* A {@link IMesh} is a set of {@link IFace}, their half-edges {@link IHalfEdge}, vertices {@link IVertex<P>} and points {@link P}
* A {@link IMesh} is a set of {@link IFace}, their half-edges {@link IHalfEdge}, vertices {@link IVertex} and points {@link P}
* defining a geometry. It also is a factory for those geometric base elements: points, vertices, half-edges and faces. The user should use one mesh
* for exactly one geometric and the user should never create any base element without calling its mesh. Furthermore, the user is responsible for the
* correctness of the mesh definition e.g. no overlapping edges. There are some classes for automatic mesh generation like
* {@link org.vadere.geometry.mesh.triangulation.triangulator.ITriangulator} or other factory methods like {@link IMesh#createSimpleTriMesh}
* </p>
* <p>It uses the half-edge data structure to store all information and is a generic interface to provide different implementations such as:
It uses the half-edge data structure to store all information and is a generic interface to provide different implementations such as:
* <ul>
* <li>A pointer based version which implements a doubled-linked-list data structure {@link org.vadere.geometry.mesh.gen.PMesh}</li>
* <li>An index based version which implements an array data structure {@link org.vadere.geometry.mesh.gen.AMesh}</li>
* </ul>
* </p>
* <p>
* It should be impossible to create faces, edges, and vertices of the mesh without using the mesh i.e. IMesh is a factory for faces, edges and vertices.
* A boundary can be a hole or the border. A hole is surrounded by faces and the border is the infinite large face representing the space which is not
* iterate over the list {@link List} while changing elements in the mesh. The mesh offers a large set of different iterators and streams to iterate over all neighbouring
* faces of a face, vertices of a vertex, edges of a vertex or over all edges / vertices / points of a face.
* </p>
* <p>
* We define as base elements: points {@link P}, vertices {@link V}, half-edges {@link E} and faces {@link F}.
* <ul>
* <li>
* point {@link P}: </br>
* point {@link P}:
* A point is a container object which can be identified by its 2-D coordinates (x,y) and is part of a vertex {@link V}. A point has no reference to
* any other base element of the mesh data structure.
* </li>
* <li>
* vertex {@link V}: </br>
* vertex {@link V}:
* A vertex is the end node / point of a half-edge. Each vertex has exactly one distinct point {@link P}. One can access the point
* of a vertex in O(1). A vertex has also a 1 to 1 relation to a half-edge and the half-edge of a vertex can accessed in O(1) time. Furthermore, it has
* a reference to one arbitrary of its half-edges (half-edges ending in it). If the vertex is at the boundary (hole or border) the half-edge should be
* its half-edge and extracting from the half-edge the face.
* </li>
* <li>
* half-edge {@link E}: </br>
* half-edge {@link E}:
* A half-edge is part of a full-edge i.e. the half-edge and its twin fully define the full-edge. Each half-edge has a predecessor
* and a successor and a twin half-edge {@link E} which can be accessed in O(1). Furthermore, each half-edge is part of exactly one face {@link F} and ends
* in exactly one vertex {@link V} both can be accessed in O(1) time. As one can see the half-edge has the most amount of references (5).
* </li>
* <li>
* face {@link F}: </br>
* face {@link F}:
* A face can be a interior face i.e. a simple polygon, a hole (also a polygon but representing empty space) or the border i.e. the infinite
* face which represents all the space which is not represented by any finite face. An arbitrary half-edge {@link E} can be accessed in O(1).
