Ceramics is taking advantage of Additive Manufacturing technologies and continuous improvements in processes and materials are increasing the possibilities for a wide spreading and industrialization of these technologies. Among the technologies used for ceramic 3D printing, stereolithography and extrusion-based technologies are now expanding the most, mainly due to the low-budget and open-source solutions available in the market. Major consideration needs the geometric modeling and the preparation of the file to be printed. The complexities of the geometries feasible by ceramics match the ones of thermoplastic and photocurable resins. Though particular attention should be given to the model design to avoid failure during the printing process or undesired distortions after the heat treatment phase. Therefore, the designer should focus on the CAD and CAM phases.  
Aim of this contribution is to provide an overview of the recently developed methods that can be adopted to take advantages of the design freedom allowed by additive manufacturing with a special regard to shape complexity. Adopting the following modeling strategies, different models were manufactured in the context of the Funglass research projects.
Particular interest is given to the realization of lattice structures, that can be used in various applications that need high porosity and lightweight structures, from the industrial to the biomedical field. Several approaches for the geometric modeling of lattices, based on different representation schemes, are available in the literature.
Through discrete surface approaches, polygonal mesh modeling can be used. The method gives the possibility to model beam and shell-like structures using low-poly meshes and if needed use a subdivision algorithm to smooth the whole mesh. In this manner, minimal surface lattices can be also generated by successive approximations and the approach can be extended to lattices with porosity gradients.
When dealing with triply period minimal surfaces (TPMS), implicit modeling can be applied, resulting in a more complex implementation since it uses mathematical functions. This approach permits the designer the generation of relative density graded, cell size graded and multi-morphology lattices. The functions are evaluated at a certain value (iso-value) and the B-rep is obtained.
A hybrid modeling approach can also be applied to simplify the realization of a coherent CAD model of a lattice structure. Firstly, the structure is modeled with lines (if beam-like lattice) and surfaces (if shell-like lattice) and then these geometric entities are used to compute distance functions evaluated at a certain distance to create the B-rep to be printed.
These and other approaches that will be illustrated can have several applications if matched with the ceramic material in functional 3D printed parts, especially in the biomedical field, since the modeling phase can be guided by using volumetric data such as the density map derived from a DICOM grayscale image dataset to replicate a biological structure