Evolutionary optimization of mass-spring models

Abstract

With present available solutions the interactive simulation of flexible parts in Virtual Reality (VR) applications is still a problem. Due to missing possibilities for the physically correct representation of deformation characteristics the informative capability of such simulations is reduced clearly. Considering the deformation of flexible parts is advantageous for a lot of applications like dynamic assembly/disassembly simulations or essential for virtual surgery simulations. Discrete approaches for simulations like mass-spring models are computationally efficient and can handle large deformations. Therefore they are suitable for real-time simulations, hence often used in interactive deformation simulations. There are however a few drawbacks concerning this model. The behaviour of this model is dependent on mesh resolution and topology. The main problem is to find suitable parameters for the spring elements. There is no analytic solution for direct distribution of material properties in triangle or tetrahedral meshes. One approach to address the problem of finding appropriate mesh parameters is to use learning algorithms like simulated annealing, genetic algorithms or neural networks. Our method to identify the spring constants and simultaneously optimize the topology of the mesh is based on evolutionary algorithms. On this behalf, we combined functions for estimation, selection, recombination, and mutation inspired by biological evolution, which we adopted on a set of initialized meshes. Our method is suitable for triangle and tetrahedral meshes. Physically plausible deformation behaviour can be obtained by the optimized models within a certain scope of load. Compared to reference deformations, the initial deviation can be reduced by approximately 90% applying the optimization process.