Support for constructive geometry

[jondea]

As part of a FEM project I have implemented an Annulus<:Primitive type and several related functions. Does this count as a primitive, as in there isn't some clever way to make it from two balls? And if not, is this something that would be welcome for a PR?

[juliohm]

Hi @jondea thank you for proposing the primitive. I think what we really need is an API for constructive geometry. There are some packages out there already like

• https://github.com/plut/ConstructiveGeometry.jl
• https://github.com/JuliaGeometry/Descartes.jl

implementing subtraction, intersection and union of primitives. Ideally, we will be able to introduce these same operations in Meshes.jl reusing our primitive types to avoid inefficiencies with type conversion, and to help new users who just want to load a single ecosystem to get things done quickly.

[jondea]

Hi @juliohm, thank you for the pointers! That approach is certainly more elegant. I've made a branch with the Annulus type so I don't lose it https://github.com/jondea/Meshes.jl/tree/add-annulus-primitive, and I hope to be able to come back to this when I have more time.

[bjarthur]

i see the "Intersection" part of the manual, but don't see a union method anywhere. does it exist?

i ask because i have a mesh with overlapping quadrangles. would like to simplify it. in the MWE below, there are two quadrangles, but there could be just one ngon. how do i make it so? have tried simplify and repair to no avail. in the more general case, i have an arbitrary number of quadrangles, some of which might overlap, and others not. thx!

julia> using Meshes, GLMakie

julia> points1 = [(0,0), (2,0), (0,2), (2,2), (1,1), (1,3), (3,1), (3,3)];

julia> quads1 = connect.([(1,2,4,3), (5,6,8,7)], Quadrangle);

julia> mesh1 = SimpleMesh(points1, quads1)
2 SimpleMesh
  8 vertices
  ├─ Point(x: 0.0 m, y: 0.0 m)
  ├─ Point(x: 2.0 m, y: 0.0 m)
  ├─ Point(x: 0.0 m, y: 2.0 m)
  ├─ Point(x: 2.0 m, y: 2.0 m)
  ├─ Point(x: 1.0 m, y: 1.0 m)
  ├─ Point(x: 1.0 m, y: 3.0 m)
  ├─ Point(x: 3.0 m, y: 1.0 m)
  └─ Point(x: 3.0 m, y: 3.0 m)
  2 elements
  ├─ Quadrangle(1, 2, 4, 3)
  └─ Quadrangle(5, 6, 8, 7)

julia> viz(mesh1, color=:blue)

[juliohm]

All these boolean operations (union, difference, ...) in 2D can be implemented in terms of a clipping algorithm. We have one clipping algorithm implemented and two other algorithms in open PRs that still need some work. Em qui., 15 de mai. de 2025, 18:34, Ben Arthur ***@***.***> escreveu:

…

*bjarthur* left a comment (JuliaGeometry/Meshes.jl#251) <#251 (comment)> i see the "Intersection" part of the manual, but don't see a union method anywhere. does it exist? i ask because i have a mesh with overlapping quadrangles. would like to simplify it. in the MWE below, there are two quadrangles, but there could be just one ngon. how do i make it so? have tried simplify and repair to no avail. in the more general case, i have an arbitrary number of quadrangles, some of which might overlap, and others not. thx! julia> using Meshes, GLMakie julia> points1 = [(0,0), (2,0), (0,2), (2,2), (1,1), (1,3), (3,1), (3,3)]; julia> quads1 = connect.([(1,2,4,3), (5,6,8,7)], Quadrangle); julia> mesh1 = SimpleMesh(points1, quads1) 2 SimpleMesh 8 vertices ├─ Point(x: 0.0 m, y: 0.0 m) ├─ Point(x: 2.0 m, y: 0.0 m) ├─ Point(x: 0.0 m, y: 2.0 m) ├─ Point(x: 2.0 m, y: 2.0 m) ├─ Point(x: 1.0 m, y: 1.0 m) ├─ Point(x: 1.0 m, y: 3.0 m) ├─ Point(x: 3.0 m, y: 1.0 m) └─ Point(x: 3.0 m, y: 3.0 m) 2 elements ├─ Quadrangle(1, 2, 4, 3) └─ Quadrangle(5, 6, 8, 7) julia> viz(mesh1, color=:blue) Screenshot.2025-05-15.at.5.32.23.PM.png (view on web) <https://github.com/user-attachments/assets/0be88e06-13c8-480e-95af-5d30d6dafe8b> — Reply to this email directly, view it on GitHub <#251 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAZQW3LR6W5MV3KVQJGQIHD26UB75AVCNFSM6AAAAAB5HGNQXSVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDQOBVGEYDKNZZGY> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[bjarthur]

so the idea is that if i create a second geometry which bounds both those quadrangles above, then i can use it to clip them and in the process they will be merged into a single geometry?

just tried it and seemingly SutherlandHodgman can't input meshes:

julia> other = Meshes.Box((0,3), (3,3))
Box
├─ min: Point(x: 0.0 m, y: 3.0 m)
└─ max: Point(x: 3.0 m, y: 3.0 m)

julia> clip(mesh1, other, SutherlandHodgmanClipping())
ERROR: MethodError: no method matching clip(::SimpleMesh{…}, ::Meshes.Box{…}, ::SutherlandHodgmanClipping)
The function `clip` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  clip(::Polygon, ::Geometry, ::SutherlandHodgmanClipping)
   @ Meshes ~/.julia/packages/Meshes/7KLYh/src/clipping/sutherlandhodgman.jl:21
  clip(::Ring, ::Ring, ::SutherlandHodgmanClipping)
   @ Meshes ~/.julia/packages/Meshes/7KLYh/src/clipping/sutherlandhodgman.jl:27

[juliohm]

Sorry, I was typing from my phone and wasn't clear enough in my previous comment. Some of these clipping algorithms allow the calculation of set operations, see https://dl.acm.org/doi/pdf/10.1145/274363.274364

In particular, we could finalize the PR #1125 and use the data structures therein to compute the union.

The short answer for your question is that we don't currently support it. It is in the plans.