58
votes
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.
...
- 102k
43
votes
Accepted
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.
...
- 102k
41
votes
Accepted
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 ...
- 102k
25
votes
Accepted
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 ...
- 102k
24
votes
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 ...
- 6,453
24
votes
Accepted
Making holes from maze generated Graphics3D
Here's an approach that unions the primitives as rasters, meshes, and smooths.
Data from OP:
...
- 34.7k
23
votes
Accepted
How to access FEM shape functions?
There are no surface element shape functions. There are, however, the normal shape functions.
Load the package:
Needs["NDSolve`FEM`"]
This gives you the ...
- 38.5k
23
votes
Accepted
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. ...
- 69.7k
21
votes
Accepted
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 ...
- 7,375
20
votes
Accepted
Eliminate an unexpected mesh line
The blue line occurs at the edge of the function, where ϕ wraps from 2π to 0. We can get ...
- 7,782
20
votes
Accepted
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 ...
- 231k
19
votes
Accepted
Hexagonal Mesh on a 3D surface
Update: With the function top defined in the original post you can replicate all the cool things you see in rm-rf's answer in the linked Q/A. For example, with a ...
- 363k
19
votes
DelaunayMesh in a specified closed region - creating a concave hull from a set of points
What you want is the 2D alpha shape to try to get close to the outline you seek. Of course, it's no longer a Delaunay triangulation since you're deleting certain polygons from the ...
- 32.8k
19
votes
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 ...
- 3,783
19
votes
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-...
- 102k
19
votes
Accepted
18
votes
Accepted
FEM: how to choose FEM element type
There is good news and bad news. So right now there is no option to make MeshRegion use Hex elements. However, you can use ...
- 38.5k
18
votes
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 ...
- 38.5k
18
votes
Accepted
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-...
- 102k
17
votes
Accepted
How to convert a surface into a solid
Method 1: Construct mesh elements manually
We can triangulate a periodic quad-lattice on the surface:
...
- 228k
17
votes
Lloyd relaxation on VoronoiMesh
Here's my take on Lloyd's algorithm. The code I present here should not be too hard to encapsulate into a routine; I have only elected to present it in this way so that I can animate the progress of ...
17
votes
Accepted
How to mesh a region using adaptive cubic elements
I discarded my previous approach to generate cubes, then fuse them together, since it seems to do a lot of wasted work. Instead, I propose here my version of a cartesian mesher.
The approach is ...
- 64.5k
17
votes
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 ...
- 102k
17
votes
Accepted
16
votes
DelaunayMesh in a specified closed region - creating a concave hull from a set of points
I was writing this code because when I googled "Concave Hull Mathematica" I didn't find this post. I went through the trouble of taking this code and improving the performance, and bringing it up to ...
- 66.3k
16
votes
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
...
- 38.5k
16
votes
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.
...
- 38.7k
16
votes
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 ...
- 6,453
15
votes
Accepted
How to calculate a Delaunay mesh nerve?
The approach I would take is the following:
Clear definitions, load a sample image, find corners in the image using the method you indicated in the OP:
...
- 64.5k
15
votes
Only top scored, non community-wiki answers of a minimum length are eligible