高级检索

基于七折水雷及格型纹样的对称曲面逆向建模

Inverse Modeling of Symmetrical Surface based on the Seven-crease Waterbomb and Lattice Tessellations

  • 摘要: 纹样设计常用于三维折纸结构建模. 为了拓展纹样类型并提升折纸结构稳定性, 提出一种基于七折水雷及格型纹样的对称曲面逆向建模方法, 实现了三维模型与二维折痕图之间可逆展开. 首先将六折水雷纹样中心点拉伸为边形成七折水雷纹样; 然后基于七折水雷纹样拟合广义圆柱和轴对称曲面, 并对模型施加可展开、平面及边长优化; 接着将满足几何约束的七折水雷纹样模型中心边扩展为面, 生成格型纹样模型; 将构建的三维模型通过展开方式获得相应二维折痕图, 并对其刚性折叠运动进行了模拟和分析. 在建模与刚性折叠模拟上的实验结果表明, 与传统的六折水雷纹样相比, 七折水雷及格型纹样在保持其变形能力的同时降低了内部自相交风险; 所提方法为三维折纸模型的构建以及机械结构的探索提供了一种可行方案.

     

    Abstract: Tessellation design is widely used in modeling 3D origami structures. To expand tessellation types and enhance stability, a symmetric modeling method based on the seven-crease waterbomb and lattice tessellations is proposed, enabling reversible unfolding between 3D models and 2D crease patterns. Firstly, the seven-crease waterbomb tessellation is formed by stretching the center points of the six-crease waterbomb tessellation into edges. Then, generalized cylindrical and axisymmetric surfaces are approximated by the seven-crease tessellation with constraints on foldability, planarity and section. The center edges of the optimized seven-crease tessellation are expanded into surfaces to generate the lattice tessellation. The model is unfolded to obtain the crease pattern, and its rigid folding motion is simulated and analyzed. Experimental results on modeling and rigid folding simulations show that, compared to the six-crease tessellation, the seven-crease and lattice tessellations reduce the risk of internal self-intersection while maintaining the deformability. This method provides a feasible solution for constructing 3D origami models and exploring mechanical structures.

     

/

返回文章
返回