How to create mesh refinement 1?

[kabukunz]

Hello there. Thank you for this tool. I'm toying with it and it's very cool.
I'd like to recreate the mesh in the picture MeshRefinement_1.png, that is:

But there's no example. How to do that?

On a more general basis, I'd like to understand how to generate a mesh with best possible regularity and simmetry...

[FloSewn]

Hey there,

thank you for these kind words and for your interest in this little project :-)

The mesh given above is actually just a simple mesh of six triangles and subsequent refinements, where each triangle is split into three quads.

Attached you find the parameter file to reproduce the figure above.

Again, thank you so much for you interest! :-)

Greetings
Flo

SymmetricalRefinement.para.txt

[kabukunz]

Aww, thank you for your prompt reply.
So basically here it is the code generating that refinement

/*
* This file is part of the TQMesh library.  
* This code was written by Florian Setzwein in 2022, 
* and is covered under the MIT License
* Refer to the accompanying documentation for details
* on usage and license.
*/

#include <iostream>
#include <cassert>

#include <TQMeshConfig.h>

#include "run_examples.h"

#include "Vec2.h"
#include "Log.h"

#include "Vertex.h"
#include "Edge.h"
#include "Domain.h"
#include "Mesh.h"
#include "Smoother.h"

using namespace CppUtils;
using namespace TQMesh::TQAlgorithm;

/*********************************************************************
* This example covers the generation of a simple triangular mesh
*********************************************************************/
void run_example_11()
{
  /*------------------------------------------------------------------
  | First, we define the size function. This function describes
  | the size of the mesh elements with respect to their location 
  | in the domain. In this case, we use a constant size of 0.35
  ------------------------------------------------------------------*/
  UserSizeFunction f = [](const Vec2d& p) 
  { 
    return 0.5; 
  };

  /*------------------------------------------------------------------
  | Next, we need to define the domain. It requires the size function
  | as argument.
  ------------------------------------------------------------------*/
  Domain domain { f };

  /*------------------------------------------------------------------
  | Now we define the exteriour boundary of the domain. The boundary 
  | itself is created from four connected edges, which in turn are 
  | defined by the four vertices v0, v1, v2 and v3.
  | Our final exterior boundary will look like this:
  |
  |                   v3                 v2
  |                     *---------------*
  |                     |               |
  |                     |               |
  |                     |               |
  |                     |               |
  |                     |               |
  |                     |               |
  |                     |               |
  |                     *---------------*
  |                    v0                v1
  |
  | Notice the orientation of the edges (v0,v1), (v1,v2), (v2,v3) 
  | and (v3,v0). 
  | Exterior boundary edges must always be defined in counter-
  | clockwise direction.
  ------------------------------------------------------------------*/
  Boundary&  b_ext = domain.add_exterior_boundary();

  Vertex& v0 = domain.add_vertex(  0.0,   0.0,   1.0,  1.0 );
  Vertex& v1 = domain.add_vertex(  1.0,   0.0,   1.0,  1.0 );
  Vertex& v2 = domain.add_vertex(  1.0,   1.0,   1.0,  1.0 );
  Vertex& v3 = domain.add_vertex(  0.0,   1.0,   1.0,  1.0 );

  b_ext.add_edge( v0, v1, 1 );
  b_ext.add_edge( v1, v2, 1 );
  b_ext.add_edge( v2, v3, 1 );
  b_ext.add_edge( v3, v0, 1 );
  
  /*------------------------------------------------------------------
  | In the following lines, the mesh will be initialized, as well 
  | as its advancing front structure (which is nescessary for the 
  | mesh generation)
  | After that, we simply triangulate the domain.
  ------------------------------------------------------------------*/
  Mesh mesh { domain };
  mesh.init_advancing_front();
  mesh.triangulate();

  /*------------------------------------------------------------------
  | In order to obtain a mesh that only consists of quad elements,
  | we will refine the mesh
  ------------------------------------------------------------------*/
  mesh.refine_to_quads();
  mesh.refine_to_quads();
  mesh.refine_to_quads();
  mesh.refine_to_quads();

  /*------------------------------------------------------------------
  | Here we use a smoother, in order to improve the mesh quality.
  | The smoothing is applied for four iterations. 
  ------------------------------------------------------------------*/
  Smoother smoother {};
  smoother.smooth(domain, mesh, 4);

  /*------------------------------------------------------------------
  | Finally, the mesh is exportet to a file in VTU format.
  ------------------------------------------------------------------*/
  std::string source_dir { TQMESH_SOURCE_DIR };
  std::string file_name 
  { source_dir + "/auxiliary/example_data/Example_11" };
  LOG(INFO) << "Writing mesh output to: " << file_name << ".txt";

  mesh.write_to_file( file_name, ExportType::txt );

} // run_example_11()

Sounds like using sort of templates, like ones used in tilings... interesting. I have to check this.
Thank you again