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Research

Summary

Geometry has been my overriding interest since high school in the 1960s. Geometry is the "branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids" 1. The Geo in geometry is from the Greek Γη meaning, ''earth, ground, land''. 2. My major recently concluded project was Geo*, a DARPA–funded project for representing and operating on terrain, that is, elevation.

My big long-term unsolved problem is to devise a mathematics of terrain, which would respect its physical properties. To date, I've been nibbling around the edges.

One recently ended project3 attempted to predict how erosion occurs in levee failure by overtopping, and, after a failure, to reverse-simulate what happened.

A earlier major project was Geo*, funded by DARPA, studied representing and operating on terrain, that is, elevation.

I've applied the same underlying principles in Computational Geometry producing algorithms useful for large datasets, mostly in 3D, and usually implemented.

Both topics are applications of my long term theme of emphasizing small, simple, and fast data structures and algorithms. Note that efficiency in both space and time can become more important as machines get faster. This research is applicable to computational cartography, computer graphics, computational geometry, and geographic information science.

16 PhD students (7 currently employed at a college), and 68 masters students have been graduated under my advisement, (names and theses).

My research has been externally funded by the National Science Foundation under Grants ENG-7908139, ECS-8021504, ECS-8351942, CCF-9102553, CCF-0306502, DMS-0327634, CMMI-0835762 and IIS-1117277 by DARPA/DSO, via the NGA, under the GeoStar program, by the US Army Topographic Engineering Center, and by IBM, Sun Microsystems, and Schlumberger-Doll Research.

Many of the algorithms have been implemented. The code is available for nonprofit research and education. RPI Computer graphics group

  • A 2-slide summary of my research is here.
  • A good summary talk is this:

Geometric Operations on Millions of Objects.

  • An overview talk of the future of the field is my keynote talk at GeoInfo 2013, XIV Brazilian Symposium on GeoInformatics.
  • Some research results that I particularly like are here.

Research Details

 

1 (Merriam–Webster dictionary)

2 The American Heritage� Book of English Usage

3 Cutler, Zimmie, Franklin. NSF CMMI-0835762: CDI-Type I: Fundamental Terrain Representations and Operations