generation of a quadrilateral mesh based on nurbs for gyroids of variable thickness and porosity

The gyroid is a periodic minimal surface explored in different applications, such as architecture and nanotechnology. the general topology is suitable for the construction of porous structures. this paper presents a non-iterative, novel methodology for the generation of a nurbs-based gyroid volume. the gyroid fundamental patch is defined with the weierstrass parameterization. furthermore, the geometry is manipulated to generate a structured mesh, allowing better element quality for fem and iga simulations. the re-parametrization is carried out by a least-squares approximation with a parametric nurbs surface, enabling a better definition of the mid-surface normals for the generation of the complete gyroid volume. different cases of variational thickness and porosity are presented to validate the versatility of our method.