# Tag Info

Accepted

### A geometric multigrid solver for Mathematica?

Background Details about multigrid solvers can be found in this pretty neat script by Volker John. That's basically the source from which I drew the information to implement the V-cycle solver below. ...
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### How to perform Loop subdivision on a triangle mesh with Mathematica?

We need quite a bit of preparation. In the first place we need methods to compute cell adjacency matrices from here. I copied the code for completeness. ...
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### Smoothing 3D contours as post processing

As announced before, here my take on the mean curvature flow for surfaces. The code is rather lengthy and I tried to recycle as much as possible from this post about finding minimal surfaces (solving ...
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### Catmull-Clark and Doo-Sabin Subdivision Implementations

Catmull-Clark Subdivision Indeed, I have some code for Catmull-Clark subdivision and I planned to post it here for quite some time. This seems to be a good opportunity. The code is optimized for ...

### Making holes from maze generated Graphics3D

Lets start by making a symbolic representation of maze, with BooleanRegion using graphic primitives. That will be our basis for discretization by any method. Number ...
• 6,523
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### Making holes from maze generated Graphics3D

Here's an approach that unions the primitives as rasters, meshes, and smooths. Data from OP: ...
• 36.4k
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### Making a graph or network interactively over an image

There are many ways to do this, modifying, improving my method or doing a completely different thing. My goal here is to show a very basic idea that should give you a start. ...
• 73.4k
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### How to generate a mesh with quadrilateral elements?

Based on the tutorial here QuadElement meshes behave exactly the same as TriangleElement meshes, with the exception that, for linear quad elements, four incidents per element are needed, and, for ...
• 7,515
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### How to get a specified number of points that are nearly equally spaced in a closed rectangle

There is a neat (and widely known) trick to produce n approximately evenly distributed points in a disk, or on any surface of revolution. Points are placed on a ...
• 236k

### A geometric multigrid solver for Mathematica?

3D Example The problem with direct solvers is that starting in 3 dimensions, their performance for dealing with matrices stemming from PDEs drops rapidly. This is why I wanted to show at least one 3-...
Accepted

perhaps: ...
• 399k

### Voronoi tessellations on meshed surfaces

Using the Geodesics in Heat Algorithm implemented here, we can calculate the distances of all vertices on the surface to a given vertex. By repeating this algorithm on a selected subset of vertices on ...
• 4,093

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

Doo-Sabin Subdivision To my own surprise, Doo-Sabin subdivision is in many ways much easier to implement than Catmull-Clark subdivision. The only real problem I met was to compute the faces created at ...

### How to generate a mesh with quadrilateral elements?

Here is a different approach. The idea is to first generate a second order triangle mesh. Next a center coordinate is added in every triangle. Then we split every triangle into three first order quads ...
• 40.3k
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### How to obtain the cell-adjacency graph of a mesh?

I think, I found a general and even faster way, but I haven't tested it for $1$- or $3$-dimensional MeshRegions. The following function computes the cell-vertex-...
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### Creating a Hexagonal Lattice with VoronoiMesh

Here is what I was suggesting in comments: ...
• 67.5k

### How to generate a mesh with quadrilateral elements?

That's not possible in general in V11.0. The only primitive from which a quad mesh can be generated is ToElementMesh[Rectangle[]] or ...
• 40.3k

### How to generate a mesh with quadrilateral elements?

this is a bit of a hack but it works for this example: generate separate rectangle meshes -- note the connected edge nodes must be exactly coincident. ...
• 39k

### How to generate a mesh with quadrilateral elements?

Edit: This method is now implemented as StructuredMesh function (2D and 3D) in FEMAddOns package. With minor enhancements it is also implemented in MeshTools ...
• 6,523
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### How to mesh part of sphere

The curve is smooth, and the great circles tangent to the curve never pass through the interior point {0, 0, 1} over φ: Hence ...
• 20.4k

### Finite element mesh not resolving features

These should work: Method 1 ...
• 40.3k
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### Crop a Voronoi diagram and get a proper MeshRegion

First Try (doesn't work due to a bug) That's very frustrating. I thought that it might be a good idea to discretize the disk first and compute the intersections afterwards. That improves the timing by ...
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### A Smooth and Round Voronoi Mesh

1 + 4 We can discretize the rounded Polygon objects and then add the negative of the mesh through Prolog. ...
• 36.4k

### 3D Inclusion with structured mesh and coarse and arbitrary matrix

There is an example of something similar in the PDEModel collection in the Acoustic Cloak Model. Here is a 3D version. Some setup: ...
• 40.3k

### Polygon mesh: Compute vertex normals for smooth shading

In case the undocumented internal function RegionMeshMeshCellNormals[meshregion, dimension] is of use to someone: ...
• 240k
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### Is it possible to re-mesh, downsample & upsample a DiscretizeRegion object?

Is it possible to re-mesh, downsample & upsample a DiscretizeRegion object? I believe the answer to all of those questions is yes, but just the body of the mesh and not the boundary – with a ...
• 70.9k
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### DensityPlot with equal mesh and a certain boundary

As you did not make it supper clear which aspect you wanted to change, I just share some intermediate steps as well. Combination of different tricks perhaps allows you to get the figure you need. ...
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### Computing the surface area and volume of molecules

I can offer a solution by discretization to ElementMesh with external meshing software Gmsh. Currently it produces better quality mesh on curved surfaces that built-...
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### Smoother jelly / water effect on an image

This method seems to work quite well. Instead of changing the positions randomly, I rotate each vertex around in a small circle centered at each original vertex position. Every vertex starts at a ...
• 25.6k