title: Smooth operator: The effects of different 3D mesh retriangulation protocols on the computation of Dirichlet normal energy.
abstract: Dirichlet normal energy (DNE) is a metric of surface topography that has been used to evaluate the relationship between the surface complexity of primate cheek teeth and dietary categories. This study examines the effects of different 3D mesh retriangulation protocols on DNE. We examine how different protocols influence the DNE of a simple geometric shape-a hemisphere-to gain a more thorough understanding than can be achieved by investigating a complex biological surface such as a tooth crown.
  
  
  
  We calculate DNE on 3D surface meshes of hemispheres and on primate molars subjected to various retriangulation protocols, including smoothing algorithms, smoothing amounts, target face counts, and criteria for boundary face exclusion. Software used includes R, MorphoTester, Avizo, and MeshLab. DNE was calculated using the R package "molaR."
  
  
  
  In all cases, smoothing as performed in Avizo sharply decreases DNE initially, after which DNE becomes stable. Using a broader boundary exclusion criterion or performing additional smoothing (using "mesh fairing" methods) further decreases DNE. Increasing the mesh face count also results in increased DNE on tooth surfaces.
  
  
  
  Different retriangulation protocols yield different DNE values for the same surfaces, and should not be combined in meta-analyses. Increasing face count will capture surface microfeatures, but at the expense of computational speed. More aggressive smoothing is more likely to alter the essential geometry of the surface. A protocol is proposed that limits potential artifacts created during surface production while preserving pertinent features on the occlusal surface.
authors.affiliation: Department of Evolutionary Anthropology, Duke University, Durham, North Carolina, 27708.
authors.forename: Jackson P
authors.identifier: 0000-0003-2358-8794
authors.initials: JP
authors.lastname: Spradley
authors.affiliation: Department of Evolutionary Anthropology, Duke University, Durham, North Carolina, 27708.
authors.forename: James D
authors.initials: JD
authors.lastname: Pampush
authors.affiliation: Department of Anthropology, University of Florida, Gainesville, Florida.|Florida Museum of Natural History, University of Florida, Gainesville, Florida.
authors.forename: Paul E
authors.initials: PE
authors.lastname: Morse
authors.affiliation: Department of Evolutionary Anthropology, Duke University, Durham, North Carolina, 27708.|Division of Earth and Ocean Sciences, Nicholas School of the Environment, Duke University, Durham, North Carolina, 27708.
authors.forename: Richard F
authors.initials: RF
authors.lastname: Kay
mesh_terms: D000465:Algorithms; D000818:Animals; D000885:Anthropology, Physical; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008963:Molar / Q000033:anatomy & histology*; D009811:Odontometry / Q000379:methods*; D011323:Primates / Q000033:anatomy & histology*; D012984:Software; D013499:Surface Properties
keywords: DNE; Laplacian smoothing; PLY file; dental topography; hemisphere