Elastically deformable models

TLDR

Elasticity theory describes deformable materials such as rubber, cloth, paper, and flexible metals, and elastically deformable models respond naturally to applied forces, constraints, ambient media, and obstacles. The study employs elasticity theory to construct differential equations modeling the time‑dependent behavior of non‑rigid curves, surfaces, and solids. The models are dynamic, and realistic animation is achieved by numerically solving the underlying differential equations. The approach unifies the description of shape and motion.

Abstract

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.