Curvature and Feature-Aware Print-Paths from Hexahedral Meshes for Additive Manufacturing

Erkan Gunpinar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Recently proposed meshing techniques allow the generation of high-quality hexahedral meshes (hex-mesh) whose edges follow the surface feature and curvature-lines. This study investigates their use in additive manufacturing for the generation of curvature and feature-aware print-paths (tool-paths). A hex-mesh consists of 8-noded hexahedra (hex-cells) and a cuboid-like sub-volume is structured (i.e., valence for the inner edges is only four), which is represented using a three-dimensional (3D) array of hex-cells. All cuboid-like sub-volumes (called C-partitions) are first enumerated by growing them from singular-edges (i.e., a series of connected same-valence singular-edges that are not two on the boundary or four in the interior). These C-partitions are then selected one-by-one according to a cost function based on several criteria including alignment of print-paths along the feature curves and curvature directions. Remaining C-partitions are split if they intersect the (previously) selected C-partitions. The C-partitions are iteratively chosen and split until all hex-mesh is covered by the (selected) C-partitions. Print-paths are arranged along (predetermined) direction(s) in a C-partition, and tubes representing deposited material (in AM) around the print-path overlap at some locations. Thus, these tubes are repaired via tube adjustment operators, in which their location and material deposition radii at those locations are modified. As a proof of concept, curvature and feature-aware print-paths are finally validated using an AM simulator and machine.

Original languageEnglish
Article number103101
JournalCAD Computer Aided Design
Publication statusPublished - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Ltd


The authors would like to thank Serhat Cam, Arash Armanfar and Alper Tasmektepligil to manufacture the parts in this paper, Gershon Elber for his valuable discussions on accessibility of print-paths in additive manufacturing, David Bommes related to his valuable comments on hexahedral meshes, Elena Gaidar and Fedor Gridnev from 5AxisMaker company for their technical support, the RWTH Computer Graphics Group for making the OpenFlipper/OpenVolumeMesh geometry processing and rendering framework available, HexaLab [13] for making hexahedral mesh models available on the internet and Scientific Research Center of Istanbul Technical University, Turkey for supporting this research (Project Number: 42541).

FundersFunder number
Istanbul Teknik Üniversitesi42541


    • Additive manufacturing
    • Hexahedral mesh
    • Print-paths


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