## 1 Introduction
The process allows fabrication of materials with high spatial resolution (about 40 \(\upmu\)m in the printing plane, and 10 \(\upmu\)m in the direction perpendicular to the printing plane). Printed green parts are then heated for several hours to remove polymer binder. Further on, the parts are sintered to impart the final shape and desired mechanical properties. Both these processes are traditional for ceramics manufacturing. There are multiple applications of SLA and a large variety of commercially available 3D printers and ceramic pastes. This method is used for 3D printing of ceramics for at least 20 years. SLA (and its modification, a Digital Light Processing (DLP) method is considered one of the best methods for ceramics manufacturing due to the high precision, low defects, and high density and strength of the produced parts. Other methods, such as Fused Deposition Modeling (FDM) or Selective Laser  
Figure 1: Stereolithographic printing process. Sintering (SLS), produce inferior results in terms of resolution and microstructural properties of the material. A video demonstrating the 3D printing process of ceramic parts based on the SLA process can be found at the 3D Ceram company website [39]. In practice, all fabricated ceramic implants would be customized, i.e., tailored to individual patient needs. This raises the question of the quick design of parts with complex porous structure. Traditional methods of geometric modeling based on surface representation of a model cannot be applied here due to a very large amount of computations required to build models with complex internal structure [40]. Considering the above, we used the Function Representation (FRep) approach for geometric modeling of complex shapes with porous, cellular, and irregular microstructure [41]. This approach defines any geometrical object by non-negative values of a real continuous function procedurally evaluated at any given point of coordinate space. Whether a point belongs to an object depends on the sign of the defining function evaluated at that point. Typically, points with positive and zero function values are included in a set, while a zero-level subset is considered a boundary. Basically, FRep modeling is the \"extended\" implicit modeling [42] with explicitly introduced elementary objects (primitives). Compared to boundary representation-based Computer-aided design (CAD) systems, the FRep approach offers significant advantages for microstructure modeling. First, the FRep format always ensures the accuracy of the obtained model, as opposed to traditional polygonal representation used in CAD systems where the probability of ending up with cracks or nonmatching edges in a model is rather high, even in simple operations such as offsetting. Second, the FRep has the advantage of complete parametrization of obtained microstructures, giving high flexibility in fast generation of variable 3D models. Third, the FRep offers a wide variety of tools to model various meshed structures, including periodic functions, Triply Periodic Minimal Surfaces (TIMPS) [43; 44], and replication of a unit cell, based on the method of skeleton-based surfaces [45]. In addition, FRep-based software makes it possible to use controlled blending versions of set-theoretic operations on geometric primitives. It is important for most applications to be able to combine a microstructure with the given external shape of an object or with a rigid platform. In this study, we investigated the applicability of 3D printing for fabrication of easily modified cellular ceramic structures. While FRep is not a novel method, there are no publications on such application of this approach. Here, we used the FRep method to design 4 mm diameter cylindrical implants. The designed 9.5 mm long implants are intended to fill hole-like defects in the trabecular bone. The implants reproduce the structure of the trabecular bone, having a dense cylindrical base similar to the structure of cortical bone tissue, and porous main body similar to the structure of cancellous bone tissue.