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

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19
votes
3answers
1k views

Removing unwanted appearance of underlying mesh

Let us first define two positive definite matrices: M1 = {{2, -6}, {4, 8}}; M2 = {{2, 3}, {4, 8}}; then set two points ...
29
votes
4answers
4k views

Creating a 2D meshing algorithm in Mathematica

As what is proving to be a difficult, but entertaining task, I am attempting to adapt a 2D meshing algorithm created for MATLAB and port it to Mathematica. I understand meshing functions already exist ...
15
votes
3answers
3k views

Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
14
votes
3answers
2k views

Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
10
votes
3answers
1k views

Dashed mesh behind 3D object

I am trying to create a simple, almost transparent 3D sphere with a mesh that is made of solid lines if they are on the front surface (i.e. if they are directly visible) and of dashed lines if those ...
6
votes
1answer
378 views

Meshing the surface of a non-convex object

I would like to mesh the surface of a cloud of points that may not be completely convex, for example the points in this question. Mathematica does not provide triangulation of 3D points, but there is ...
20
votes
3answers
1k views

Build a refined grid based on intersecting line

I honestly have no idea where to begin with this problem. In summary, I have a 2D coarse grid with an intersecting line. For an easy example, let's assume it's a 4x4 grid. I wish to pass through ...
16
votes
4answers
2k views

How to get actual triangles from DelaunayTriangulation[]?

The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
20
votes
2answers
566 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
7
votes
2answers
289 views

Mesh at Ticks positions

In a ListPlot3D[ ] I want to have the Mesh at the same positions as the ticks. For some reason this isn't default if both are ...
6
votes
1answer
1k views

Construct a simple mesh or tetrahedral mesh from 3D image surface

I have a 3D Y-Shape hollow tube, not so good surface. Import["http://dl.dropbox.com/u/68983831/tube02.vtk", "Graphics3D"] I tried to use following vertex data ...
12
votes
2answers
633 views

How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
7
votes
3answers
344 views

Converting Mesh in Density Plots to a Graph

Consider the following line of code: ...
9
votes
4answers
542 views

How discretize a region placing vertices on a specific non-uniform grid

Given a generic region, for example: Ω = ImplicitRegion[ 2 x^2 + 3 y^2 + 2 x y - 2 <= 0 ∧ x^2 + y^2 > .1, {x, y}]; and a non-uniform grid, for ...
7
votes
2answers
1k views

How can I mesh a solid cylinder with triangular or tetrahedral elements

I need to plot triangular mesh on a cylinder. However the function Cylinder doesn't have a mesh option. By using ...
11
votes
1answer
240 views

How to specify PDE Boundary condition on Bspline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a ...
10
votes
1answer
621 views

How do I place a texture on an irregular 3D model?

I'm trying to reproduce a textured head in Mathematica, and I'm using a kind of 'net' of a head which contains all the features on the face. The texture looks like this: which is supposed to look ...
5
votes
1answer
205 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
7
votes
2answers
169 views

Poor/wrong sampling in 1D DiscretizeRegion of splines?

Bug introduced in 10.1 and persisting through 10.2 or later Context In relation to this question I have would like to use splines to define a ...
6
votes
2answers
82 views

How to scale values for ColorFunction in SliceContourPlot3D?

Trying to help out in the question, Finite Elements 3D, I came across this behavior of SliceContourPlot3D: ...
3
votes
1answer
90 views

Problem with MeshOrderAlteration to create a 2nd order ElementMesh

After working on this 2D domain, I'm trying to reproduce the same ideas to create a mesh of a sphere composed of QuadElement, instead of more simple and common ...
3
votes
2answers
424 views

Different MeshStyle for different functions

By using Plot command I want to get one curve in form if circles and other like a solid line. ...
1
vote
1answer
583 views

Drawing a shape on the mesh of a Plot3D [duplicate]

My question pertains to modifying the output of a typical Plot3D object, and overlaying a 2D shape, like a circle, on the 3D surface. Thinking of the surface as a stretchy surface, I want to put the ...
8
votes
1answer
148 views

ParametricPlot MeshStyle bug in v10?

Bug introduced in 10.0.1 or earlier and fixed in 10.0.2.0 Original Post The documentation gives the following code and says "Use a red mesh in the x direction and a blue mesh in the y direction:" ...
4
votes
2answers
211 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
3
votes
1answer
115 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
3
votes
1answer
262 views

Writing loops for triangle elements

I'm kind of new to using Mathematica, so any help is great. I'm trying to write a program that will create a list or matrix that will give each small triangle's point numbers. For example if given ...
3
votes
1answer
683 views

Explanation about RegionFunction and MeshFunctions?

In the link, ParametricPlot3D, consider the example(Variation on the Spheres) given in the Neat Examples section. Can someone please explain how ...
2
votes
1answer
150 views

How does one get Mesh lines at 0 in ParametricPlot3D?

The following is in the documentation (MMA 10) under ParametricPlot3D -> Options -> Mesh : ...
1
vote
2answers
123 views

How to find adjacent polygons of a specific polygon in a VoronoiMesh?

I have developed a code for VoronoiMesh. I am also able to find the polygon with highest number of adjacent polygons. How do I find the indices of the adjacent ...
1
vote
1answer
283 views

Create hexagonal mesh on 3D Parametric Plot and 3D spheres?

I am looking to put a cool geometric mesh on this object. I came across this question that explained how to put a hexagonal mesh on a parametric equation but I have a series of geometric objects of ...