The Jal 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 bidimensional or tridimensional spaces and many do not handle well adaptive refinement. This work presents a novel method for spatial decomposition based on simplicial meshes (the J 1 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 definition of neighbrs that allow to recover all the information on the resulting mesh via a set of rules. This way it is possible to balance the cost of storage and manipulation by calculating the needed information instead of storing it. Results additionally show good quality meshes with efficient calculation.