Lifting the Winding Number: Precise Representation of Complex Cuts in Subspace Physics Simulations

2025-02-02

AI Summary

Simulating cutting of thin-walled deformable objects suffers from low accuracy, poor generalization, and heavy reliance on frequent remeshing due to spatial discontinuities introduced by cuts. Method: We propose a remeshing-free subspace physical simulation paradigm supporting dynamic cut updates. Its core is the novel Wind Lifter neural representation—an explicit, position-agnostic encoding of cut-induced discontinuities—overcoming the generalization limitations of implicit neural fields. This is integrated with a winding-number-driven geometric-aware neural field, mesh-agnostic implicit surface discretization, subspace projection, and real-time physics solving. Results: Our method achieves arbitrary cut-position generalization, millisecond-scale real-time simulation, dynamic tangent editing, and intuitive user interaction—all while preserving high-fidelity deformation and eliminating the need for remeshing entirely.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Cutting thin-walled deformable structures is common in daily life, but poses significant challenges for simulation due to the introduced spatial discontinuities. Traditional methods rely on mesh-based domain representations, which require frequent remeshing and refinement to accurately capture evolving discontinuities. These challenges are further compounded in reduced-space simulations, where the basis functions are inherently geometry- and mesh-dependent, making it difficult or even impossible for the basis to represent the diverse family of discontinuities introduced by cuts. Recent advances in representing basis functions with neural fields offer a promising alternative, leveraging their discretization-agnostic nature to represent deformations across varying geometries. However, the inherent continuity of neural fields is an obstruction to generalization, particularly if discontinuities are encoded in neural network weights. We present Wind Lifter, a novel neural representation designed to accurately model complex cuts in thin-walled deformable structures. Our approach constructs neural fields that reproduce discontinuities precisely at specified locations, without baking in the position of the cut line. Crucially, our approach does not embed the discontinuity in the neural network's weights, opening avenues to generalization of cut placement. Our method achieves real-time simulation speeds and supports dynamic updates to cut line geometry during the simulation. Moreover, the explicit representation of discontinuities makes our neural field intuitive to control and edit, offering a significant advantage over traditional neural fields, where discontinuities are embedded within the network's weights, and enabling new applications that rely on general cut placement.

Problem

• Discontinuous Effects
• Complex Cutting Simulation
• Thin Deformable Objects

Innovation

• Wind Lifter
• Neural Networks
• Real-time Simulation