Surface vertices located further than REffector from the center of effector remain unaffected. The effector influence results in external forces acting on in-range vertices. Typically the effector-induced force is inversely proportional to the distance between vertex and the center of effector:
DS = SEffector – S
Fnew = EffectorStrength · DS/|DS|, |DS| < REffector
Fext = Fext + Fnew
When simulating more or less complete physical system one can account for surface resistance by updating total force acting on effector:
FTotalEffector = FTotalEffector – Fnew
Models of common surfaces
Based on the described 2D surface model different common surfaces can be represented by varying surface parameters:
Setting damping constant to 1 will produce infinite oscillations generated by a single effector. Deformation pattern will never be the same. This might be a good idea for infinite water waves modeling for seascapes.
Typically a deformable surface has some fixed vertices, i.e. vertices that can not be displaced from their original location. Such fixed vertices correspond to surface edges or to attachment edges / points. Seashore and curtains are examples of fixed edges and fixed attachment points respectively.
Trees and vegetation can be modeled as a hierarchy of surfaces with cylinder / cone global topology and stiff rubber (elasticity > 1, damping < 1) properties, where individual cylinders correspond to branches, stems or trunks. Root and attachment edges must be marked as fixed points. Particle effectors that simulate wind can be applied to such ‘rubber’ trees to produce realistic grass fields or woods experience.
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