用于复杂几何形状定向生长的时空圆盘堆积
Spatiotemporal Disk Packing for Directed Growth of Complex Geometries
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中文总结 AI 辅助
研究利用圆盘堆积算法及最大间隙算法，通过控制圆盘中心和半径实现复杂二维形状的定向生长，生成高覆盖率堆积并转化为时空指令，经实验验证，为生长的几何与动力学建立简单联系。
中文摘要 AI 辅助
生长复杂形状需要控制生长起始位置和随时间的演变方式。本文引入一种使用圆盘堆积算法生长规定二维形状的几何框架。目标几何形状由圆盘填充，其中心确定生长起始位置，半径确定各区域生长时长。允许的圆盘大小受生长速度、启动每个生长事件所需时间和并行启动次数等物理过程限制。为生成物理上可实现的堆积，引入最大间隙算法（LGA），它用满足几何和动力学约束的最大圆盘依次填充目标形状中最大的剩余间隙。结果表明该方法可为多种几何形状生成高覆盖率堆积，所得堆积可直接转换为时空堆积指令，且能通过实验实现，为生长的几何形状和动力学提供了简单联系。
英文摘要
Growing complex shapes requires control over both where growth begins and how it evolves in time. Here, we introduce a geometric framework for growing prescribed 2D shapes using a disk packing algorithm. In this approach, a target geometry is filled by disks whose centers define where growth is initiated and whose radii define how long each region is allowed to grow. The allowed disk sizes are constrained by the physics of the process, including the growth velocity, the time required to initiate each growth event, and the number of initiations that can occur in parallel. To generate physically realizable packings, we introduce the Largest Gap Algorithm (LGA), which sequentially fills the largest remaining gaps in a target shape with the largest disk that satisfies both geometric and kinetic constraints. We show that this method produces high coverage packings for a variety of geometries and that the resulting packings can be directly converted into spatiotemporal packing instructions. We then demonstrate that these instructions can be realized experimentally using multi-point initiation of frontal polymerization in viscosified dicyclopentadiene (DCPD) resin using CO$_2$ laser. Our results show that complex shapes can be grown by programming a small number of local initiation events, providing a simple connection between geometry and dynamics of growth.
