Smooth operator: The effects of different 3D mesh retriangulation protocols on the computation of Dirichlet normal energy.

Journal Article (Journal Article)


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.

Materials and methods

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.

Full Text

Duke Authors

Cited Authors

  • Spradley, JP; Pampush, JD; Morse, PE; Kay, RF

Published Date

  • May 2017

Published In

Volume / Issue

  • 163 / 1

Start / End Page

  • 94 - 109

PubMed ID

  • 28218399

Electronic International Standard Serial Number (EISSN)

  • 1096-8644

International Standard Serial Number (ISSN)

  • 0002-9483

Digital Object Identifier (DOI)

  • 10.1002/ajpa.23188


  • eng