Feynman Algorithm Implementation for Comparison with Euler in a Uniform Elastic Two-Layer 2D and 3D Object Dynamic Deformation Framework in OpenGL with GUI

TL;DR

This paper implements the Feynman algorithm for real-time softbody simulation in OpenGL, comparing its performance with Euler integration, and introduces a GUI for enhanced control and analysis of elastic two-layer objects.

Contribution

The paper presents a novel implementation of the Feynman algorithm within a flexible framework, enabling detailed comparison with Euler integrator and real-time user interaction.

Findings

Feynman algorithm shows different performance characteristics compared to Euler.

Enhanced framework allows real-time deformation and interaction with complex elastic objects.

GUI facilitates fine control over simulation parameters for comparative analysis.

Abstract

We implement for comparative purposes the Feynman algorithm within a C++-based framework for two-layer uniform facet elastic object for real-time softbody simulation based on physics modeling methods. To facilitate the comparison, we implement initial timing measurements on the same hardware against that of Euler integrator in the softbody framework by varying different algorithm parameters. Due to a relatively large number of such variations we implement a GLUI-based user-interface to allow for much more finer control over the simulation process at real-time, which was lacking completely in the previous versions of the framework. We show our currents results based on the enhanced framework. The two-layered elastic object consists of inner and outer elastic mass-spring surfaces and compressible internal pressure. The density of the inner layer can be set differently from the density of the outer layer; the motion of the inner layer can be opposite to the motion of the outer layer. These special features, which cannot be achieved by a single layered object, result in improved imitation of a soft body, such as tissue's liquid non-uniform deformation. The inertial behavior of the elastic object is well illustrated in environments with gravity and collisions with walls, ceiling, and floor. The collision detection is defined by elastic collision penalty method and the motion of the object is guided by the Ordinary Differential Equation computation. Users can interact with the modeled objects, deform them, and observe the response to their action in real-time and we provide an extensible framework and its implementation for comparative studies of different physical-based modeling and integration algorithm implementations.