Multi-level approximating 3D printing of curved surface with continuous carbon fiber for solid parabolic antenna

Efficient manufacturing of curved surface structures remains both a challenge and a priority in advanced engineering applications, even by 3D printing. To address this, we introduce a multi-level approximation (MLA) strategy, coupled with a floating 3D printing approach using continuous carbon fiber–reinforced composites. Inspired by curve subdivision and triangular mesh generation in computer graphics, we establish a manufacturable structural design method that discretizes curved geometries into fractal polyhedral frameworks, within which smooth curves or surfaces are progressively approximated by tensioned straight segments. This approach significantly reduces support requirements, lightens structural weight, and improves fabrication efficiency. Theoretical analysis shows that MLA can reduce material consumption by more than 81.8 % compared with conventional layer-stacking. Using this method, we fabricated parabolic reflectors with diameters of 200 mm, 400 mm, and 1000 mm. For the 1 m reflector, the floating-printed structure achieved a surface accuracy of RMSE = 0.485 mm and a radiation gain of 22.81 dB at 3.95 GHz, validating both the feasibility and scalability of the proposed method. Beyond parabolic antennas, this MLA floating 3D printing strategy offers a pathway toward rapid, lightweight, and support-free manufacturing of large-scale curved structures, with promising applications in aerospace and in-orbit additive manufacturing.