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Compression Algorithm for Implicit 3D B-Spline Solids

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    Yanzhi Song, Yixin Luo, Jiansong Deng & Zhouwang Yang

  2. School of Mathematics, HeFei University of Technology, Hefei, China

    Yuan Liu

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  1. Yanzhi Song
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  2. Yixin Luo
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  3. Yuan Liu
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  4. Jiansong Deng
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  5. Zhouwang Yang
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Correspondence to Zhouwang Yang.

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Song, Y., Luo, Y., Liu, Y. et al. Compression Algorithm for Implicit 3D B-Spline Solids. Commun. Math. Stat. 6, 119–140 (2018). https://doi.org/10.1007/s40304-018-0128-y

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  • DOI: https://doi.org/10.1007/s40304-018-0128-y

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