Questions tagged [mesh]

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

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3
votes
2answers
73 views

How to change the ● to ◆ in the given code by using MeshStyle?

I use this code ...
5
votes
3answers
152 views

How to convert cuboid to mesh efficiently

cuboids = Table[Cuboid @@ (pts = RandomReal[100, {2, 3}]), {i, 10000}]; Method1: ...
5
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4answers
182 views

CantorMesh for a fat cantor set

CantorMesh[n] gives the $n$-th level approximation to the standard no-middle-(1/3)-Cantor set. Is there a quick way to obtain a similar mesh region for the no-...
4
votes
3answers
253 views

How can I add a few specific mesh (altitude-like level) curves to a plot?

I'm plotting the numerical solution of a differential equations, using the altitude-like level curves as a mesh. It's fine, but I would like to add three specific altitude levels as thick red, green ...
3
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2answers
91 views

How to change color of the points and remove the joined line in the given code?

I use this code ...
4
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3answers
188 views

How to draw borders around tiles of the same color?

I'm having difficulties with a project to show random tiles with a few random colors. Here's the code that I need to modify: ...
4
votes
1answer
106 views

ElementMeshInterpolation on a BoundaryMesh

It appears as though ElementMeshInterpolation does not play nice with the element meshes produced by BoundaryMesh ...
4
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2answers
265 views

1D mesh generation for PDE solution

I'm trying to solve a system of two PDE that are dependent on time and distance (H[x,t] and P[x,t]). I'm solving the problem using the method of lines but I want to generate myself the mesh and ...
0
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0answers
36 views

Define BoundaryMeshRegion from matrix of data

Say I have a matrix 'm' with 2 columns and 'r' rows. I want to define a mesh region using each row in the matrix as a point coordinate. Something like the R=BoundaryMeshRegion[{m},Line[1,2,3....,r]] . ...
6
votes
3answers
228 views

Regions for numerically defined Toroidal surfaces

I have data like this: DataVisualizationPlot = ListPointPlot3D[data] And would like to obtain the representing surface like this: ...
4
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1answer
70 views

How to obtain a Region from a numerical (!) function

I'd like to achieve a Region from a purely numerically defined function. Like this one: ...
16
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2answers
460 views

3D Inclusion with structured mesh and coarse and arbitrary matrix

I am wondering if there is a simple way to define a structured 3D mesh (inclusion) like e.g. that and surround it with a corse and unstructured Matrix. It should be possible to refine both more or ...
17
votes
2answers
1k views

Smoother jelly / water effect on an image

I'm trying to achieve a jelly / water surface effect. I'd like it to be a bit smoother. Here I am taking a triangulated rectangle and perturbing all points by a little random noise for each frame. ...
3
votes
1answer
63 views

How do I create an STL file from nearest neighbour graph edges?

I'm trying to figure out to deal with (and design) .stl files within Mathematica. As an example, I would like to generate a FCC lattice without the atoms (but connecting all nearest neighbours), and ...
2
votes
1answer
127 views

Exporting several Pyramid to a stl file

I made some 3D structure including several Pyramid and tried to export it to stl file. (I have referenced this link : Exporting several prisms (or Polyhedrons) to stl (with filled inner space)) It ...
2
votes
1answer
42 views

CountourPlot3D problem when intersecting semiplanes

I have the following code: ...
5
votes
2answers
307 views

Using fewer mesh lines, 3D graphics

I want to make the Final use fewer mesh lines, the ideal version will look like the second image. Where the triangle shape is more clear and clean. Can anyone give me some advice on how to fix my code?...
1
vote
0answers
61 views

MeshRegion automatically merges vertices that have the same position in space

I sometimes work with surface meshes that have self-intersections (immersions rather than embeddings). MeshRegion usually doesn't have any problems dealing with ...
0
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0answers
58 views

Intersection Region of two Conic Hull

I have the following semi-infinite conic hull, r1=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{1,0,1}}]; r2=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{0,1,1}}]; ...
4
votes
0answers
51 views

Drawing tools eyedropper crashes Mathematica 12.1 with MengerMesh

Mathematica 12.1.1 under macOS Catalina 10.15.7. In a new notebook, evaluate: MengerMesh[0, 3] Click once on the output's graphic image, which causes the bounding ...
3
votes
3answers
144 views

Equipotential surfaces using ParametricPlot

So I'm trying to plot lines on which the following function is a constant $$ \frac{\left(-\Sigma (r,0.99,\theta )+2 r^2-0.99^2 r \sin ^2(\theta )\right)^2}{\Delta (r,1,0.99) \Sigma (r,0.99,\theta )^3}+...
7
votes
3answers
304 views

Identify the Vertices and Lines around the edges of a free surface - Mesh/DiscreteGraphics

To write a mesher that closes a mesh surface using an implied surface from a boundary spline curve and mesh generated using DiscreteGraphics, I need to identify the Vertices and Lines around the edges ...
0
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0answers
81 views

Closing Boundary Mesh with closed 3D Spline Curve

I am trying to make a 3D solid (with BoundaryMeshRegion) from surfaces created by spline curves. In the follow simple example, I need to close the ends of this irregular tubular shape using boundaries ...
2
votes
1answer
71 views

How to remove the parallelepiped that encloses the writing or make it invisible?

I have this code that I found somewhere and I love what it does, I've been checking the "line" command to remove the line or make it invisible but I can't get it, and the other part of the ...
1
vote
2answers
125 views

Create a “loft” surface from two BSplineCurves?

Is there a way to take two arbitrary BSplineCurves and create a loft surface? I would like to then create a mesh to send to NDSolveValue.
2
votes
1answer
154 views

Create graded mesh

I want to create graded mesh inside a cube, with finer mesh in the left half and a coarser mesh in the right half. My plan was to partition the cube with a 2D plane and then generate boundary mesh ...
3
votes
1answer
86 views

Export Discretized ImplicitRegion as step using OpenCascade

Following the reply by @user21 to this post on exporting a region to a step file, I tried to do the same for a Discretized ImplicitRegion, but OpenCascadeShape didn't appear to work. Is there a switch ...
7
votes
1answer
208 views

Smoothing the Region?

There is a 2D Pi I successed transformed it to 3D. ...
1
vote
1answer
93 views

How do I properly define and work with region unions?

Suppose I have two regions defined by two hexahedrons (slightly adapted from this question): ...
1
vote
1answer
50 views

How do I get `ArrayMesh` to reverse the order of data in a 3D array?

The following array has non-zero entries in the cells where all three indices are equal: foo = SparseArray[{i_, i_, i_} -> 1, {4, 4, 4}] When I try to render ...
4
votes
2answers
133 views

OpenCascadeLink Viewing and Assigning Element Markers

I recently upgraded to MM 12.1 so I could use OpenCascadeLink for 3D meshing following the excellent answer to a question regarding 3D meshing: 3D Meshing Internal regions Assigning boundary element ...
10
votes
1answer
344 views

How to mesh a French biscuit (modulated ellipsoid)

I would like to create a boundary mesh of the following ellipsoid, whose thickness is modulated along its long axis: The surface parametrization I used for it is: ...
6
votes
1answer
215 views

3D FEM Meshing Internal Regions

I am trying to set up a 3D element mesh with intersecting regions having different mesh densities. I am having difficulty setting up the defining boundary meshes from which I will then apply ...
3
votes
1answer
155 views

Turn a region and points inside that region into a mesh

I have a region defined by a polygon and a few points that are inside that region. I'd like to create a mesh where its boundary is the boundary of the region and the vertices interior to the mesh are ...
0
votes
0answers
45 views

Dump Curvature Information for 3d Models

Is anyone aware of any utility to generate and dump Principal, Gaussian and Mean Curvatures for a 3D Model or a set of points? I have reserched following tools - meshlab cloudcompare They are able to ...
5
votes
1answer
230 views

Mass Transport FEM Using Quad Mesh

This question is a follow-up to my previous question and an attempt to implement @Tim Laska's excellent approach of setting up an anisotropic quad mesh. I'm solving a similar problem to @Tim Laska's ...
1
vote
0answers
99 views

Why is there no heat being transfered in my program?

I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
5
votes
2answers
310 views

How to fill in interior in a mesh region

Say I have a mesh region which encloses a region. How do I get a mesh region where this region is filled? Take for example the meshregion below: ...
1
vote
0answers
54 views

obtain the analytics region from mesh or vtk file

Is it possible to obtain the region inequalities from a mesh file (vtk-file). On gmsh I build a Sphere, and with Mathematica I would like to obtain the analytics region function, that's is possible?. ...
2
votes
1answer
101 views

ToElementMesh Error/General meshing strategies

I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
6
votes
1answer
229 views

Improving mesh and NDSolve solution convergence

I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
5
votes
2answers
270 views

Mesh Generation help

I am having trouble generating a mesh of a rectangle inside another rectangle. I have been following the steps on this article: https://reference.wolfram.com/language/PDEModels/tutorial/HeatTransfer/...
5
votes
3answers
297 views

How to discretize a parametric polar surface ensuring the correct periodicity of the mesh

I am trying to discretize a polar surface using a combination of ParametricPlot3D and DiscretizeGraphics. Unfortunately, the ...
1
vote
0answers
53 views

Why does ConvexHullMesh give inconsistent output stuctures?

I know much of the stuff in ConvexHullMesh needs some TLC convexhullmesh-inconsistency But, can anyone see why this would produce inconsistent output: Case 1 (expected behavior): ...
5
votes
1answer
125 views

ConvexHullMesh inconsistency

I am seeing an inconsistency in ConvexHullMesh that I don't understand. Here is Rhull = ConvexHullMesh[pts8] where the $8$ ...
2
votes
2answers
95 views

How to discretize the boundary of two regions?

Problem How to discretize a surface constructed with multiple components? Unsuccessful attempts include combining the objects top and ...
4
votes
1answer
105 views

Strange behaviour in ToElementMesh

Why would that not work: ...
9
votes
1answer
381 views

Help to create a 2D mesh generator (FEM)

I'm working in a finite element mesh generator. I built this function which generates an 8 node mesh (polynomials of order 2) without any interior node: ...
1
vote
1answer
56 views

How can I specify the output mesh resolution for ListPlot3D?

I am using a grayscale image to generate a 3D topology, with the help of ListPlot3D. However, the output mesh resolution is far too high for my purposes. I need to ...
1
vote
1answer
53 views

Unable to affect mesh regions with DiscretizeGraphics

Problem On the sphere, it is easy to control the resolution of the mesh in DiscretizeGraphics using the MaxCellMeasure ...

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