The J₁^a triangulation: An adaptive triangulation in any dimension

Spatial sampling methods have acquired great popularity due to the number of applications that need to triangulate portions of space in various dimensions. One limitation of the current techniques is the handling of the final models, which are large, complex and need to register neighborhood relationships explicitly. Additionally, most techniques are limited to Euclidean bi-dimensional or tri-dimensional spaces and many do not handle adaptive refinement well. This work presents a novel method for spatial decomposition based on simplicial meshes (the J₁^a triangulation) that is generally defined for Euclidean spaces of any dimension and is intrinsically adaptive. Additionally, it offers algebraic mechanisms for the decomposition itself and for indexing of neighbors that allow to recover all the information on the resulting mesh via a set of rules. With these mechanisms it is possible to save storage space by calculating the needed information instead of storing it.