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Efficiency Issues in Multi-resolution Terrain Modeling

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This study addresses efficiency challenges in multi-resolution terrain modeling, focusing on dynamic resolution adaptation to user needs while balancing accuracy and data size. By analyzing regular and irregular multi-resolution models, including the Multi-Triangulation (MT) approach, we compare data structures and query efficiency. Modifications like vertex insertion and simultaneous triangle bisection optimize mesh refinement and decimation processes. The research highlights storage costs and query performance across various resolution strategies, culminating in a comprehensive summary of findings and future directions.

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Efficiency Issues in Multi-resolution Terrain Modeling

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  1. Efficiency Issues in Multi-resolution Terrain Modeling Leila De Floriani * Paola Magillo Department of Computer Science University of Genova, Genova (Italy) * currently at the University of Maryland, College Park, MD

  2. Terrain Models • Terrain data • points in the plane • height values • Terrain model • triangle mesh connecting the points • linear interpolation of heights

  3. Multi-Resolution • Large-size data sets • high storage space and processing time multi-resolution • Dynamically adapt resolution to user needs • tradeoff accuracy / size

  4. Regular and Irregular Multi-Resolution Models • Data on a grid / scattered data • Regular / irregular multi-resolution models • Both are instances of a Multi-Triangulation • Compare efficiency of data structures and of queries

  5. Changing the Resolution of a Mesh • Modification:two alternative sets of triangles covering a region at lower / higher resolution • Can adapt resolution by playing with modifications

  6. The Multi-Triangulation (MT) • A base mesh • A set of modifications • A partial order (dependency relation) M2 depends on M1 iff M2 changes some triangles changed by M1

  7. Irregular MT: Vertex-Based MT • Data: scattered • Modification: vertex insertion • Built while refining a mesh through vertex insertion (VI) OR • Built while decimating a mesh through vertex removal • single vertex (VR) • set of independent vertices (IVR)

  8. Regular MT: Hierarchy of Right Triangles (HRT) • Data: on a regular grid • Modification: simultaneous bisection of two adjacent right triangles

  9. Data Structure for Vertex-Based MT • Partial order • As a directed acyclic graph • Modifications • modification M = two triangle meshes (M-,M+) • triangles of M+ uniquely defined • triangles of M- must be encoded • Coordinates and heightvalues of vertices • Approximationerrors of triangles

  10. Data Structure for Vertex-Based MT • Encode the triangles of M- • anchor edge • bit stream (depth-first traversal of a tree of triangles) 10 00 11 11

  11. Data Structure for HRT • Each triangle uniquely identified by a location code • Partial order and modifications are retrieved from location codes and not stored • Height values of vertices • Approximationerrors of triangles

  12. Comparison:Storage Costs of the Data Structures n = number of data points • Full-resolution mesh = 54n bytes • Vertex-based MT • in theory = 33n bytes • in practice depends on construction process (VI, VR, IVR) • HRT = 6n bytes

  13. Comparison: Queries to Extract a Mesh • Uniform resolutionon the whole domain • Variable resolution focused in a window Worse (more triangles) Plot: triangles Better (fewer triangles) error

  14. Comparison: Uniform Resolution • Best = VI • Motivation: error-driven construction strategy VR IVR HRT VI HRT VR IVR VI Mount Marcy Devil Peak

  15. Comparison: Uniform Resolution HRT 22045 triangles VI 16208 triangles

  16. Comparison: Uniform Resolution HRT 3648 triangles VI 1951 triangles

  17. Comparison: Variable Resolution • Best = HRT Worst = VR • Motivation: smaller modifications, fewer dependency links VR VI IVR HRT VR VI IVR HRT Mount Marcy Devil Peak

  18. Comparison: Variable Resolution HRT 1614 triangles VI 2072 triangles

  19. Summary

  20. The End

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