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.
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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.
Yue Xie received his BS in computer science from Jiangnan University, China in 2008. He is currently a PhD student in computer science at Zhejiang university, China. His research focuses on computer-aided design.
Ye Yuan received his BS in computer science from Zhejiang University, China in 2015. From September 2015, He became a master student in computer science at Carnegie Mellon University, USA. His research interests include physically based simulation, rendering and animation.
Xiang Chen received his PhD in computer science from Zhejiang University (ZJU), China in 2012. He is currently an assistant professor in the College of Computer Science and Technology, ZJU. His research interests include fabrication-aware design, image analysis/editing, shape modeling/retrieval and computer-aided design.
Changxi Zheng received his PhD in computer science from Cornell University, USA in 2012. He is currently an assistant professor in Computer Science Department in Columbia University, USA. His research interests include computer graphics, scientific computing and robotics.
Kun Zhou is a Cheung Kong Professor in the Computer Science Department of Zhejiang University (ZJU), China, and the director of the State Key Lab of CAD&CG, China. Prior to joining ZJU in 2008, he was a leader researcher of the Internet Graphics Group at Microsoft Research Asia, China. He received his BS degree and PhD degree in computer science from ZJU in 1997 and 2002, respectively. His research interests are in visual computing, parallel computing, human computer interaction, and virtual reality. He currently serves on the editorial/advisory boards of ACM Transactions on Graphics and IEEE Spectrum. He is a fellow of IEEE.
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Xie, Y., Yuan, Y., Chen, X. et al. Continuous optimization of interior carving in 3D fabrication. Front. Comput. Sci. 11, 332–346 (2017). https://doi.org/10.1007/s11704-016-5465-y
- computer graphics
- 3D printing
- interior carving
- shape optimization
- Eulerian semiderivative