Delynoi: an object-oriented C++ library for the generation of polygonal meshes


Free and open source C++ library for the generation of polygonal meshes on arbitrary domains, based on the constrained Voronoi diagram. It is the built-in polygonal mesh generator of the Veamy library.

  • The meshes are generated on arbitrary domains, created from user defined points. Domains have no restrictions on convexity.
  • It allows the inclusion of completely contained or intersecting holes, which are processed if required.
  • The meshes are generated from seed points, which can be read either directly from a text file, included one by one,
    or created from a number of generation rules included in the library. New generation rules can be easily included.
  • Meshes can be stored in OFF-style text files, or used directly in another program.
  • To generate the meshes, the library first computes the conforming Delaunay triangulation using Triangle; the triangulation
    is considered as a mesh that is left available for use if needed. Then, it computes the constrained Voronoi diagram.


Catalina Alvarez – B.Sc., M.Sc., Universidad de Chile.


Nancy Hitschfeld-Kahler – Associate Professor, Department of Computer Science, Universidad de Chile.

Alejandro Ortiz-Bernardin – Associate Professor, Department of Mechanical Engineering, Universidad de Chile.

Usage instructions

Delynoi is currently for Unix systems only.

  1. Download the source code and unpack it.
  2. In the root directory of Veamy, create a build/ folder.
  3. Go to test/ folder located in the root directory of Delynoi and: (a) add the main C++ file
    (say, mytest.cpp) containing your test example problem, (b) modify the CMakeLists.txt
    by changing the file name example.cpp in
    set(SOURCE_FILES example.cpp)

    by the name
    of your main C++ file (in this case, mytest.cpp)

  4. Inside the build folder and in the command line type:
    cmake .. 

    to create the makefiles. And to compile the program type:

  5. To run your example, go to the build/test/ folder and in the command line type:

Usage example

To generate a polygonal mesh, one needs to:

  1. List, in counterclockwise order, the points that define the domain and
    create the domain as a Region instance:
    std::vector square_points = {Point(0,0), Point(10,0), Point(10,10), Point(0,10)};
    Region square(square_points);   
  2. Include the required seed points on the domain, for which there are three alternatives:
    • Create the points as a list of Point instances, and call:
      std::vector seeds = {Point(5,5)};
    • With the points coordinates listed on a text file, say seeds.txt (an example is found in the
      test folder), call:
    • Decide on two generation rules (one for each axis) from the predifined list of functions (or create a new one inheriting
      following the instructions given in the manual), and create a PointGenerator instance. If required, include a noise function
      from the noise list provided. Then, call including the PointGenerator and the number of
      points on each axis:
      PointGenerator rules(functions::random_double(0,10), functions::random_double(0,10));
      int nX = 5, nY = 5;
      square.generateSeedPoints(rules, nX, nY); 
  3. Create a TriangleVoronoiGenerator instances with the points inside the domain, and the domain
    std::vector seeds = square.getSeedPoints();
    TriangleVoronoiGenerator generator (seeds, square);
  4. To obtain the Voronoi diagram, call:
    Mesh voronoi = generator.getMesh();
  5. To use the Delaunay triangulation instead of the Voronoi diagram, a different class is used, TriangleDelaunayGenerator,
    which can return the constrained Delaunay triangulation or the conforming Delaunay triangulation:
    TriangleDelaunayGenerator generator (seeds, square);
    Mesh constrained_delaunay = generator.getConstrainedDelaunayTriangulation();
    Mesh conforming_delaunay  = generator.getConformingDelaunayTriangulation();

    It is also possible to define a number of constrained segments inside the domain, that will not be flipped
    when the Delaunay triangulation is computed:

    Mesh constrained_delaunay = generator.getConstrainedDelaunayTriangulation(restrictedSegments);
  6. To print the mesh to a text file use:


Delynoi depends on two external open source libraries, whose source codes are included in the repository.


This project is licensed under the GPL License. This program is free software; it can be redistributed or modified under the terms of the GNU General Public License as published by the Free Software Foundation.


>> Latest stable version of Delynoi (7-April-2019): Delynoi v2.0

Download: Source code (zip) | Delynoi Primer (PDF manual)

GitHub: Browse the source code on GitHub

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