A mesh is, by definition, a set of points and cells, when connected to form a network. This network can have many forms of geometry and topology, as will be discussed later. Often, meshes are also called grids, and that is generally related to the intrinsic organization of the mesh and/or when those meshes are related to Finite Differences problems.
Questions tagged [meshing]
32 questions
4
votes
1 answer
Lower and upper bound of discrete gaussian curvature.
In a triangle 2-manifold mesh, or symplicial complex (but I'll stick with the former terminology) the discrete gaussian curvature is usually defined
$$
K(v_i) = \frac{1}{A(i)}\left(2\pi - \sum_{(v_i,v_j,v_k)} \theta_i^{jk}\right)
$$
Where $v_i$ is a…
user8469759
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- 4
- 20
- 54
4
votes
1 answer
How many distinct ways to flatten a cube?
Think of cutting open a cubical box with the smallest possible cuts to lay it flat. A cube has 12 edges and it seems in all the possible meshes, you have to cut along 7 edges. So, the most possible number of distinct ways to lay a cube flat should…
Rohit Pandey
- 7,547
3
votes
1 answer
point of intersection of two lines in barycentric coordinate system
I am looking for an efficient way to determine the intersection point of two lines which go through a triangle (face) of a 3D triangular surface mesh.
For both lines I know the two points at which they intersect with the edges of a triangle…
Fab
- 33
3
votes
0 answers
Generating a Quadrilateral Finite Element Mesh Over a Solid Circular Domain
Consider a solid circular domain defined by the set
$$\text{Circle}=\{(r \cos\theta, r \sin\theta)|r\in[0,1],\theta\in[0,2\pi]\}.$$
I want a simple algorithm for producing a quadrilateral finite element mesh over this domain. For a hollow circle, I…
Hosein Rahnama
- 15,554
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votes
0 answers
How to optimize a 2D triangle mesh for number of triangles?
I am currently writing a program where I have a set of points within a 2D plane that I would like to convert to a triangle mesh in such a way, that the mesh has the least number of triangles possible.
Currently I use constrained delaunay…
frankenapps
- 193
2
votes
1 answer
Can the Euler characteristic be calculated for an open surface?
I have an open, three-dimensional mesh that looks similar to the one drawn here (in that it contains no volume).
I am using ORS Dragonfly, an image processing software, to visualize this mesh and have access to the number of faces, edges, and…
Esper
- 21
2
votes
0 answers
Do meshfree methods suffer from a curse of dimensionality?
I think I am quite confused by the nuance of meshfree methods https://en.wikipedia.org/wiki/Meshfree_methods for solving some PDE over $\Omega$. From what I gather they do not require the discretisation of $\Omega$. Therefore if say $\Omega$ was…
PDE methods
- 61
2
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0 answers
Hexahedral mesh generation around two cylinders junction
I need to design a mesh for Finite Element Method around the junction of two hollow cylinders.
Here is an example of mesh geometry: https://i.sstatic.net/V0hVX.png.
I've found how to generate a mesh around one cylinder using cylindrical coordinates…
mikrymar
- 21
2
votes
3 answers
Could you explain the definition of mesh?
For the context, I have seen various definitions, like this:
Or this:
I would like to concentrate to the first one (Definition 19.) and understand this definition. I think mesh there is supremum of some metric stuff. However, I don´t know, what is…
Tereza Tizkova
- 2,750
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0 answers
A question about 'onions' in $\varepsilon$-nets on 2-dim manifolds
Let $(M,g)$ be an arbitrary $2$-dimensional Riemannian manifold. For the meaning of a $\varepsilon$-net on $M$ I refer to the wikipedia-page. When $X_{\varepsilon}\subseteq M$ is an epsilon net and $x\in X_{\varepsilon}$, let me recursively define…
Hecatonchires
- 2,560
2
votes
2 answers
Voronoi diagrams and Delaunay triangulations: does every Voronoi cell contain exactly one node of a Delaunay triangle?
Looking at the diagrams on Wikipedia here and here:
In 2D: Clearly every triangle in the Delaunay mesh (black lines) does not have to contain a node of the Voronoi diagram (red points) (it can contain any number 0, 1, 2,...).
In 2D: Is every cell…
smörkex
- 649
1
vote
1 answer
Maximum of the ratio of the incircle radius to the circumcircle radius for an arbitrary triangle
For an arbitrary triangle, let $r$ = incircle radius and $R$ = circumcircle radius. Consider the ratio $r/R$? What is its maximum value? For an equilateral triangle this ratio is $1/2$. For very skewed triangles, this ratio approaches $0$. I am…
user89699
- 181
1
vote
0 answers
Element Volume: Jacobian at hex center
I am hoping someone could point me in the right direction in finding resources for a project I am doing. I need to derive a formula that will calculate the volume of 4 child hexahedrals that will form one parent tetrahedron. This is for a metric…
Adam
- 11
1
vote
1 answer
Conformal map from quadrilateral to a sector of a circle.
Can anyone advise me on how to derive a conformal map for this mapping? I am familiar with how to apply Schwarz-Christoffel from the upper half plane to the quadrilateral, but how do I then map from the quadrilateral to the sector?
niran90
- 477
1
vote
1 answer
Mesh a circle with quadrilateral elements
I'm having some problems understanding an exercise. The domain $\Omega$ is the unit circle. Then it says:
"To mesh it with quadrilateral elements, compose $\Omega$ from five mapped squares,
one of them being a square centered at the origin. Propose…
Chiray
- 307