用微分生长模拟植物花瓣卷曲，生成无自交的高质量网格。
Cabbage: A Differential Growth Framework for Open Surfaces
- 基于边细分提升分辨率，动态扩展表面实现渐进褶皱。
- 可稳定生成数百步模拟的复杂褶皱结构，网格质量高且无自交。
- 适合几何建模、数字制造与形状分析数据集构建。
我们提出 Cabbage，一种用于模拟自然界中三维开曲面（如花蕾卷曲）屈曲行为的微分生长框架。Cabbage 能生成无自交的高质量三角网格。Cabbage-Shell 通过边细分动态增加离散化精度，壳体力推动表面扩张，随时间产生褶皱。特征感知平滑与重网格化保障网格质量，校正碰撞机制有效防止紧密空间内的自碰撞。我们还提供近似版本 Cabbage-Collision 及 CAD 可用的表面生成能力。Cabbage 是首个具备此等精度与鲁棒性的开源方案，在形态表达能力、网格质量及长时间模拟稳定性上超越现有最优方法，能稳定生成大而复杂的图案。它不仅可用于计算建模、数字制造与教育，还可产出高质量、带标注的几何处理与形状分析数据。
原文摘要 · Abstract (English)
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.
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