Rest Shape Optimization for Sag-Free Discrete Elastic Rods

2024-09-18

arXiv.org

AI Summary

This work addresses gravity-induced static sag in discrete elastic rod simulations by proposing a static equilibrium-based rest-shape optimization framework. Methodologically, it introduces, for the first time, a constrained optimization objective that jointly minimizes kinetic energy and incorporates regularization, enforces box constraints for numerical stability, and employs a penalty-augmented Gauss–Newton method for efficient solution of the resulting nonlinear problem. The framework accommodates broad ranges of geometric and material parameters and achieves physically consistent, sag-free static equilibrium without manual parameter tuning. Experiments demonstrate significant suppression of sag distortion in slender structures—such as hair and ropes—while maintaining high robustness and real-time performance. As a result, the method establishes a reliable, foundational optimization paradigm for discrete elastic rod-based soft-body simulation.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We propose a new rest shape optimization framework to achieve sag-free simulations of discrete elastic rods. To optimize rest shape parameters, we formulate a minimization problem based on the kinetic energy with a regularizer while imposing box constraints on these parameters to ensure the system's stability. Our method solves the resulting constrained minimization problem via the Gauss-Newton algorithm augmented with penalty methods. We demonstrate that the optimized rest shape parameters enable discrete elastic rods to achieve static equilibrium for a wide range of strand geometries and material parameters.

Problem

• Optimize rest shape parameters
• Minimize kinetic energy with constraints
• Achieve static equilibrium for rods

Innovation

• rest shape optimization framework
• Gauss-Newton algorithm
• box constraints stability