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Efficiency Issues in Multi-resolution Terrain Modeling

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. Terrain Models. Terrain data

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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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