1. SpaDaGIS 2003 1 Efficiency Issues in Multi-resolution Terrain Modeling Leila De FlorianiPaola Magillo Leila De Floriani * Paola Magillo Department of Computer Science University of Genova, Genova (Italy) * currently at the University of Maryland, College Park, MD

2. SpaDaGIS 2003 2 Terrain Models  Terrain data points in the plane height values  Terrain model triangle mesh connecting the points linear interpolation of heights

3. SpaDaGIS 2003 3 Multi-Resolution  Large-size data sets  high storage space and processing timemulti-resolution  Dynamically adapt resolution to user needs  tradeoff accuracy / size

4. SpaDaGIS 2003 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. SpaDaGIS 2003 5 Changing the Resolution of a Mesh  Modification:  Modification: two alternative sets of triangles covering a region at lower / higher resolution  Can adapt resolution by playing with modifications

6. SpaDaGIS 2003 6 The Multi-Triangulation (MT) base mesh  A base mesh modifications  A set of modifications partial order  A partial order (dependency relation) M2 depends on M1 iff M2 changes some triangles changed by M1

7. SpaDaGIS 2003 7 Irregular MT: Vertex-Based MT  Data  Data: scattered  Modification  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. SpaDaGIS 2003 8 HRT Regular MT: Hierarchy of Right Triangles (HRT)  Data  Data: on a regular grid  Modification  Modification: simultaneous bisection of two adjacent right triangles

9. SpaDaGIS 2003 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  Coordinatesheightvalues  Coordinates and height values of vertices  Approximation  Approximation errors of triangles

10. SpaDaGIS 2003 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. SpaDaGIS 2003 11 Data Structure for HRT location code  Each triangle uniquely identified by a location code  Partial order and modifications are retrieved from location codes and not stored  Height values  Height values of vertices  Approximation errors  Approximation errors of triangles

12. SpaDaGIS 2003 12 Comparison: Storage Costs of the Data Structures n = number of data points  Full-resolution mesh  Full-resolution mesh = 54n bytes  Vertex-based MT in theory = 33n bytes in practice depends on construction process (VI, VR, IVR)  HRT  HRT = 6n bytes

13. SpaDaGIS 2003 13 Comparison: Queries to Extract a Mesh  Variable resolution  Variable resolution focused in a window error triangles Worse (more triangles)  Uniform resolution  Uniform resolution on the whole domain Better (fewer triangles) Plot:

14. SpaDaGIS 2003 14 Comparison: Uniform Resolution  Best = VI  Motivation: error-driven construction strategy VR IVR HRT VI Mount Marcy Devil Peak HRT VR IVR VI

15. SpaDaGIS 2003 15 Comparison: Uniform Resolution HRT 22045 triangles VI 16208 triangles

16. SpaDaGIS 2003 16 Comparison: Uniform Resolution HRT 3648 triangles VI 1951 triangles

17. SpaDaGIS 2003 17 Comparison: Variable Resolution  Best = HRT Worst = VR  Motivation: smaller modifications, fewer dependency links Mount Marcy VR VI IVR HRT VR VI IVR HRT Devil Peak

18. SpaDaGIS 2003 18 Comparison: Variable Resolution HRT 1614 triangles VI 2072 triangles

19. SpaDaGIS 2003 19 Summary Data distribution Space required wrt the mesh at the maximum resolution LOD Queries Vertex- based anyabout halfbetter at a uniform resolution Right triangles on a gridabout 1/9better at a variable resolution

20. SpaDaGIS 2003 20 The End