ISSN 1000-1239 CN 11-1777/TP

计算机研究与发展 ›› 2017, Vol. 54 ›› Issue (3): 549-556.doi: 10.7544/issn1000-1239.2017.20150911

• 人工智能 • 上一篇    下一篇



  1. (中国科学技术大学数学科学学院 合肥 230026) (
  • 出版日期: 2017-03-01
  • 基金资助: 

Stable Equilibrium Optimization for 3D Printed Objects

Wu Fenfen, Liu Ligang   

  1. (School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026)
  • Online: 2017-03-01

摘要: 3D打印日渐流行,赋予大众创造物体的能力.首先通过计算机中3D建模软件构造3D数字模型,再借助3D打印加以制造.虚拟环境中无物理规则的特点使得模型千姿百态,但是通过3D打印之后发现物体无法平衡站立.首次提出3D打印物体的稳定平衡优化问题,针对这一问题,研究不倒翁的原理,提出稳定平衡优化算法,使得物体达到稳定平衡.具体做法为先将物体体素化,迭代式从水平、垂直方向进行逐体素的挖空,选取最佳的挖空方式;对于个别极端例子,再通过对底部小范围内的修改来达到稳定平衡.逐体素的启发式挖空策略避免了挖空可能出现的悬浮、自相交等问题;底部局部小范围的修改也保证了物体的形状基本不变,该方法的可行性通过多个例子的成功优化得到证明.

关键词: 稳定平衡, 优化, 3D打印, 体素化, 不倒翁

Abstract: 3D printing is increasingly popular, giving the public the ability to create objects. First of all, a 3D digital model is constructed by 3D modeling software, and then manufactured via 3D printer. Virtual environment with no physical rules makes the model stand with diverse gesture, but failed in the real world. We put forward the stable equilibrium optimization problem for 3D printed object for the first time. To solve this problem, we propose a stable equilibrium optimization algorithm based on the principle of the tumbler, which can make the object achieve stable equilibrium. Specifically, we voxelize the object iteratively from horizontal and vertical direction voxel by voxel until obtaining the best carving result, measured by an equation; for some exceptions, we continue to modify the bottom within an acceptable small range to achieve stable equilibrium. This novel heuristic carving strategy avoids possible problems such as suspension, self-intersection, etc. Modification of the bottom part within the small range also ensures that the shape of the object is basically unchanged. The feasibility of the proposed method is demonstrated by several examples of successful optimization. The limitation is that multiple material is not considered in this paper for the complexity of operation, which is to be explored in the future.

Key words: stable equilibrium, optimization, 3D printing, voxelization, tumbler