Catching Up With Chris Hoffmann
Writer(s): Kristyn Childres
Professor Chris Hoffmann’s career has followed an unconventional path. In academia, it’s often considered wise to keep working in the same area – to build upon one’s research, continue publishing and develop a reputation – but Hoffmann has switched research areas – twice.
After joining the Purdue faculty in 1976, Hoffmann worked in the area of compiler construction and nonprocedural programming languages. But in 1984, during a summer visit to Cornell University while working with John Hopcroft, he became deeply interested in graph isomorphism – an interest so deep that it completely changed the direction of his career.
“It wasn’t strategic – it was what was interesting. My new projects present themselves to me as things that I become very interested in, even obsessed with,” Hoffmann said. “The world wants you to follow a certain, predictable trajectory. But I always did what interested me – and that has brought me success.”
Hoffmann’s second major research area was graph isomorphism, the computational problem of determining whether two graphs are isomorphic. Hoffmann and Hopcroft studied how group theory, a branch of mathematics that studies algebraic structures known as groups, applies to graph isomorphism.
“When group theory was first invented in the early 1900s, mathematicians considered it to be the least useful branch of mathematics,” Hoffmann said. “But today, group theory is used to understand symmetries of crystals, viruses, subatomic particles, error-correcting codes, and many other areas.”
At the time Hoffmann and Hopcroft used group theory to calculate whether two graphs were isomorphic, fewer than 30 computer scientists worldwide investigated group theory computationally.
During an extended stay at Cornell from 1984-1986, Hopcroft and Hoffmann changed research directions and began studying how to model shapes using computer-aided design (CAD). This work has applications in mechanical engineering, like the architecture of various product designs – from large things like ships, airplanes, or cars to something much smaller, such as the shape of a plastic bottle of laundry detergent you might buy at the store.
Once represented by computer, the next step is to prototype and simulate products and physical systems. Early on, Hoffmann and Hopcroft developed this application of CAD with their “Project Newton,” which simulated rigid body mechanics. Interestingly, rigid body simulation is used in the movies: in one of the Star Wars movies, one of the characters wears bangles. How these bangles rattle in response to arm movement was computed with a simulation like the ones done by the Newton system.
Computers can only work with a limited set of numbers, and this fact often led to subtle mistakes in shape modeling that crashed early CAD systems because their root cause was not understood. Hoffmann’s work on this issue has impacted all areas where shapes are represented, manipulated, and reasoned about by computers. He and his collaborators also developed the basic algorithms and solvers that allow virtually all modern CAD systems to help construct a shape – for example, constructing a shaft from a cylinder when a user specifies length and radius, and placing it in the emerging shape using geometric constraints.
In 2002, Hoffmann worked with colleagues from civil engineering to create a simulation of the 9/11 attacks – both the Pentagon and the World Trade Center. They created a video that became the most seen video ever produced by Purdue. The website that made it available to the world was visited more than any other website at Purdue at the time.
Hoffmann served as director of the Rosen Center for Advanced Computing (now ITaP Research Computing), receiving a $6 million grant from the United States Department of Energy to build the Northwest Indiana Computational Grid (NWICG) in 2006, a network that raised the bar of computational capability in Indiana by connecting Purdue’s West Lafayette campus to Purdue Calumet in Hammond (now Purdue Northwest) and Notre Dame in South Bend.
In 2011, Hoffmann was awarded the Pierre Bezier award by the Solid Modeling Association for his lasting contributions to the field, including numerous papers and a monograph in the field.
“If you ask my colleagues about my work, it depends on when they knew me,” Hoffmann said. “That happens a lot with me: people are surprised about my previous work in programming languages or graph isomorphism. You won’t find anyone else who made this shift.”
“The shifts in my work haven’t been strategic from the point of view of the world,” Hoffmann said. “It has been something more selfish: what’s interesting? My work has to excite me and interest me, and the topics that have excited me have always been wide-ranging. They present themselves as things that I become intrigued by and spend a lot of time with. So it’s not that the appeal of what I was originally working on wore off – it’s more about the allure of the new. It’s fun to learn something new.”
What interests Chris Hoffmann now is topological interlocking, a concept proposed by an Australian researcher in fracturing of materials. The topologically interlocking building blocks such as cubes or tetrahedra are laid out in a flat sheet in such a way that you can’t pull up or push out one block without removing the ones around it. The roots of such arrangements go back to the Renaissance when vaulted ceilings were a hot engineering topic.
With his student, Hoffmann is exploring the geometry of topological interlocking configurations, moving the concept from the plane to more complex surfaces. This work could be of interest to the military and to civil engineers, as the material could be used to create panels for structures like parking garages that would be thin, yet exhibit superior strength.