高级检索

基于水雷折纸拟合自由曲面的优化建模

Optimization Modeling for Fitting Freeform Surfaces Based on Waterbomb Origami

  • 摘要: 水雷折纸单元的形状多样性和灵活性使其能够适应不同曲面, 实现复杂模型构建. 针对优化后水雷折纸的顶点容易偏离目标表面导致模型近似不够精确, 以及水雷折纸折痕图中水雷单元面积差异较大, 增加了折痕图不规则性的问题, 提出基于水雷折纸技术的自由曲面建模方法. 在满足可展和可平坦折叠约束的前提下, 采用基于多目标优化的数值逼近方法, 使得水雷网格更精确地贴合在目标表面; 利用等面积的水雷单元构建三维模型, 减少水雷单元面积差异, 获得更加规则的折痕图. 在不同曲面上的实验结果表明, 最大距离残差在添加距离约束后均显著下降, 最大面积残差均小于1E−12, 验证了所提方法的有效性和可行性, 为基于折纸拟合自由曲面建模的研究提供了新思路和方法.

     

    Abstract: The shape diversity and flexibility of waterbomb origami units enable them to adapt to various surfaces and realize the construction of complex models. To address the issues of vertex deviation from the target surface after optimization, leading to insufficient model approximation accuracy and large area differences among waterbomb units in the crease pattern which increase its irregularity, this paper proposes a freeform surface modeling method based on waterbomb origami. Under the constraints of developability and flat-foldability, a numerical approximation method based on multi-objective optimization is employed to fit the waterbomb mesh on the target surface more precisely. Equal-area waterbomb units are used to construct 3D models, reducing area differences and producing more regular crease patterns. Experimental results on various surfaces show that the maximum distance residuals significantly decrease after introducing distance constraints, and the maximum area residuals are all less than 1E−12. These results verify the effectiveness and feasibility of the proposed method, offering new insights and approaches for freeform surface modeling based on origami.

     

/

返回文章
返回