# How can I generate a 3D annulus surface and mesh it using Meshes.jl?

**URL:** <https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949>\
**Category:** Specific Domains\
**Tags:** meshes\
**Created:** [February 29, 2024, 12:34pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949 "2024-02-29T12:34:07Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [February 29, 2024, 12:34pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/1 "2024-02-29T12:34:07Z")

</div>

I have tried using `PolyArea`. Here is MME:

```julia
ring1=Meshes.Ring([(cos(t),sin(t),0) for t in 0.1:0.1:2pi])
ring2=Meshes.Ring([(2cos(t),2sin(t),0) for t in 0.1:0.1:2pi])
annulus = PolyArea([ring2, ring1])
discretize(annulus, FanTriangulation())

```

with error:

```julia
ERROR: DimensionMismatch: Sizes (Size(3,), Size(2,)) of input arrays do not match 
Stacktrace:
  [1] _throw_size_mismatch(::Meshes.Vec3, ::Vararg{Any})
    @ StaticArrays C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\traits.jl:113
  [2] same_size
    @ C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\traits.jl:107 
[inlined]
  [3] macro expansion
    @ C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\mapreduce.jl:74 [inlined]
  [4] _map
    @ C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\mapreduce.jl:40 [inlined]
  [5] map
    @ C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\mapreduce.jl:37 [inlined]
  [6] +
    @ C:\Users\Administrator\.julia\packages\StaticArrays\Uc4hE\src\linalg.jl:12 [inlined]
  [7] +(A::Meshes.Point3, v::Meshes.Vec2) @ Meshes C:\Users\Administrator\.julia\packages\Meshes\1sXKx\src\primitives\point.jl:95
  [8] bridge(rings::Vector{Meshes.Ring{…}}, rinds::Vector{Vector{…}}, δ::Float64) 
    @ Meshes C:\Users\Administrator\.julia\packages\Meshes\1sXKx\src\transforms\bridge.jl:81
  [9] apply
    @ C:\Users\Administrator\.julia\packages\Meshes\1sXKx\src\transforms\bridge.jl:30 [inlined]
 [10] discretize(polygon::Meshes.PolyArea{3, Float64, Meshes.Ring{…}}, method::Meshes.FanTriangulation)
    @ Meshes C:\Users\Administrator\.julia\packages\Meshes\1sXKx\src\discretization.jl:52
 [11] top-level scope
    @ e:\Mesh the manifolds\MeshRing.jl:16

```

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [February 29, 2024, 12:47pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/2 "2024-02-29T12:47:33Z")

</div>

You can discretize `PolyArea` embedded in 2D space. Your 3rd coordinates are all zero, just drop them:

```julia
using Meshes

import GLMakie as Mke

ring1 = Ring([(cos(t),sin(t)) for t in 0.1:0.1:2pi])
ring2 = Ring([(2cos(t),2sin(t)) for t in 0.1:0.1:2pi])
annulus = PolyArea([ring2, ring1])

viz(annulus)

```

![image](https://global.discourse-cdn.com/julialang/original/3X/9/8/98befab60f1de25b3cff7f5f7f0a307df35fc598.png)

Given that this polygonal area is not convex, you cannot use `FanTriangulation`. Simply omit the method, and the package will pick the most appropriate one:

```julia
mesh = discretize(annulus)

```

```julia
124 SimpleMesh{2,Float64}
  124 vertices
  ├─ Point(1.9900083305560516, 0.1996668332936563)
  ├─ Point(0.9800665778412416, 0.19866933079506122)
  ├─ Point(0.9950041652780258, 0.09983341664682815)
  ├─ Point(0.9965420970232175, -0.0830894028174964)
  ├─ Point(0.9832684384425845, -0.18216250427209588)
  ⋮
  ├─ Point(1.7710390338826378, -0.9292043588275147)
  ├─ Point(1.8549568614880718, -0.747753329660472)
  ├─ Point(1.920340573300732, -0.5588309963978517)
  ├─ Point(1.966536876885169, -0.36432500854419175)
  └─ Point(1.993084194046435, -0.1661788056349928)
  124 elements
  ├─ Triangle(92, 93, 94)
  ├─ Triangle(92, 94, 95)
  ├─ Triangle(91, 92, 95)
  ├─ Triangle(91, 95, 96)
  ├─ Triangle(90, 91, 96)
  ⋮
  ├─ Triangle(68, 69, 1)
  ├─ Triangle(67, 68, 1)
  ├─ Triangle(66, 67, 1)
  ├─ Triangle(65, 66, 1)
  └─ Triangle(1, 64, 65)

```

---

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [February 29, 2024, 1:00pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/3 "2024-02-29T13:00:51Z")

</div>

Hello, Thank you for correcting my misuse of `FanTriangulation`. This concrete example does not need a 3-dimensional mesh. However, I have to implement what I have described in the title. Can you give me another suggestion?

---

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [February 29, 2024, 1:13pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/4 "2024-02-29T13:13:32Z")

</div>

I have an idea. Maybe I can create an annulus and mesh it in the plane. Map the vertices of the mashed annulus to 3d space by some linear or nonlinear mapping, and reuse the mesh structures of the origin mash.

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [February 29, 2024, 1:22pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/5 "2024-02-29T13:22:57Z")

</div>

Do you mean a Torus?

```julia
using Meshes

t = Torus((0,0,0), (1,0,0), (0,1,0), 0.1)

viz(torus)

```

 ![image](https://global.discourse-cdn.com/julialang/original/3X/3/d/3d2dc5c269f942b01434c40b13786096f3174e21.png)

You can discretize it similarly.

---

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [February 29, 2024, 1:49pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/6 "2024-02-29T13:49:15Z")

</div>

No. I just mean a surface annulus in 3d space. I have implemented this idea:

> [@xiaoming](#):
>
> I have an idea. Maybe I can create an annulus and mesh it in the plane. Map the vertices of the mashed annulus to 3d space by some linear or nonlinear mapping, and reuse the mesh structures of the origin mash.

The codes:

```julia
using Meshes, GLMakie, Rotations

ring1 = Meshes.Ring([(cos(t), sin(t)) for t in 0.1:0.1:2pi])
ring2 = Meshes.Ring([(2cos(t), 2sin(t)) for t in 0.1:0.1:2pi])
annulus = PolyArea([ring2, ring1])

mymesh = discretize(annulus)

function rotate_annulus(x)
    rmatrix = RotZXZ(1, 1, 1)
    p = [x.coords[1], x.coords[2], 0]
    rp = rmatrix * p
    Meshes.Point3(rp[1], rp[2], rp[3])
end

function to3d(annulus, map)
    vertices = annulus.vertices
    topology = annulus.topology
    newvertices = map.(vertices)
    SimpleMesh(newvertices, topology)
end

viz(to3d(mymesh, rotate_annulus), showfacets=true)

```

gives

 ![image](https://global.discourse-cdn.com/julialang/original/3X/c/9/c98713b82912719b22285cd77d673fea8e2ac76d.jpeg)  
I am new to Meshes.jl. Probably there are better ways.

---

<div class="post-metadata">

**Author:** ![KevinMoerman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kevinmoerman/32/44947_2.png) [@KevinMoerman](https://discourse.julialang.org/u/KevinMoerman)\
**Post date:** [May 26, 2025, 3:20pm UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/7 "2025-05-26T15:20:38Z")

</div>

@xiaoming With [Comodo’s](https://github.com/COMODO-research/Comodo.jl) `regiontrimesh` function you can create triangulations with boundary constraints. [This Comodo demo](https://github.com/COMODO-research/Comodo.jl/blob/main/examples/demo_regiontrimesh.jl) includes a related but more advanced example:

 ![image](https://global.discourse-cdn.com/julialang/original/3X/4/3/43eff6d23bcabb6a535dda2c97947dec90fd0d47.jpeg)  
You give it boundary curves and desired mesh spacings as input. Each meshed region can have its own mesh spacing. The code also keeps track of (e.g. material) regions (i.e. the colors in the visualisation).

---

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [May 27, 2025, 11:46am UTC](https://discourse.julialang.org/t/how-can-i-generate-a-3d-annulus-surface-and-mesh-it-using-meshes-jl/110949/8 "2025-05-27T11:46:18Z")

</div>

Thanks. I will give it a try.