following ...
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### Unfold/develop a RevolutionPlot3D mesh onto a 2D plane?

I'm making my own blimp out of emergency blankets (Mylar), and I want it to have a NACA0025 airfoil shape. I'm new to Mathematica, but I still managed to create the shape I wanted with ...
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### Ordering Problem With VoronoiMesh

Imagine I want to model 2D cells moving in a tissue. Consider, as an example, Lloyd's relaxation algorithm. Using VoronoiMesh I'm able to mimic some cell movement. ...
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### Capturing mesh information

Mesh information Using the helpful tips from Triangular mesh of random points on a sphere, it's easy to generate solids: ...
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### How to make a structured mesh with a hole and extrude it

I am trying to use the FEMAddOns package to make a structured mesh with a hole and then extrude it. As a warm up example this worked nicely. ...
167 views

### MeshRefinementFunction analogue for ToElementMesh

MeshRefinementFunction according to the documentation is an option for DiscretizeRegion. Is there an analogue for ...
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### How to create a 1D mesh from a curved line (with ToElementMesh)

I want to create an element mesh from an arc $x=Rcos(\varphi), y=Rsin(\varphi)$, with $R=100, \varphi \in [0,\pi/4]$ which looks like this: ...
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### Computing volume of intersection of two regions

I am trying to compute the volume of intersection of the following two regions: ...
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### Convert ConvexHull to Inequality

I have the following convex hull. P0={0,0,0}; P1={1,0,0}; P2={0,1,0}; P3={0,0,1}; ConvexHullMesh[{P0,P1,P2,P3}] Now I want the region algebraically as equality ...
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### Surface area of a list of points

I would like to know how I can get the area of the following point list. I am using the following script to make a mesh region and then find the area. However, the area is much larger than the value ...
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### RegionResize works improperly with different digital accuracy

The data is copied from the output cell of my original data. ...
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### Plotting Cartesian mesh on Sphere with SphericalPlot3D

I really want to know how to plot the Cartesian grid lines on a 2D plane onto a sphere in the context of stereographic projection. I found this image showing what I want to plot. Can anyone help me to ...
728 views

### How to determine if a point is within a concave 3D polyhedron?

Generally, if you have a 3D polyhedron and wanted to check if a point was within it, you would use something like a ConvexHullMesh to create a region, which you can ...
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### How to efficiently animate changing mesh on a fixed 3D plot?

Say I'd like to visualise a height function of a torus by animating a plane going upwards, and highlighting the intersection via Mesh/...
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### Why do some PlotThemes not work with Mesh as expected? What can be done about it?

While updating my answer for (189038) I noted that some PlotThemes do not work with Mesh in a meaningful way: ...
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### How to draw surface with four space curves as boundaries

How to draw a surface with four space curves as boundaries of the surface? ...
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### MeshTools package: can one translate 3d meshes in order to then merge them?

I have created a 3d region for Laplace's eqn ...
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### Area/Volume of a 2D/3D object as it is filled up with water

How could I get the volume of water on a region as it is filled up with water from below? Assume gravity points in some appropriate downward axis like -y (or -z in 3D) so the water fills upward from ...
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### RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver

I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf This method inspired by random-walks and ray-tracing ...
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### DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
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### Periodic Voronoi Mesh in a box

Is it possible to generate a periodic Voronoi Mesh inside a rectangular domain? I would also like to obtain the coordinates of each cell separately so that I can perform further operations on each ...
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### Removing polygons from exported RegionPlot

I have the following code that runs a RegionPlot ...
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### How to find out the number of nodes in the interval of mesh [closed]

I have a mesh created for the femur. I need to apply a total load of 800 N in the range 480 < z < 500. To do this, I need to know the number of nodes in this interval in order to apply Force to ...
579 views

### How to add 'border' to Voronoi diagram

Suppose I have a set of points pts, from which I generate a Voronoi diagram VD: ...
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### FEM 2D mesh with inclusion

I want to create a FEM mesh with an inclusion, but I want to define the coordinates of the edge nodes manually, since I need the nodes for a problem that requires periodic boundary conditions. The ...
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### How can I convert such a model into a BoundaryMeshRegion

The obj file is here As you see, I cannot import such a house model into Mathematica with BoundaryMeshRegion Option. Import[objFile, "BoundaryMeshRegion"] So my ...
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### How to find intersection of higher dimensional convex hull?

I have often used ConvexHullMesh to obtain a convex hull for 2-d and 3-d points. But when I try to find it for 4-D points I encounter error even for simple cases. <...
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### Represent a Concave Mesh Volume

I programmatically generate a shape, where the top surface is defined by a series of polygons. I generate all the points of the polygon. ...
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### Finding mesh elements within a given region

I write a code that generates the following mesh. I would like to find out the elements that completely lie within a certain circular region inside this meshed area. How do I do that? The code that I ...
62 views

### Euler Characteristic of MengerMesh

When I ask Mathematica to give me the Euler characteristic of MengerMesh[1, 3], it returns 16. It seems to me the 1-step Menger sponge has genus 5 and should ...
188 views

### Projecting a 3D mesh region to 2D

How do I project a 3D MeshRegion to a 2D MeshRegion (or equivalent for a BoundaryMeshRegion). This question is similar to ...
175 views

### How to export a volume mesh?

Let's say that I generate a volume mesh using the following command: Icosahedron[] // BoundaryDiscretizeGraphics // TriangulateMesh which gives the following: As ...
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### NearestMeshCells in Mathematica 11.3

Is there an efficient way of writing a function equivalent to NearestMeshCells (Mathematica 12.1) in Mathematica 11.3? I'm trying to write my own code, which I can ...
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### Generating a Periodic Voronoi Mesh

Consider the following hexagonal mesh, created from VoronoiMesh ...
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### Colour Change of a Convex Hull

I have the following code to draw a convex hull. ...
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### How can I calculate volume of such a MeshRegion Object

The Data is here: meshData === PolygonData is here ...
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### Assigning ElementMarkers to existing ElementMesh boundaries

I've imported a 2D element mesh from another program as a list of triangle coordinates {{x1,y1},{x2,y2}....} ("nodes") and element connections {{n1,n2,n3},...} ("elements"). Then I create an ...
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### How to divide a region in FEM with a parametric curve?

I'm using NDSolve with finite element to try to solve a heat transfer problem. The region I have is a rectangle where the four vertices are at ...
57 views

### Different style for vertical and horizontal lines in ListStepPlot

I would like to color the horizontal portions (the data) of a ListStepPlot in one style (e.g., blue) and the vertical (linking lines) in a different style (e.g., ...