Frontiers of Computer Science

, Volume 11, Issue 2, pp 332–346 | Cite as

Continuous optimization of interior carving in 3D fabrication

  • Yue Xie
  • Ye Yuan
  • Xiang ChenEmail author
  • Changxi Zheng
  • Kun Zhou
Research Article


In this paper we propose an optimization framework for interior carving of 3D fabricated shapes. Interior carving is an important technique widely used in industrial and artistic designs to achieve functional purposes by hollowing interior shapes in objects. We formulate such functional purpose as the objective function of an optimization problem whose solution indicates the optimal interior shape. In contrast to previous volumetric methods, we directly represent the boundary of the interior shape as a triangular mesh. We use Eulerian semiderivative to relate the time derivative of the object function to a virtual velocity field and iteratively evolve the interior shape guided by the velocity field with surface tracking. In each iteration, we compute the velocity field guaranteeing the decrease of objective function by solving a linear programming problem. We demonstrate this general framework in a novel application of designing objects floating in fluid and two previously investigated applications, and print various optimized objects to verify its effectiveness.


computer graphics 3D printing interior carving shape optimization Eulerian semiderivative 


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We would like to thank the reviewers for their constructive comments. Xiang Chen is partially supported by NSFC (Grant No. 61303136) and the Fundamental Research Funds for the Central Universities. Kun Zhou is partially supported by NSFC (Grant No. 61272305) and National Program for Special Support of Eminent Professionals of China.

Supplementary material

11704_2016_5465_MOESM1_ESM.ppt (980 kb)
Supplementary material, approximately 979 KB.


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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yue Xie
    • 1
  • Ye Yuan
    • 1
  • Xiang Chen
    • 1
    Email author
  • Changxi Zheng
    • 2
  • Kun Zhou
    • 1
  1. 1.State Key Lab of CAD&CGZhejiang UniversityHangzhouChina
  2. 2.Columbia UniversityNew YorkUSA

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