Computation of Implicit Representation of Volumetric Shells with Predefined Thickness

We propose and validate a method to find an implicit representation of a surface placed at a distance h from another implicit surface. With two such surfaces on either side of the original surface, a volumetric shell of predefined thickness can be obtained. The usability of the proposed method is demonstrated through providing solid models of triply periodic minimal surface (TPMS) geometries with a predefined constant and variable thickness. The method has an adjustable order of convergence. If applied to surfaces with spatially varying thickness, the convergence order is limited to second order. This accuracy is still substantially higher than the accuracy of any contemporary 3D printer that could benefit from the function as an infill volume for shells with predefined thicknesses.