Cabbage: A Differential Growth Framework for Open Surfaces

2025-04-25

AI Summary

This work addresses the challenge of simulating large-deformation 3D buckling of natural open surfaces—such as curled petals—where existing methods struggle with stability and geometric fidelity. We propose the first open-source differential growth framework specifically designed for open surfaces. Methodologically, it integrates edge-subdivision-driven adaptive discretization, thin-shell mechanical modeling, feature-aware smoothing and remeshing, and corrective collision detection to enable robust simulation of buckling deformations exceeding one hundred time steps. Compared to prior approaches, our framework significantly improves morphological fidelity, triangle mesh quality, and robustness against self-intersection. It generates self-intersection-free, CAD-ready high-precision surfaces and geometrically annotated datasets. This represents a threefold advancement in open-surface buckling modeling: enhanced morphological expressiveness, superior mesh quality, and unprecedented numerical stability.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds

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

We propose Cabbage, a differential growth framework to model buckling behavior in 3D open surfaces found in nature-like the curling of flower petals. Cabbage creates high-quality triangular meshes free of self-intersection. Cabbage-Shell is driven by edge subdivision which differentially increases discretization resolution. Shell forces expands the surface, generating buckling over time. Feature-aware smoothing and remeshing ensures mesh quality. Corrective collision effectively prevents self-collision even in tight spaces. We additionally provide Cabbage-Collision, and approximate alternative, followed by CAD-ready surface generation. Cabbage is the first open-source effort with this calibre and robustness, outperforming SOTA methods in its morphological expressiveness, mesh quality, and stably generates large, complex patterns over hundreds of simulation steps. It is a source not only of computational modeling, digital fabrication, education, but also high-quality, annotated data for geometry processing and shape analysis.

Problem

• Model buckling behavior in 3D open surfaces
• Generate high-quality triangular meshes without self-intersection
• Provide stable simulation for large complex patterns

Innovation

• Differential growth framework for 3D open surfaces
• Feature-aware smoothing and remeshing ensures quality
• Corrective collision prevents self-collision effectively