Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

Abstract

In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.

Application of Multiobjective Optimization Integrating Numerical and Scientific Computing in Graph Theory Coloring Algorithm

“…When solving graph coloring problems using common intelligent algorithms, there is a limitation that is limited to solving graph coloring problems with a single constraint, for example, ant colony algorithm, BP neural network algorithm, tree algorithm, etc. However, when faced with the problem of multiconstraint graph coloring, the effect of common algorithms is often unsatisfactory [15].…”