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Towards additive manufacturing oriented geometric modeling using implicit functions

Li, Qingde; Hong, Qingqi; Qi, Quan; Ma, Xinhui; Han, Xie; Tian, Jie


Qingqi Hong

Quan Qi

Xie Han

Jie Tian


Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools. However, it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology, the object has to be converted into a solid representation. However, converting a known surface-based geometric representation into a printable representation is essentially a redesign process, and this is especially the case, when its interior material structure needs to be considered. To specify a 3D geometric object that is ready to be digitally manufactured, its representation has to be in a certain volumetric form. In this research, we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects. Like surface-based geometric representation is subtractive manufacturing-friendly, implicitly described geometric objects are additive manufacturing-friendly: implicit shapes are 3D printing ready. The implicit geometric representation allows to combine a geometric shape, material colors, an interior material structure, and other required attributes in one single description as a set of implicit functions, and no conversion is needed. In addition, as implicit objects are typically specified procedurally, very little data is used in their specifications, which makes them particularly useful for design and visualization with modern cloud-based mobile devices, which usually do not have very big storage spaces. Finally, implicit modeling is a design procedure that is parallel computing-friendly, as the design of a complex geometric object can be divided into a set of simple shape-designing tasks, owing to the availability of shape-preserving implicit blending operations.


Li, Q., Hong, Q., Qi, Q., Ma, X., Han, X., & Tian, J. (2018). Towards additive manufacturing oriented geometric modeling using implicit functions. Visual Computing for Industry, Biomedicine, and Art, 1(1), Article 9.

Journal Article Type Article
Acceptance Date Mar 16, 2018
Online Publication Date Sep 5, 2018
Publication Date Dec 1, 2018
Deposit Date Sep 11, 2018
Publicly Available Date Sep 12, 2018
Journal Visual Computing for Industry, Biomedicine, and Art
Electronic ISSN 2524-4442
Publisher Springer (part of Springer Nature)
Peer Reviewed Peer Reviewed
Volume 1
Issue 1
Article Number 9
Keywords Additive manufacturing; 3D printing-friendly CAD; Implicit function; Isosurface; Level-set; Function-based shape modeling; Implicit modeling
Public URL
Publisher URL


Published article (2.1 Mb)

Copyright Statement
© The Author(s) 2018

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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