Discrete Differential Geometry and Its Applications in Design and Manufacturing

In recent years, the interplay of differential geometry, physics-based modelling, and computer graphics has led to the birth of a new subject called discrete differential geometry. This new subject investigates the differential geometric and topological properties of discrete geometric data such as meshes, graphs, and point sets. It provides an indispensable theoretical foundation for digital geometry processing and has been successfully utilized in various applications of computer graphics, such as mesh processing, graphics simulation, and computer animation. This project aims at new developments on discrete differential geometry with robust operators and its engineering applications in design and manufacturing. Both mesh-based and subdivision-based approaches will be considered. Key issues to be addressed include the development of algorithms on multi-resolution model interrogation and manipulation for NC (numerical control) tool path generation. In connection with other ongoing research on rapid tooling, some case studies will be conducted for high-speed CNC (computer numerical control) tool path generation. Major project outcomes will include new methodologies, efficient and robust algorithms for multi-resolution digital geometry processing, and NC tool path generation. The research will also advance subdivision-based modelling with new development in model property evaluation and further strengthen engineering applications of subdivision surfaces.