(in WR FranklinResearch)

My research interests since high school have centered on geometry, including graphics, cartography, and efficient implementations thereof. A recent major theme was GeoStar, a DARPA-funded project for representing and operating on terrain, that is, elevation. Recent successes, with the assistance of my students and collaborators, include the following.

1. Using ODETLAP, an overdetermined extension of a Laplacian PDE, to compress the terrain about a factor of 100 while minimizing the elevation error. This technique has several other applications, such as fitting a surface from a set of nested curved contours so that the contours are not visible in the surface, and so that local maxima can be inferred.
ODETLAP built on my Triangulated Irregular Network (TIN) program, which can process a grid of 10,000x10,000 elevations to a piecewise triangular approximation on a laptop. This method, like everything listed here, operates in memory, usually on a laptop. This makes these programs much faster than those requiring secondary storage. Unlike some other TIN programs, mine is incremental, and therefore sorts the points in order of importance. Therefore they can be used to progressively transmit the surface. This current TIN program is an extension my 1973 version, which was the first TIN implementation in cartography or GIS.
2. Siting hundreds of observers, e.g., border guards, to cover the terrain, then planning a minimal cost smuggler's path to avoid them.

to extend the terrain compression algorithm so that the slope is accurate to within 2°. That is, the slope computed on the restored terrain should match the slope of original terrain within 2°. That means that if the elevation posts are on a 30 meter grid, then the elevation deltas should be accurate within 1 meter, altho the elevations themselves might drift somewhat. A secondary goal is that, in addition to RMS elevation error, "features" of the terrain should be preserved.

A good first paper is #10, presented at 2007 ACM-GIS in Seattle.

Here is a good summary Geo* talk (7/2010); Videos in talk: 1, 2, 3.

# Public Publications / Presentations

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Student theses

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 Compressing terrain elevation datasets, Metin Inanc, PhD, Computer Science, May 2008. Thesis. (:row:) (:celli# align=right:) Parallel terrain compression and reconstruction, Jared Stookey, Master of Science, Computer and System Engineering, Dec 2008. Thesis. (:row:) (:celli# align=right:) Representation, compression and progressive transmission of digital terrain data using over-determined Laplacian partial differential equations Zhongyi Xie, Master of Science, Computer Science, May 2008. Thesis. (:row:) (:celli# align=right:) Evaluating and compressing hydrology on simplified terrain, Jon Muckell, Masters, Computer and Systems Engineering, April 2008. Thesis. (:row:) (:celli# align=right:) Path planning and slope representation on compressed terrain, Dan Tracy, PhD, Computer Science, May 2009. Thesis.

# Personnel

## Faculty

Who What
Dr Marcus A V Andrade, Universidade Federal de Viçosa, Brazil Visited RPI from April 2007 to April 2008 sponsored by the government of Brazil. Continuing to collaborate.
Dr Barbara M Cutler Computer Graphics, assistant director of GeoStar project at RPI
Dr W Randolph Franklin PI
Dr Frank Luk Numerical analysis; moved to Hong Kong to be Vice-President (Academic) of Hong Kong Baptist University

## Students

Who What
Dr Metin Inanc ODETLAP etc.
You Li bathymetry
Jon Muckell Hydrology
Jake Stookey Adapting ODETLAP to the massively parallel IBM BG/L machine in RPI's CCNI.
Chris Stuetzle Fitting slopes with ODETLAP. Transitioned to our newer CDI project.
Dr Dan Tracy Path planning and siting
Zhongyi Xie ODETLAP etc. Graduated, May 2008 with M.Sc.
Eddie Lau Tsz Yam bathymetry

# Video

1. Video by Dan Tracy showing the path planning

# Press and Blog Mentions

## Inside RPI

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 RPI Press release, 10/31/2005 (:row:) (:celli# align=right:) RPI School of Engineering Press Release (:row:) (:celli# align=right:) Rensselaer School of Engineering News (:row:) (:celli# align=right:) Improving Terrain Maps, Rensselaer Alumni Magazine Winter 2005-06

## Outside RPI

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 Better terrain maps of Earth... and beyond, in Roland Piquepaille's Technology Trends, 5 nov 2005 (:row:) (:celli# align=right:) ZDNet, 11/5/2005 (:row:) (:celli# align=right:) Surfwax Government News (:row:) (:celli# align=right:) Defence Talk, 11/1/2005 (:row:) (:celli# align=right:) Advanced Imaging (no longer online) (:row:) (:celli# align=right:) ACM Technews 7(862), 11/2/2005 (:row:) (:celli# align=right:) Interview on WGY AM-810 radio, 11/3/2005

# Commercialization

In 2007.2, two SBIRs hit the street that were clearly based on my research.

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 That led to two phase I awards: (:row:) (:celli# align=right:) A07-126 Optimal Intervisibility Site Selection. The solicitiation cited me four times. That led to the phase I award W9132V-08-C-0005 Optimal Intervisibility Site Selection to Toyon Research Corp.

(Unfortunately) I have no connection to any of those companies.

The fact that someone in the ARO considers this work important enough to issue solicitations to extend it says that DARPA is succeeding in having Geo* research transition to the Army.