Questions tagged [meshing]
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.
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Euler's mesh characteristic and watertightness properety of a 3d STL surface mesh [SOLVED}
I need to determine if a 3D volume triangular surface mesh (STL) represents a watertight volume or not. If I use python trimesh module it tells me if it is or it is not, but it does not tell why.
It ...
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Energy Function Expansion in Deform by Laplacian Coordinates
I am currently working on the strain energy function for a particular graph.
The paper I am currently referencing is "Spatial Relations Preserving Character Motion Adaptation".
I am asking ...
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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
$$
K(v_i) = \frac{1}{A(i)}\left(2\pi - \sum_{(v_i,...
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Surface described by an implicit function
I'm testing a surface mesh generator that takes a function $f:\mathbb{R}^3 \rightarrow \mathbb{R}$ and builds the surface described implicitly by $f(x,y,z)=0$. I already tested with a torus, a ball ...
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Can the Euler characteristic be calculated for an open surface?
I have an open, three-dimensional mesh that looks similar to the one drawn here (in that it contains no volume).
I am using ORS Dragonfly, an image processing software, to visualize this mesh and have ...
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Hexahedral mesh generation around two cylinders junction
I need to design a mesh for Finite Element Method around the junction of two hollow cylinders.
Here is an example of mesh geometry: https://i.sstatic.net/V0hVX.png.
I've found how to generate a mesh ...
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What are the four rules, that the 2D subdivision matrix describes?
I got the following 2D subdivision mask (which is used to subdivide a given quad-mesh):
$$
M = \frac{1}{8}
\begin{bmatrix}
1 & 2 & 1\\
3 & 6 & 3\\
3 & 6 & 3\\
1 & 2 & 1\...
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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 ...
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How is a matrix connected to a grid?
I have a hard time finding information about and understanding how a matrix (adjacency matrix) is connected to a grid used in numerical analysis. What would the nodes be and are the matrix weighted or ...
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Measure of error in smoothness of approximation of sphere
I'm meshing a sphere and am solving a physics problem on this. What I want to show is that the error in the model scales like$$
\varepsilon = \epsilon^p,
$$
where $\epsilon$ is the "error" in the ...
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What are the parameters in mesh parameterization?
I recently heard about mesh parameterization as a way of parameterizing the geometry of an arbitrary mesh by mapping it onto a surface, like a sphere. I am not a mathematician, so I don't know how to ...
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Conformal map onto a circle, from an identification space composed of five square regions.
I am looking to derive a conformal map for the problem illustrated in this image. I've read a bit about how to map a square onto a circle, but I'm struggling to extend the concepts for the domain at ...
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"Area" vs "Angle" heuristic for triangular mesh vetrex normal calculation
I am trying to compare the two heuristics below for calculating vertex normals in a triangular mesh:
the weighted average of face normals of the faces incident to the vertex where the weights are the ...
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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 ...
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From a triangulation of a sphere to a 4-regular planar graph in the minimum number of topological changes?
Given a triangulation of a sphere (coming from the convex hull of some points on that sphere), I need to get to a graph with these points as the vertices, where each vertex is connected by edges to ...
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Plane clipping by cubic limits
I have a plane equation given by a point and a normal vector, for example. This plane has to lay between $xyz$ limits, $300<x<2700$, $150<y<1350$, $130<z<1370$. I want to know the ...
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