Geometric modelling based on non-classical NURBS for 3D printing: accelerating the design of complex-organic texture surfaces

Abstract The geometric design of surface textures plays a critical role in determining the functional performance of products, particularly in applications demanding high precision and advanced surface behavior. Conventional computer-aided design (CAD) tools remain limited in their capacity to efficiently generate and manipulate complex, organically inspired geometries with parametric control. Our work introduces a novel method for rapid and flexible design of complex and nature-inspired surface textures at the product development stage. The proposed framework combines two key innovations: (i) a parametric interpolation-based surface representation that offers compact, computationally efficient modeling of highly detailed textures, and (ii) an extended, non-classical NURBS formulation that generalizes traditional B-spline approaches to capture free-form organic geometries with enhanced quality. Quantitative evaluation indicates reductions of 70–85% in computational time and up to 60% in polygon count relative to classical NURBS modeling, while maintaining geometric accuracy within 1% RMS error. These gains enable up to 95% reduction in overall design-to-manufacture preparation time. The method was successfully applied to generate through the generation of 3D reliefs and diverse surface textures, showcasing versatility across multiple non-classical NURBS configurations. The results establish this approach as a robust foundation for accelerating the creation and optimization of complex textured surfaces, particularly for additive manufacturing applications. Graphical abstract