I-nteract is a cyber-physical system that enables real-time interaction with both virtual and real artifacts to design 3D models for additive manufacturing by leveraging mixed-reality technologies. This paper presents novel advances in the development of the interaction platform to generate 3D models using both constructive solid geometry and artificial intelligence. In specific, by taking advantage of the generative capabilities of deep neural networks, the system has been automated to generate 3D models inferred from a single 2D image captured by the user. Furthermore, a novel generative neural architecture, SliceGen, has been proposed and integrated with the system to overcome the limitation of single-type genus 3D model generation imposed by differentiable-rendering-based deep neural architectures. The system also enables the user to adjust the dimensions of the 3D models with respect to their physical workspace. The effectiveness of the system is demonstrated by generating 3D models of furniture (e.g., chairs and tables) and fitting them into the physical space in a mixed reality environment. The presented developmental advances provide a novel and immersive form of interaction to facilitate the inclusion of a consumer into the design process for personal fabrication.