Porous Structure Design Using Parameterized Hexahedral Meshes and Triply Periodic Minimal Surfaces.

Porous structures had traditionally been generated using triply periodic minimal surfaces (TPMS), which however often encounter problems with the continuity and integrality of the generated curved surfaces when applying to irregular models. The present work describes a new porous-structure designing method using a combination of parameterized hexahedral mesh and traditional TPMS surfaces. The primary steps of the proposed method include: 1) re-meshing an input model into a hexahedral mesh; 2) solving parametric expressions of 12 geodesic lines using heat conduction models; 3) constructing quadrilateral surface meshes, and hexahedral volume meshes with harmonic-map; 4) generating standard TPMS surfaces within a regular hexahedron using the Marching Cube (MC) algorithm and then mapping the generated surface onto the parameterized hexahedral mesh using tri-linear interpolation. The experimental results have shown that the present method can solve the problem of discontinuity when the constraint hexahedron is deformed.