The Mathematics of Surfaces
Suppose a manufacturer wants to design a hand lotion bottle. In the past, a designer would create physical prototypes of possible bottle designs. Nowadays. the designer can sit at a computer workstation and create a three-dimensional image of the bottle, rotate the image to see it from different angles, and automatically make adjustments in the size and shape. The computer can show the bottle in various colors, it can create and position a label, it can even simulate how the bottle would look on a store shelf. At the heart of such high-tech computer graphics are mathematical equations that describe surfaces—equations that efficiently encode geometric information about the twists, turns, curves, and proportions of the shapes being represented.
This is Rosemary Chang’s specialty. She is the expert on geometric surfaces on the research staff at Silicon Graphics, in Mountain View, California, which produces state-of-the-art graphics workstations and servers used in industries and laboratories all over the world. Rosemary’s job is to continually improve and expand the mathematical methods used for computer representation of geometric surfaces.
Integrating computer-aided geometric design, analysis, and manufacturing is a major challenge for industry. For example, with the hand lotion bottle, one can run into problems in converting from the computer that created the bottle design to the computer that will cut the mold for manufacturing the bottles. “It’d be a lot easier if there were a generic way of representing information so that the various systems available were compatible with each other and so that you could move easily from design to analysis to manufacture,” Rosemary explains. “But right now we don’t have that.” She and others are working on new mathematical methods that may help to solve this problem.
Rosemary received her bachelor’s degree from New York University and her PhD from Brown University, both in applied mathematics. Before coming to Silicon Graphics in 1987, she worked at Sandia National Laboratories in Livermore, California, and at Control Data Corporation in Minneapolis.
Rosemary’s parents are natives of China and emigrated to the United States in the 1940s. She grew up in New York City with three sisters, all of whom went on to get advanced degrees. “My parents always believed in education,” she says. “When we were growing up, each daughter had a savings account. It wasn’t saving up for college, it wasn’t saving up for when you got married, it was saving up for graduate school… Education was a way that you could get a good job with prestige.”
“I always liked math because it was precise, unambiguous, and it made a lot of sense,” she recalls. “I thought the problems were fun.” Through mathematics, Rosemary has found a career in which she can see her ideas and knowledge contribute to the solution of important problems.
This brochure was published in 1991, so some information may be out-of-date.