Compression Algorithm for Implicit 3D B-Spline Solids

  • Yanzhi Song
  • Yixin Luo
  • Yuan Liu
  • Jiansong Deng
  • Zhouwang Yang


Due to advantages in solid modeling with complex geometry and its ideal suitability for 3D printing, the implicit representation has been widely used in recent years. The demand for free-form shapes makes the implicit tensor-product B-spline representation attract more and more attention. However, it is an important challenge to deal with the storage and transmission requirements of enormous coefficient tensor. In this paper, we propose a new compression framework for coefficient tensors of implicit 3D tensor-product B-spline solids. The proposed compression algorithm consists of four steps, i.e., preprocessing, block splitting, using a lifting-based 3D discrete wavelet transform, and coding with 3D set partitioning in hierarchical trees algorithm. Finally, we manage to lessen the criticism of the implicit tensor-product B-spline representation of surface for its redundancy store of 3D coefficient tensor. Experimental results show that the proposed compression framework not only achieves satisfactory reconstruction quality and considerable compression ratios, but also supports progressive transmissions and random access by employing patch-wise coding strategy.


Implicit tensor-product B-spline Compression 3D discrete wavelet transform 3D SPIHT Progressive transmission Additive manufacturing 

Mathematics Subject Classification

65D17 94A24 



We would like to thank the anonymous reviewers and our laboratory group for helpful discussions and comments. The work is supported by the NSF of China (No. 11771420) and the Fundamental Research Funds for the Central Universities (WK 001046003).


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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yanzhi Song
    • 1
  • Yixin Luo
    • 1
  • Yuan Liu
    • 2
  • Jiansong Deng
    • 1
  • Zhouwang Yang
    • 1
  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of MathematicsHeFei University of TechnologyHefeiChina

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