DURHAM, N.C. -- Geometry is universal. It pervades the warp and woof of nature, and is an essential tool for engineers, architects and cartographers.
Given the power of the computer, computerized geometry has naturally become an essential tool for engineers and scientists designing jetliners, automobiles and even computer circuitry. Computer geometry is also essential to creating the molecular models used by chemists and drug designers. And the discipline lies at the heart of geometric imaging technologies that range from satellite pictures of Earth's surface to medical CAT scans of lungs and livers.
The problem is that, like people speaking different languages, computers and geometry do not mesh well together. Although computers can rapidly add, multiply, divide or subtract numbers with definite values, they have problems doing other mathematical manipulations important to geometry, said Duke University's Pankaj Agarwal.
One example is calculating pi, the infinitely indivisible ratio between a circle's circumference and its diameter. "I cannot precisely write pi on a computer," said Agarwal, a Duke associate professor of computer science who specializes in geometric computing. "So as a result you have some round-off errors in any computations you do. Not only do those give you inaccurate results. They may crash the program."
To address such problems, on Oct. 18 and 19 Duke will host a broad-based Workshop on Computational Geometry that will feature invited speakers from the Massachusetts Institute of Technology, Purdue University, two Army Research Laboratory facilities, and the Electric Boat Co. There will also be shorter presentations from other leading U.S. and foreign researchers in the field.
Sessions will run from 8:15 a.m.-5:30 p.m. on Oct. 18, and 8:30 a.m.-4:45 p.m. on Oct. 19, in the auditorium and adjoining Hall of Science at Duke's Levine Science Research Center. They are being organized by Duke's new Center for Geometric Computing, an Army Research Office funded venture that was begun in July to encourage multi-disciplinary research on campus.
The workshop is also intended to spur dialogue among academic, industrial and military researchers who encounter geometric computation in their fields.
While scientists and engineers have already managed to finesse computers through some of their geometric shortcomings, those who study computer systems see enormous room for improvement. And so does the Army Research Office, which has contributed $4.5 million to Multi University Research Initiative (MURI) Center for Geometric Computing consortium involving Brown and Johns Hopkins universities as well as Duke.
Duke's own center, an outgrowth of that larger center, is being co-directed by Agarwal, John Harer, professor and chairman of Duke's mathematics department, and Jeffrey Vitter, Lehrman professor and chairman of the computer science department. One big goal is to spawn joint research in the university's computer science, chemistry and mathematics departments as well as at its School of Engineering and Nicholas School of the Environment.
"We intuitively understand what shape is," said Michael Prisant, a Duke assistant professor of computer science and assistant research professor of chemistry who uses computers to study how shapes of molecules relate to their functions. "If we present human infants with a number of differently shaped toys they would probably be able to group them fairly easily. But it's actually a very difficult thing to do on a computer."
Prisant is hoping the center can develop new computational rules -- or "algorithms" -- to help his group better define the shapes of molecular models they draw on computer screens with a "ray-casting" technique pioneered at Duke.
George Stetten, an assistant research professor in biomedical engineering, also encounters geometric problems as he studies new ways to display three-dimensional images of living hearts on computer screens. The images are created with ultrasound, a technology employing computers to process reflected sound waves to reveal the shapes of internal organs.
"Anyone working with such multi-dimensional data who wants to develop new methods for processing and displaying that information quickly runs into issues concerning computational geometry," Stetten said.
Stetten, a medical doctor turned engineer, is now working on a Ph.D. in the computer visualization area and attends seminars at the Duke Center for Geometric Computing. "It's a very fertile field," Stetten added. "There's a lot of underlying work that needs to be done."
Meanwhile, the Nicholas School of the Environment's Landscape Ecology Laboratory uses computers to download the huge amounts of information that remote sensing satellites beam down from orbit.
The satellite signals are converted into geometrically rooted data that can be incorporated into geographic information systems (GIS). Those are map-like displays of landscapes and statistics valuable for both environmental research and teaching.
The Nicholas School lab is also beginning a collaboration with Duke's Center for Geometric Computing to help devise quicker ways to process all that information. "One of the areas we hope the center can help with is coming up with more efficient algorithms," said Patrick Halpin, an assistant professor of the practice of landscape ecology.
"They're interested in newer, faster and more efficient analysis techniques and computational methods. Our interest is putting these to use on real world applications."
Agarwal said remote-sensing satellite images involve billions of units of computer data that can arrive faster than machines can process them. Such a data avalanche creates what is called an "input-output" bottleneck that is another major headache in geometric computing.
Other "large-data-set" challenges of that kind includes the military's interest in creating virtual reality simulations of ongoing battles to give commanders of the future better control over the chaos of combat. "Right now, we don't have the technology to do that by the techniques of plane geometry," Agarwal said.
NASA also is interested in computer geometry to create high-resolution models of climate and vegetational changes over the entire northeastern United States. "You need new paradigms and new technologies to do that," Agarwal added. "You have to come up with really new algorithms to handle really large data."
Topics to be discussed at the Oct. 18-19 workshop will include geometrical computational problems that arise in GIS, in building a model of an entire nuclear-powered submarine, and in creating simulations of artillery attacks and their repercussions.
More conference information is available on the center's web page at