Rest Shape Optimization for Sag-Free Discrete Elastic Rods

TL;DR

This paper introduces a novel rest shape optimization framework for discrete elastic rods that ensures sag-free behavior and stable static equilibrium across various geometries and materials.

Contribution

It presents a new optimization method using Gauss-Newton and penalty techniques to determine rest shapes that prevent sagging in elastic rods.

Findings

Optimized rest shapes enable sag-free static equilibrium.

Method is effective across diverse geometries and materials.

Ensures system stability through regularized minimization.

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.