A Deformable Object Model for Virtual Manipulation Based on Maintaining Local Shapes

This paper proposes a new fundamental model of deformable objects for real-time and interactive applications. It is based on the mass-and-spring model, but in which the unit of elastic force definition for computation of dynamics is expanded from a spring to a volume element divided by the boundaries formed by mass-and-spring lattice. Displacements of the vertices of the volume element are defined to decide the elastic forces similar to the mass-and-spring model. Solving the equations of the equilibrium of internal force and moment of force derives them. As a result, proper elastic forces are operated for restoring the natural shape even if the object is rather soft and easily deformed, although they are becoming improper ones with the increase of displacement of the spring in mass-and-spring models. As the calculation is performed numerically and approximately, a method of reducing the approximation error is also presented.