Compression Algorithm for Implicit 3D B-Spline Solids
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Compression Algorithm for Implicit 3D B-Spline Solids Yanzhi Song1 · Yixin Luo1 · Yuan Liu2 · Jiansong Deng1 · Zhouwang Yang1
Received: 9 October 2017 / Revised: 16 January 2018 / Accepted: 1 March 2018 / Published online: 16 May 2018 © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018
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. Keywords Implicit tensor-product B-spline · Compression · 3D discrete wavelet transform · 3D SPIHT · Progressive transmission · Additive manufacturing Mathematics Subject Classification 65D17 · 94A24
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Zhouwang Yang [email protected]
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School of Mathematical Sciences, University of Science and Technology of China, Hefei, China
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School of Mathematics, HeFei University of Technology, Hefei, China
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Y. Song et al.
1 Introduction By building up complex shapes layer by layer, 3D printing is able to create intricate, bespoke designs far easier and at a much lower cost than traditional manufacturing techniques. The implicit representation solid, as an input geometry, is very suitable for additive manufacturing, because there are many advantages over traditional boundary representation in slicing and tool paths generation [9]. In addition, implicit representation has another clear advantage that its inside and outside part is mathematically constrained, which is essential for the high precision requirement in modern manufacturing. Rather than a simple binary inside and outside, implicit representation solids can have spatially varying properties, such as partial densities, different materials, color and other characteristics embedded into its 3D space, which is ideal representation for intricate models with complex internal structures for 3D printing, such as internal organs. Fasotec, a Japanese firm, has created 3D printed body organs having blood vessels, which are
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