This paper explores the application of elliptic partial differential equations (PDEs) as a method for generating smooth and continuous vase designs, which can optimize 3D object workflows. Elliptic PDEs, such as Laplace’s equation, are well-suited for surface modeling as they maintain equilibrium and ensure smooth transitions between boundaries. With clear definitions and precise conditions, the proposed approach enables the generation of customized vase shapes while providing effective control over curvature and surface continuity. This method allows intuitive manipulation of parametric constraints, offering flexibility in design customization while minimizing computational complexity. Additionally, this paper demonstrates how boundary adjustments influence PDE-generated shapes, showing the diverse vase designs achievable through elliptic PDEs. By integrating these mathematical frameworks into computational design, this study highlights their potential to bridge the gap between theoretical modeling and real-world applications in art, design, and manufacturing. Furthermore, it emphasizes the role of PDE-based modeling in preserving cultural heritage through traditional vase design while fostering innovation in modern aesthetics.