Additive Manufacturing 78 (2023) 103876 Available online 14 November 2023 2214-8604/© 2023 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Additive Manufacturing journal homepage: www.elsevier.com/locate/addma Research paper Efficient Slicing of rational Bézier triangles for additive manufacturing Rita de Cássia Jerônimo da Silva, Thiago de Aguiar Leal Domingues, Marlos Antônio Pinheiro Rolim, Suzan Diniz, Silvio de Barros Melo ∗ Centro de Informatica - Universidade Federal de Pernambuco, Av. Jornalista Anibal Fernandes, s/n - Cidade Universitaria, Recife, 50.740-560, Pernambuco, Brazil ARTICLE INFO Keywords: Rational Bézier triangle 3D printing Direct slicing ABSTRACT In additive manufacturing a three-dimensional model is created by adding successive layers of material. In recent years, several companies have emerged in the 3D’ printing market in the wake of their advantages over other manufacturing technologies. For one, the 3D printing pipeline allows for a more straightforward prototyping from 3D CAD models, resulting in a faster feedback loop in the prototyping phase thus allowing defects to be corrected more promptly when compared to traditional methods. Despite this, the method still has some shortcomings that can affect some use cases, such as the precision loss produced by the conversion of high-degree curved surfaces to simpler ones, such as polygonal meshes. The proposed method tackles this problem by proposing an efficient conversion-free way to sample points at the intersection between cutting planes and rational Bézier triangles of any degree to an arbitrary precision requirement. 1. Introduction According to ASTM International, additive manufacturing or 3D printing is the process of joining materials to create parts from three- dimensional digital models through a layer-by-layer material deposi- tion [1]. Due to the rapid growth in hardware resources, the accuracy of 3D printing has reached a point where software characteristics can directly impact the quality of the final object. The additive manufacturing technology that pioneered 3D printing came about in 1984 when the engineer Chuck Hull developed stereo- lithography [2]. Currently, its advances have driven a vast chain of related areas, revolutionizing many sectors such as automobile, aero- nautics, architecture, engineering, medicine, and design, producing from light parts to heavy objects and reducing operating costs in product design and manufacturing. In addition, it has become very useful in the development of new inventions. This is due to the fact that such three-dimensional digital processing provides a better spatial understanding (shortening paths that lead to a prototype). In 3D printing, to generate the material layers in object produc- tion, pipelines need slicing algorithms. Most 3D printing technologies (e.g. FDM, SLA, LOM, SLS, SIS, SGC, IJT, MJM, 3DP, and DoD) take commands to control the tool path inside a layer. While still in the digital realm, it is necessary to compute intersections between the model and the representations of the layers as planes parallel to the printing base. As a result, planar curves or straight-line segments are obtained. The object is then recreated as the plane moves orthogonally away from the printing base until it reaches the top of the object. ∗ Corresponding author. E-mail address: sbm@cin.ufpe.br (S. de Barros Melo). The quest for more realistic virtual and physical prototypes has caused 3D printing to continue to grow in flexibility and capabilities. Additionally, the means to print parts in a shorter period of time and in a more decentralized way have advanced together with the production of ever more complex objects [3,4]. Additive manufacturing-based prototyping has resulted in better accuracy as compared to traditional prototyping methods, for they can be identified and corrected before the actual printing is done, ultimately contributing to the production of better-finished parts. The design of complex CAD Models (CADM) usually employs para- metric representations such as NURBS (Non-Uniform Rational B-Splines), Coons Patches, and Bézier Surfaces; implicit representations such as quadrics, tori, and revolution surfaces; or procedural repre- sentations, such as subdivision surfaces. In the 3D printing pipeline, in order to avoid the hard-to-produce plane/CADM intersection al- gorithms, the models are usually converted into meshes of triangles, a process called tessellation, almost always consistent with the STL (Stereo Lithography) file format, which can represent data describing the layout of three-dimensional objects composed of planar polygonal faces. The STL file format is also a standard for 3D objects interchange and communication and has become an important component for algorithms that aim at improving the 3D printing pipeline, such as the ones that optimize the build orientation of the object in order to reduce support material usage, to maximize material strength [5,6] or to correct gaps and cracks that may occur in STL files due to their lack of connectivity information [7]. https://doi.org/10.1016/j.addma.2023.103876 Received 2 June 2023; Received in revised form 18 October 2023; Accepted 9 November 2023