# A Computational Geometry Generation Method for Creating 3D Printed Composites and Porous Structures
## 1 Introduction  
Additive manufacturing is becoming more accessible and with an increasing variety of materials. Additive can be a cost efficient alternative to subtractive manufacturing as it can reduce the amount of waste material and produce customized and complex designs [1]. Similarly porous materials and structures could be produced by means of additive manufacturing. However the limitations in terms of resulting material behavior could be restrictive in the use of 3D printing for functional parts with specific mechanical property requirements. 3D printing has been used to produce porous structures as biological cell scaffolds in tissue regeneration applications [2; 3; 4; 5]. The produced structures can be heterogeneous with functionally gradient porosity [6] and are often regular in terms of pore shape [7; 8]. Porous scaffolds tend to be insufficiently similar to bone pores and are mechanically weak [9]. Obtaining exact bone geometry through X-ray micro-tomography can be expensive and is not always available [9; 10]. The geometrical and mechanical properties can be relevant to cell development e.g., enhanced with applied mechanical stimuli. It has been found that the introduction of small strains during bone growth enhances the tissue development [11; 12]. The control of the mechanical properties of implanted cell scaffolds is important both in providing structural support but also in regulating the amount of strain that can be accommodated. 3D printed structures are also considered for controlled drug release applications with the use of impregnated bioresorbable materials [13; 14]. Complex 3D printed porous scaffolds could also be suitable for creating biomimetic structures that could replicate or provide a realistic tumor cell microenvironment for 3D in vitro studies of cancer cells [15]. Furthermore, new materials and technologies offer promising opportunities in designing better protection equipment. Strain rate sensitive materials suitable for additive manufacturing techniques [16] can be combined with intelligent designs to enhance impact energy absorption. Lightweight lattice structures can be designed to absorb substantial amounts of energy and outperform conventional materials [17; 18; 19]. The additive manufacturing techniques enable the design of custom and personalized equipment. Furthermore, different materials can be combined to produce composites that could work synergistically for specific applications. The mechanical properties of 3D printed lightweight cellular composites can be controlled by controlling the design and print process that can affect their elastic properties and strength [20]. This possibility could be useful in applications including prototyping, small scale production, and custom functional parts. Computer aided design, using stochastic strategies, has been previously used to represent porosity [21]. The Voronoi tessellation has also been used in a variety of applications. Extruded 2D Voronoi cells can be mapped on 3D surfaces to resemble nacre structures in biomimicking composites [22]. Complex antennas based on the Voronoi tessellation can be 3D printed [23], and high porosity Voronoi 2D patterns can be optimized and used as low density fillers [24]. 3D Voronoi cells have been used to virtually represent high porosity and using the edges as struts [25]. Voronoi cells following a size distribution and with a proximity criterion were used with finite element modelling for predicting material properties of porous structures [26; 27]. This study features a method using 3D Voronoi cells as space holders for generating medium density porous structures and composites. The properties and geometrical features can be controlled to fit specific applications e.g., to mimic bone microstructure. Combinations of materials that might be difficult to mix using traditional methods, could be combined structurally in intertwined configurations.