## Tuesday July 26/4:15/Grande Ballroom

Invited Presentation 5

**Chair: Rosemary E. Chang, Silicon Graphics Computer System**
# The Mathematics of Surface Modeling: Impacts of Design and Manufacturing

In industry today, product designers often model complex surfaces such as sheet-metal panels, plastic containers and optical lenses on CAD systems. These mathematical surfaces then become the starting point for important downstream applications including computer-aided engineering (for example, finite element structural analysis) and manufacturing (for example, NC programming). Despite the importance of manufacturing applications, the concerns related primarily to product design have usually driven the specific mathematics and computational approaches used to represent surfaces. Consequently, surfacing mathematics developed for product design has not always produced representations good for manufacturing. The speaker will describe how design and manufacturing issues have together defined the mathematics and computer algorithms used to represent sheet-metal panels and related manufacturing die surfaces at General Motors.
**James C. Cavendish, Department of Mathematics, General Motors Research and Development Center**

James Cavendish is a principal research scientist in the mathematics department at General Motors Research and Development Center. He earned his M.A. in mathematics from Columbia University and his Ph.D. in mathematics from University of Pittsburgh. His research interests include surface modeling, numerical methods in computational fluid dynamics, and automatic, finite element-mesh generation.