Elastically deformable models

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.

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Index Terms

• Computing methodologies

  • Artificial intelligence

    • Computer vision

      • Image and video acquisition

        • 3D imaging

  • Computer graphics

    • Animation

    • Shape modeling

      • Parametric curve and surface models

      • Volumetric models

• Mathematics of computing

  • Mathematical analysis

    • Differential equations

      • Partial differential equations