1. Applied Mathematics 1 Distributed visualization of terrain models How to get the whole world into a coffee mug... Rune Aasgaard

2. Applied Mathematics 2 Where to put the workload? Do everything at the server Requires a powerful server... …and fast network connection......but simple client. Render in the client Reduces load on server and network… …smooth interactive movement actually possible… …but requires a smart and complex client... …and more sophisticated hardware.

3. Applied Mathematics 3 Where to put the data? Client terrain database Near graphics system Fast updating from server data Limited size Some support for simple analysis Server terrain database Huge data volume Fast query access No traversal of data Integration of new and improved data sets?

4. Applied Mathematics 4 Level-of-Detail Triangulation Consists of: A coarse base triangulation: T 0 A set of refinement operations:  T i Results in: A set of triangulations: T i View dependent expansion of client data structures: Only show what is necessary for generating an image Use screen-space error tolerance Approximation error estimates for each refinement operation

5. Applied Mathematics 5 Client data structures Should support the graphics system Triangle strips 3D coordinates Surface normals Texture coordinates Map to a set of texture tiles Portability - Java and Java3D

6. Applied Mathematics 6 Client data structures Update with data from server Start with coarse base triangulation Request data from server when: Area becomes visible More detail is required (viewpoint moved in) Reduce to coarser level when: Area becomes invisible Less detail is required (viewpoint moved out)

7. Applied Mathematics 7 Server data structures Can be huge! Whole earth, 30” grid (DTED Level 0): 933.120.000 points! Whole earth, 3” grid (DTED Level 1): 93.312.000.000 points! Luckily, 2/3 of the earth is ocean Major parts of the land is relatively flat Can benefit from data simplification and compression

8. Applied Mathematics 8 Server data structures Server responds to client requests: in: Position out: Elevation and Elevation approximation error Queries are expected to be: chunked localized in area and resolution level

9. Applied Mathematics 9 Binary Triangle Trees Hierarchy of right-isosceles triangles Related to Lindstrom triangulations and the ROAM algorithm

10. Applied Mathematics 10 Binary Triangle Trees Simple data structures simplifies network streaming Regular refinement pattern fits well with texture tiles simple integer coordinates maps easily to regular quad trees But…. requires more triangles for representing complex objects than irregular triangulations

11. Applied Mathematics 11 Approximation error spheres One sphere for each vertex Radius = Approximation error / angular resolution If the viewpoint is inside sphere, display vertex

12. Applied Mathematics 12 Zooming in - Scandinavia

13. Applied Mathematics 13 Zooming in - Scandinavia

14. Applied Mathematics 14 Zooming in - The Oslo fjord

15. Applied Mathematics 15 Zooming in - The Oslo fjord

16. Applied Mathematics 16 Zooming in - Tønsberg

17. Applied Mathematics 17 Zooming in - Tønsberg

18. Applied Mathematics 18 San Francisco - bay area

19. Applied Mathematics 19 Islands in the sun

20. Applied Mathematics 20 Oslo fjord - elevation color coding

21. Applied Mathematics 21 Oslo fjord - elevation color coding