Hydrographic sounding selection is the process of generalizing high-resolution bathymetry data to a more manageable subset capable of supporting nautical chart compilation or bathymetric modeling, and thus, is a fundamental task in nautical cartography. As technology improves and bathymetric data are collected at higher resolutions, the need for automated generalization algorithms that respect nautical cartographic constraints increases, since errors in this phase are carried over to the final product. Currently, automated algorithms for hydrographic sounding selection rely on radius- and grid-based approaches; however, their outputs contain a dense set of soundings with a significant number of cartographic constraint violations, thus increasing the burden and cost of the subsequent, mostly manual, cartographic sounding selection. This work presents a novel label-based generalization algorithm that utilizes the physical dimensions of the symbolized depth values on charts to avoid the over-plot of depth labels at scale. Additionally, validation tests based on cartographic constraints for nautical charting are implemented to compare the results of the proposed algorithm to radius and grid-based approaches. It is shown that the label-based generalization approach best adheres to the constraints of functionality (safety) and legibility.

We propose a data structure for d-dimensional simplicial complexes, that we call the Simplified Incidence Graph (SIG). The simplified incidence graph encodes all simplices of a simplicial complex together with a set of boundary and partial co-boundary topological relations. It is a dimension-independent data structure in the sense that it can represent objects of arbitrary dimensions. It scales well to the manifold case, i.e. it exhibits a small overhead when applied to simplicial complexes with a manifold domain, Here, we present efficient navigation algorithms for retrieving all topological relations from a SIG, and an algorithm for generating a SIG from a representation of the complex as an incidence graph. Finally, we compare the simplified incidence graph with the incidence graph, with a widely-used data structure for d-dimensional pseudo-manifold simplicial complexes, and with two data structures specific for two-and three-dimensional simplicial complexes.

We address the problem of performing spatial queries on\ud tetrahedral meshes. These latter arise in several application\ud domains including 3D GIS, scientific visualization, finite el-\ud ement analysis. We have defined and implemented a family\ud of spatial indexes, that we call tetrahedral trees. Tetrahedral\ud trees subdivide a cubic domain containing the mesh in an\ud octree or 3D kd-tree fashion, with three different subdivision\ud criteria. Here, we present and compare such indexes, their\ud memory usage, and spatial queries on them