Combinatorial maps

This content has been copy-pasted from the previous guide. It is up-to-date but should be improved at some point.

Definition

Maps

N-dimensional combinatorial maps, noted N-map, are objects made up of two main elements:

• A set of darts, darts being the smallest elements making up the map
• N beta functions, linking the darts of the map

Additionally, we can define embedded data as spatial anchoring of the darts making up the map. While the first two elements hold topological information, embedded data gives information about the “shape” of the map (e.g. vertices position in a spatial domain).

With these elements, we can represent and operate on meshes.

Example

Operations on a combinatorial map can affect its topology, shape or both:

The specifics on how data is encoded is detailed in attribute-specific sections.