基于几何约束的三维折叠结构交互式建模研究

In recent years, foldable structures have received extensive attention in various fields, inspiring lots of novel research and applications. Some modeling methods for foldable structures have been proposed. However, due to the strict geometric constraints of the foldable structure, the existing modeling methods are still lacking, and the exploration of the variations of the folding structure is still insufficient. This situation will not only fail to meet the design needs of users but also limits the further development of research and applications based on foldable structures..In this project, we focus on proposing effective modeling methods for 3D foldable structures based on the consideration of geometric constraints. We innovatively propose three aspects: (1) modeling method of 3D foldable structures based on the design of the crease pattern; (2) modeling method of foldable structures based on interactive 3D editing; (3) approximating complex model based on origami tessellations, in order to efficiently realize the modeling of the 3D foldable structures. In addition, we also combine geometric constraints with the consideration of the practical application. Based on mathematics, geometry, and computer-aided design, this project aims to explore the variations of foldable structures, promoting multi-disciplinary integration, and further expanding the application of foldable structures in agricultural equipment, military, transportation, biological, aerospace, and other industries.

近年，折叠结构得到了各领域的广泛关注，启发了大量的新型研究成果，并涌现了一些面向折叠结构的造型方法。然而，由于折叠结构需要满足严格的几何约束，导致现有的折叠结构造型方法仍然比较缺乏，对折叠结构多样性的探索仍然不足。这不仅满足不了用户的设计需求，也将限制基于折叠结构的研究与应用的进一步发展。本项目聚焦前沿，针对折叠结构的造型问题，在考虑几何约束的前提下，提出有效的造型方法。我们创新性地提出三个方面：（1）基于展开图作图的三维折叠结构的造型方法；（2）基于交互式三维编辑的折叠结构的造型方法；（3）基于折纸纹样的复杂模型近似的造型方法，来高效地实现折叠结构的建模。此外，我们还独辟蹊径地将几何造型与应用实际结合起来。本项目以数学、几何、计算机辅助设计为基础，探索折叠结构多样性为目标，力求促进多学科的融合，进一步拓展折叠结构在农业设备、军事、运输、生物、航空航天等行业中的应用。

三维折叠结构是一种能够展开到具有特定功能的工作状态，同时能够收纳到较小折叠状态的结构。近年，折叠结构受到各个领域学者的广泛关注，启发了大量新型工程应用。然而，折叠结构有着很强的几何约束，用户很难正确地、高效地实现建模工作。本项目基于折叠结构的几何约束，探索并研发了三维折叠结构的交互式建模关键技术。本项目提出了具有广义圆柱和轴对称结构特征的水雷折纸纹样逆向建模方法，同时采用矩形填充方式，实现了水雷衍生纹样的逆向建模工作；本项目提出了采用非折叠水雷折纸及其变体单元，实现了复杂广义圆柱曲面的近似建模工作，有效地避免了模型局部凹凸褶皱的波纹状建模问题；本项目提出了基于水雷折纸纹样近似三维曲面的逆向建模方法，创新地展示了基于混合水雷折纸纹样的折纸近似模型的构建。本项目以数学、几何、计算机辅助设计为基础，探索了折叠结构的多样性，展示了大量未被充分探索的结果。我们的工作不仅促进了折纸作为一种手工艺术形式的发展，并将在例如航空航天、机器人、超材料等领域，启发更多的基于折叠结构的新型应用成果。