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运筹学学报

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3D打印中的优化设计

杨周旺1,*  刘源1   

  1. 1. 中国科学技术大学数学科学学院, 合肥 230026
  • 收稿日期:2017-09-01 出版日期:2017-12-15 发布日期:2017-12-15
  • 通讯作者: 杨周旺 yangzw@ustc.edu.cn
  • 基金资助:

    中央高校基本科研业务费专项资金青年创新基金(No. WK0010460003)

Design optimization in 3D printing

YANG Zhouwang1,*   LIU Yuan1   

  1. 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2017-09-01 Online:2017-12-15 Published:2017-12-15

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摘要：

3D打印技术的兴起在许多领域掀起了新的研究热点, 《3D打印中的优化设计》应用课题针对几何处理领域中的许多相关问题做了系统性的研究，其中包括在3D 打印中通过几何模型的结构优化以节省打印材料和打印时间的问题，三维几何模型保持特征的去噪和构建问题，以及三维几何模型的序贯重建和多余分支去除问题. 相关问题中多涉及含有复杂约束的优化问题，以及压缩感知和稀疏优化问题. 本文简要总结了上述问题的研究方法，并从几何优化的角度阐述了其中运筹学原理与方法的运用，表明了运筹学工具在相关领域研究中的重要性和有效性.

关键词: 3D打印, 结构优化, 节省材料, 节省时间, 特征保持, 网格去噪, 流形构建, 曲面重建

Abstract:

The rise of 3D printing technology has stimulated a lot of hot research points in a number of research fields. The project Optimal Design in 3D Printing Applications has systematically studied many related topics in geometry processing, including saving printing material and printing time by structural optimization of 3D geometric models, feature-preserving denoising and construction of surfaces, and sequential construction and spurious sheets removal of 3D models. Many of the problems involve optimization models with complicated constraints, sparse representation and compress sensing. In this paper, we briefly summary the methods used in these problems, and reinterpret the use of operations research theories and algorithms in the perspective of geometric optimization, which indicates the importance and effectiveness of operations research tools in the study of related fields.

Key words: 3D printing, structural optimization, material saving, time saving, feature preserving, mesh denoising, manifold construction, surface reconstruction