The integration of origami-inspired geometry with additive manufacturing has emerged as a transformative approach in advanced structural design, enabling compact deployable systems, energy absorption mechanisms, and mechanically tunable architectures. This study presents a computational design and geometric optimization framework for origami-inspired structures fabricated using Fused Deposition Modeling (FDM). The research investigates how mathematical origami principles, when coupled with layer-wise material deposition, can be translated into manufacturable and mechanically efficient 3D printed structures. Emphasis is placed on parametric modeling, fold-pattern optimization, and manufacturability constraints inherent in FDM processes. A comparative synthesis of additive manufacturing literature highlights challenges in dimensional accuracy, material anisotropy, and structural reproducibility, while origami-based engineering studies provide theoretical grounding for rigid foldability and deformation control. The methodology integrates computational geometry, finite element-informed design reasoning, and process parameter optimization. Findings indicate that optimized origami-based lattice configurations significantly enhance load distribution, structural compliance, and energy absorption efficiency. However, limitations arise from layer adhesion variability and fold-induced stress concentrations. The study contributes a unified framework bridging origami mathematics and FDM-based fabrication, offering implications for aerospace, biomedical scaffolds, and lightweight structural systems.