Abstract
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.
Highlights
Implicit surfaces are of considerable interest in engineering as they provide an efficient means for the modeling of complex shapes
An implicit function for the infill volume can be derived from the implicit offset functions in positive and negative directions indicated by h < 0 and h > 0
One observation is that this deterioration is less severe when the thickness is measured from the offset function to the Neovius surface than when it is measured the other way around
Summary
Implicit surfaces are of considerable interest in engineering as they provide an efficient means for the modeling of complex shapes. Sethian [8] provides a good overview over fast marching methods used for offsetting implicit surfaces He discusses how the accuracy of the the fast marching method can be improved by discretizing the required normal derivatives with finite differences of higher order. The purpose of the current paper is to propose a method to obtain a new implicit surface at a predefined distance to a given implicit surface.
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