Compression Algorithm for Implicit 3D B-Spline Solids
- 4 Downloads
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.
KeywordsImplicit tensor-product B-spline Compression 3D discrete wavelet transform 3D SPIHT Progressive transmission Additive manufacturing
Mathematics Subject Classification65D17 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).
- 2.Bowyer, A.: SVLIS: Set-Theoretic Kernel Modeller. Information Geometers, Winchester (1995)Google Scholar
- 3.Chen, W.T.F.: A fast and adaptive surface reconstruction algorithm based on the implicit tensor-product B-spline (ITPBS) surfaces. In: Tong, W., Chen, F., Feng, Y. (eds.) Proceedings of The Seventh China-Japan Seminar on Numerical Mathematics, pp. 161–178, (2006).Google Scholar
- 4.Cignoni, P., Rocchini, C., Scopigno, R.: Metro: measuring error on simplified surfaces. In: Computer Graphics Forum. 17, 167–174, Wiley Online Library (1998)Google Scholar
- 7.Group, D. M.: Hyperfun. http://hyperfun.org/
- 10.John, A.E.: Anton. 3Dprinteros. https://cloud.3dprinteros.com/
- 11.Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. In: ACM Siggraph Computer Graphics, 21, 163–169. ACM (1987)Google Scholar
- 15.Schmidt, R.: Interactive modeling with implicit surfaces. Ph.D. thesis, Masters thesis, Department of Computer Science, University of Calgary (2006)Google Scholar
- 16.Sweldens, W.: Lifting scheme: a new philosophy in biorthogonal wavelet constructions. In: SPIE’s 1995 International Symposium on Optical Science, Engineering, and Instrumentation, pp. 68–79. International Society for Optics and Photonics (1995)Google Scholar
- 19.Uformia. Symvol for rhino. http://uformia.com/products/symvol-for-rhino/