Pre-existing codebase
I was provided with a substantial amount of pre-existing code by
Vincent Chabannes, my supervisor. This codebase includes a comprehensive framework for
constructing, manipulating, and exporting meshes. The key components of
this framework are defined across several files, including point.hpp
,
mesh.hpp
, mesh.cpp
, meshio.hpp
, and meshio.cpp
.
1. Overview of the mesh framework
The relationships between the main classes involved in mesh construction and manipulation are illustrated in the following UML diagram:

At the core of this framework is the Point
class, defined in point.hpp
, which
inherits from Eigen::Matrix
. This class serves as the foundation for
geometric points in the mesh. Derived from Point
, the MeshPoint
class
represents specific points within the mesh structure.
Mesh entities are represented by classes such as MeshEdge
, MeshTriangle
,
MeshQuadrangle
, and MeshTetrahedron
, which are defined in mesh.hpp
and
mesh.cpp
. These entities are fundamental in defining the edges, faces, and
volumes within the mesh.
The Mesh
class acts as the container and manager of these entities, handling
the overall structure, operations, and transformations applied to the terrain
mesh.
Import and export functionalities, which are crucial for handling mesh data in
different formats like STL and MSH, are encapsulated
in classes defined in meshio.hpp
and meshio.cpp
. These processes are
illustrated in the following UML diagram:

2. Key components and their roles
-
MeshPoint
: Represents a 3D point with coordinates (x, y, z). This class includes methods to manipulate these points, such as applying affine transformations and accessing or modifying individual coordinates. -
MeshEdge
: Represents an edge within the mesh, connecting twoMeshPoint
instances. This class can compute the length of the edge based on the Euclidean distance between its endpoints. -
MeshTriangle
andMeshQuadrangle
: These classes represent triangular and quadrangular polygonal entities, respectively, within the mesh. They provide methods for calculating the area, managing connected edges, and determining the normal vectors for the surfaces they represent. -
Mesh
: The central class that encapsulates all mesh entities (MeshPoint
,MeshEdge
,MeshTriangle
,MeshQuadrangle
, andMeshTetrahedron
). TheMesh
class supports operations such as merging multiple meshes, applying transformations, and managing markers for different mesh regions. It plays a crucial role in ensuring the integrity and coherence of the mesh structure during generation and manipulation. -
ExporterMeshGmsh
: Handles the export of mesh data in the Gmsh format. This class was essential for converting the generated meshes into a format suitable for visualization and further processing, a task that was central to my work during this internship.
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[img:dt] Delaunay triangulation. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_circumcircles_vectorial.svg)
-
[img:dt-centers] Delaunay triangulation with all the circumcircles and their centers. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_circumcircles_centers.svg)
-
[img:dt-voronoi] Delaunay triangulation and its Voronoi diagram. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_Voronoi.svg)
-
[img:constrained-mesh] Pierre Alliez, Senior Researcher and Team Leader at Inria, Image provided during personal communication. 2024.
-
[img:constrained-refined-mesh] Pierre Alliez, Senior Researcher and Team Leader at Inria, Image provided during personal communication. 2024.