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The key issue in constraint dynamics is to model the particles obey Newton’s laws, and at the same time the geometric constraints. Metaball Constraints Currently, the modeling process of metaball-constraint deformations is lack of dynamic interaction via touch sensation. Our objective is to incorporate intuitive haptic interaction with constrained metaballs during deformation process. In our proposed haptic-constraint modeling, first the constraint skeleton Ci attached with haptic input is attracted to the target location on the object to be deformed.

E. (2M + D∆t ) , is constant, so we can solve the linear equation (3) efficiently during the iteration process only with one time of LU-decomposition of the coefficient matrix. Soft-Touch Haptics Modeling of Dynamic Surfaces Figure 3. For the local solution of linear system, we regard all vertices in the ρ rings around the vertex v as the influence region of a force applied to v, denoted by Reg(v), where ρ is some integer. Let Dis(⋅,⋅) denote the distance of two vertices in graph theory. , vk-1vk} gives the shortest path connecting v0 with vk, then Dis(v0, vk) = k.

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