Kantevektoren

Kantevektoren, also known as edge vectors or half-edge vectors, are a concept used in computer graphics and computational geometry to represent the relationship between edges and vertices in a mesh. Specifically, a kantevektor is associated with an edge and points from one of its endpoints to the other. This directional nature allows for more sophisticated data structures and algorithms to be developed for mesh manipulation and analysis.

In a typical mesh representation, each vertex has a position, and each face is defined by a set of vertices. Edges are implicitly defined as the connections between adjacent vertices on a face. Kantevektoren provide an explicit representation of these edges with a defined direction. This direction is crucial for operations that require traversing the mesh in a specific order, such as normal vector calculations or boundary finding.

The use of kantevektoren often arises in half-edge data structures. In this structure, each edge is represented twice, once for each direction. This redundancy allows for efficient traversal in both directions along an edge, as well as access to adjacent faces and vertices. For example, starting from a vertex, one can follow a kantevektor to an adjacent vertex, then use information associated with that edge to find the next edge and vertex belonging to a specific face. This makes kantevektoren fundamental to algorithms that rely on local mesh connectivity.