Problem
Research questions and friction points this paper is trying to address.
limbless locomotion
geometric shape optimization
soft body simulation
differential geometry
non-self-intersecting motion
Geometric Shape Optimization for Limbless Locomotion
🤖 AI Summary
This work addresses the challenge of high-fidelity motion simulation for limbless, deformable organisms—such as snakes—in computer graphics and soft robotics. The authors propose a differential-geometry-based optimization framework that models slender soft bodies as three-dimensional parametric curves. Shape representation is achieved through a Fourier–Chebyshev polynomial basis, while physically plausible and self-intersection-free configurations are enforced via bending and torsion energy constraints. Realistic visual rendering is subsequently obtained by interpolating from the optimized curve to a surface mesh. The method demonstrates strong robustness and generalization in complex environments, significantly outperforming existing approaches in producing more realistic and higher-quality simulations of limbless locomotion.
📝 Abstract
The simulation of locomotion in limbless, deformable organisms remains a challenging problem across computer graphics, soft robotics, and computational modeling. In this work, we present a novel differential-geometric framework for modeling the motion of slender soft bodies, such as snakes. The body is represented as a three-dimensional parametric curve using a Fourier-Chebyshev polynomial basis. Motion is computed by solving an optimization problem that determines the interaction between the curve and its environment by estimating polynomial coefficients. To ensure physically plausible and non-self-intersecting behavior, bending and torsional energy terms are incorporated into the formulation. The resulting curve is then used to drive a surface representation via interpolation, enabling realistic visualization analogous to skinning techniques. We evaluate the proposed approach across a range of complex scenarios and parameter settings to demonstrate its robustness and versatility. Comparative analysis with state-of-the-art methods indicates that our approach achieves improved simulation quality and generates more physically realistic motion.
Innovation
Methods, ideas, or system contributions that make the work stand out.
differential-geometric framework
Fourier-Chebyshev basis
shape optimization
limbless locomotion
non-self-intersecting deformation
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