Planar meshing library

Grasshopper
1

I have been searching a long time for a good meshing library and have struggled to find something that meets my criteria. My criteria are:

  • Meshes planar surfaces (potentially with holes)
  • Mesh can be constrained to mesh around a given point within the planar surface
  • Mesh can be constrained to mesh around a given line on the planar surface
  • Can be integrated into a Grasshopper based workflow

The middle two criteria seem to give me the most problem.

Bonus points would be given for:

  • Quad elements instead of triangles
  • Some way to control mesh size / refinement at features
  • Some mesh quality controls

As you may have guessed from my requirements I am looking to construct finite element meshes. These features seem pretty common across finite element software so algorithms / libraries must exist - it’s getting them into grasshopper which is hard!

The libraries I have come across so far:

  • Millipede (ticks most boxes, but is sometimes unstable, plus its wire overrides are really annoying)
  • Kangaroo mesh machine (I can’t work out how to constrain it to given points / lines)
  • Default Rhino / Grasshopper meshing (reasonable results with some subdivision, but again cannot be constrained)
  • Triangle.NET (I’ve wrapped this into a component, it’s quick and gives good elements, again cannot be constrained to points / lines, plus the licence is a bit confusing)
  • Rhino quad mesher (does not seem to suit planar surfaces)
2

Do the points/lines you want to constrain to already exist in your starting mesh as edges/vertices?
If so then you can constrain them in MeshMachine by putting these into FixV and FixV respectively.

If the points you want to constrain to don’t coincide with a mesh vertex, or the lines you want to constrain to don’t coincide with sets of edges, then you’d need to somehow adjust your mesh first so that they do.

3

Unfortunately its the second. I’d be happy to discretise my line into a sequence of points, and so the problem is how to manipulate my mesh structure to include points. Perhaps if anyone knew of a good library for doing this it would be an alternative route to a solution i.e. generate a mesh with one of the above tools and then add the required points into it.

4

Here’s one possible way of including a line in a given mesh, using mesh split. Didn’t test this approach much, so not sure how robust this is, but seems to work at least for simple cases.
remesh_fix_internal_line.gh (14.0 KB)

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2 Likes
5

For points I guess you could use ClosestMeshPoint, then
if it is on a vertex, no problem
if it is on a triangular face, split that triangle into 3, with the new point shared by all 3.
if on an edge, split both the adjacent faces into 2

6

Thanks Dan. Your example works well. I may explore the remeshing option so that I can wrap the process up in a single component.

If anyone else knows of libraries that offer this kind of meshing in a single component I’d still be interested to hear, would save me reinventing the wheel!

7

You might also want to look at this:


which can generate either triangles or quads, using 2 different external libraries.
I don’t think there’s any way with that to fix internal edges/points though

8

Thanks for the recommendation. I did look into it previously and the algorithms employed created a mesh that did not maintain connectivity to the edges of the surface, and also did not have options for including lines / points.

9

As a follow-up for anyone else who is searching, I have just found that its possible to get Triangle.NET to mesh to internal points. https://github.com/eppz/Triangle.NET

This now meets my requirements.

10

Hi,

may I ask if you could give a small guide how you did this?

I imagine you have to compile the triangle library to get the dll and reference it in VS.
Inside VS is it straight forward?May you give a pseudoCode?

Thanks in advance!

11

Sure. I’ve attached the Triangle .dll (57.8 KB) file here so you don’t have to recompile from source.

The bones of the C# code I have used is below to get it working with Rhino. It’s a bit rough but should be sufficient for you to build upon.

// Inputs
Polyline perimeter = new Polyline(); // perimeter of your mesh
List<Polyline> holes = new List<Polyline>(); // openings in your mesh
List<Point3d> pts = new List<Point3d>(); // additional points to be included on the mesh

// TO-DO - assign inputs & error check

// Main
List<Point3d> allPolPoints = new List<Point3d>();
allPolPoints.AddRange(perimeter);
foreach (Polyline h in holes)
    allPolPoints.AddRange(h);

//Perimeter
var g = new TriangleNet.Geometry.InputGeometry(perimeter.Count);

foreach (Point3d p in perimeter)
{
    g.AddPoint(p.X, p.Y);
}

for(int i = 0; i < perimeter.Count - 1; i++)
{
    g.AddSegment(i, i + 1);
}
g.AddSegment(perimeter.Count - 1, 0);
int topV = perimeter.Count;

//Holes
foreach(Polyline h in holes)
{
    foreach(Point3d p in h)
    {
        g.AddPoint(p.X, p.Y);
    }
    
    for (int i = 0; i < h.Count - 1; i++)
    {
        g.AddSegment(topV + i, topV + i + 1);
    }
    g.AddSegment(topV + h.Count - 1, topV);

    AreaMassProperties ap = AreaMassProperties.Compute(h.ToNurbsCurve());
    g.AddHole(ap.Centroid.X, ap.Centroid.Y);

    topV = topV + h.Count;
}

// Additional points
foreach(Point3d p in pts)
{
    g.AddPoint(p.X, p.Y);
}

TriangleNet.Mesh m = new TriangleNet.Mesh();

m.Triangulate(g);
m.Behavior.Quality = true;
m.Refine();

Rhino.Geometry.Mesh rMesh = new Rhino.Geometry.Mesh();

foreach(TriangleNet.Data.Vertex v in m.Vertices)
{
    Point3d p = new Point3d(v.X, v.Y, 0.0);
    rMesh.Vertices.Add(p);
}

var ts = m.Triangles;
foreach (TriangleNet.Data.Triangle t in ts)
{
    rMesh.Faces.AddFace(t.P0, t.P1, t.P2);
}

rMesh.RebuildNormals(); // I've not been super clean in how I create the Rhino mesh, this step helps clean things up!
4 Likes
12

Thanks a lot, will try it at home!