A population analysis for hierarchical data structures
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Storing a collection of polygons using quadtrees
ACM Transactions on Graphics (TOG)
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Tools for Triangulations and Tetrahedrizations
Scientific Visualization, Overviews, Methodologies, and Techniques
Speeding up construction of PMR quadtree-based spatial indexes
The VLDB Journal — The International Journal on Very Large Data Bases
External Memory Management and Simplification of Huge Meshes
IEEE Transactions on Visualization and Computer Graphics
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
A Hierarchical Data Structure for Representing the Spatial Decomposition of 3-D Objects
IEEE Computer Graphics and Applications
Morphological analysis of terrains based on discrete curvature and distortion
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Spatial indexing on tetrahedral meshes
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
A spatial approach to morphological feature extraction from irregularly sampled scalar fields
Proceedings of the Third ACM SIGSPATIAL International Workshop on GeoStreaming
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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We propose the PR-star octree as a combined spatial data structure for performing efficient topological queries on tetrahedral meshes. The PR-star octree augments the Point Region octree (PR Octree) with a list of tetrahedra incident to its indexed vertices, i.e. those in the star of its vertices. Thus, each leaf node encodes the minimal amount of information necessary to locally reconstruct the topological connectivity of its indexed elements. This provides the flexibility to efficiently construct the optimal data structure to solve the task at hand using a fraction of the memory required for a corresponding data structure on the global tetrahedral mesh. Due to the spatial locality of successive queries in typical GIS applications, the construction costs of these runtime data structures are amortized over multiple accesses while processing each node. We demonstrate the advantages of the PR-star octree representation in several typical GIS applications, including detection of the domain boundaries, computation of local curvature estimates and mesh simplification.