Discrete differential geometry : An applied introduction

We describe a discrete model for the dynamics of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by a curved undeformed configuration. Previously such thin shell models required complex continuum mechanics formulations and correspondingly complex algorithms. We show that a simple shell model can be derived geometrically for triangle meshes and implemented quickly by modifying a standard cloth simulator. Our technique convincingly simulates a variety of curved objects with materials ranging from paper to metal, as we demonstrate with several examples including a comparison of a real and simulated falling hat. This chapter is based on the publication by Eitan Grinspun, Anil Hirani, Mathieu Desbrun, and Peter Schröder which appeared in the Proceedings of the Symposium for Computer Animation 2003, and on subsequent collaborations with the group of Denis Zorin at New York University and Zoë Wood at Cal Poly San Luis Obispo.