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GeoSpatial Terrain: Algorithms and Representations

Wm. Randolph Franklin,
RPI/ECSE and NSF/CISE/C-CR
4/12/02



1. Context




2. Agency interest

Inadequacy of current systems when playing wargames.




3. Competing data structure representations




4. TIN - Triangulated Irregular Network




5. Grid (array) of elevations




6. Mathematical Properties




7. Some Existing Gridded Terrain Representations




8. Fourier Series

Good for Electrical Signals

Unsuitable for Terrain




9. Wavelets




10. Fractals




11. Towards a Formal Math Foundation

Applicability

We could formally ask about best algorithms for

Instead of testing heuristics on test samples.

The Relevant Physics

We do lose the ability to form a linear combo of a set of basis functions.


12. Other Math Problems - Multiple Layers




13. Commercial Examples of Misaligned Layers

These are from a commercial mapping product.

Users of commercial GIS packages think that these problems are natural.


14. 50 ft contour lines cross the lake shoreline




15. Stream flows obliquely to the contours




16. Conflation of Multiple Layers from Various Sources

aka data fusion




17. How the Proper Representation Helps




18. Compression




19. Visibility Index

How much can each possible observer see?

Terrain
Visibility indices



20. Higher is not necessarily better




21. Lunar Communication - Future Visibility App

Assume two points on the moon's surface want to communicate.

Obvious solutions:




22. Viewshed

What, specifically, can a particular observer see?




23. Viewshed Error Bars




24. What do we really know about visibility?




25. Just good enough computation

If...

Then...




26. Multilevel Game Theory

  1. Red side places observers to cover as much terrain as possible.

  2. Blue side, knowing the red observers, finds areas guaranteed to be hidden.




27. Data Mining




28. Themes