Mathematician puts the curves in fonts, computer graphics

by David F. Salisbury

The next time you view or print a fancy font on your computer, you might thank Larry Schumaker.

Photo by Phonethip M. Liu
Larry Schumaker

With his fine features, dark hair pulled back in a small ponytail and black T-shirt, Schumaker could easily be taken for an artist or musician. Actually, he is a mathematician who has played a key role in developing a field called spline theory that modern computers use to reproduce fonts in a wide variety of styles and sizes.

The usefulness of spline functions is by no means limited to fonts. They help turn the large quantities of data that diagnostic instruments like MRI produce into images that doctors can use to make accurate prognoses. They add realism to video games and Hollywood special effects. They are incorporated in the commercial software used to design automobiles, airplanes and a host of other products. They are used to compress graphic images and video so that they can be stored on computer disks and transmitted over the Internet.

"Mathematics is a broad umbrella and includes all kinds of things that people can be doing," said Schumaker, the Stevenson Professor of Mathematics at Vanderbilt. "I've always enjoyed doing a kind of mathematics that is close to being applicable, if not directly applied."

The application of spline functions to computer fonts is a case in point. Early computers stored letters as simple dot patterns. Of course, there were only a handful of fonts and type sizes from which to choose. As users began demanding more fonts in a broader range of point sizes, as well as the ability to display and print them in any orientation, this simple method of representing fonts became increasingly unwieldy.

Enter spline theory. Spline functions -- otherwise known as piecewise polynomial functions -- are simple mathematical equations that trace the shape of complex curves and surfaces. Polynomials are simple functions that are easy to process in the computer, but they are only accurate when reproducing simple shapes. So spline theory breaks down complex curves and surfaces into small pieces, describes each piece with a polynomial and reassembles them seamlessly to produce an accurate representation of the entire surface. While this may seem more complicated than representing a font or surface graphically, it produces objects that the computer can shrink, enlarge, rotate and stretch quickly and efficiently.

"Larry's been one of the leading figures in spline theory for the last 30 years," said Ronald DeVore, a prominent applied mathematician from the University of South Carolina at Columbia. "He has done fundamental work not only in developing the theory of splines, but also in applying them."

DeVore was among 155 mathematicians from 33 countries who visited Vanderbilt the week of May 17 to attend an international symposium held in honor of Schumaker's 60th birthday.

"In mathematics you've got a number of strange characters," said DeVore, who has known Schumaker for 30 years and considers him a close friend. "But Larry is straightforward and honest: The kind of guy that you would like to be around regardless of the mathematics."

When he was growing up in a small town in South Dakota, Schumaker had no thought of becoming a mathematician. He worked with his brothers in his father's furniture store and planned to go into electrical engineering.

That was his intention when he enrolled in the South Dakota School of Mines. "But I switched to mathematics about halfway through my undergraduate education," Schumaker recalled. "I got tired of doing all the lab work and simply found mathematics more fascinating."

After getting his bachelor's degree from the School of Mines, Schumaker went to Stanford University for graduate study. There he hooked up with the eminent mathematician Samuel Karlin, who had become an enthusiastic proponent of a new theory invented by the late I. J. Schoenberg of the University of Wisconsin.

Not surprisingly, spline functions became the subject of Schumaker's doctoral thesis. "I was fortunate to get into the area in the 1960s at a very early stage," he says. "They have turned out to be a very useful tool, so I have remained faithful to the subject throughout my career. Almost all of my papers are related to spline functions in one way or another."

In addition to solving theorems and developing practical applications for the theory, Schumaker authored Spline Functions: Basic Theory, which has become a standard reference in the field. The book, which was published in 1980, took him 10 years to write. He has spent the last 10 years working on a companion volume, which he hopes to finish within the next year.

Schumaker is not only well known for his mathematical contributions, but also because of his work with students, his role as the editor of several mathematics-related journals and as the organizer of a number of international conferences, said Manfred V. Golitschek of Würzburg University in Germany.

What's more, Schumaker makes all these activities seem effortless, said DeVore. "Most mathematicians, if you go into their office, it is a mess -- papers on the floor, papers on the chairs. But Larry's is impeccably neat. He has tremendous powers of organization."

In 1979, Schumaker shocked many of his colleagues by quitting his tenured position at the University of Texas and returning to South Dakota to run for the U.S. Senate. Although he had very little financial backing and no name recognition, the mathematician challenged veteran politician George McGovern in the 1980 Democratic primary.

"I was interested in politics, and I was concerned about where the country was headed. In contrast to other countries, there are very few academics in the U.S. Congress, and I thought it would be nice if I could change that," Schumaker said.

"It turns out that I did very well, not enough to win the primary, but I got 40 percent of the vote," he said. "I think that proves it was a winnable race. It was just a matter of getting more money to increase my name recognition."

"I was blown away when Larry decided to run for the Senate," recalled fellow spline theorist Carl de Boor at the University of Wisconsin-Madison. "He went at it hammer and tongs. He gave up his job. He goes and runs. I was amazed."

This illustrates an aspect of Schumaker's character that greatly impresses de Boor: his single-mindedness. "You don't find many mathematicians who have the ability to make up their mind to do something and go ahead and do it like Larry has done," de Boor said.