Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

• Published in: IEEE transactions on visualization and computer graphics Vol. 20; no. 2; pp. 223 - 237
• Main Authors: Bronson, Jonathan, Levine, Joshua A., Whitaker, Ross
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: adaptive meshing; Algorithms; Animals; Biological system modeling; biomedical; Computer Graphics; Computer Simulation; conformal meshing; Finite Element Analysis; Geometry; guaranteed meshing; Humans; Imaging, Three-Dimensional - statistics & numerical data; Joining processes; Lattices; Magnetic Resonance Imaging - statistics & numerical data; Materials; mesh quality; multilabel; multimaterial; Tetrahedral meshing; Topology; watertight
• ISSN: 1077-2626; 1941-0506
• DOI: 10.1109/TVCG.2013.115

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.