DNE {molaR}

Calculate Dirichlet normal energy of a surface

Description

A function that calculates Dirichlet normal energy following the method of Bunn et al. (2011) Comparing Dirichlet normal surface energy of tooth crowns, a new technique of molar shape quantification for dietary inference, with previous methods in isolation and in combination. Am J Phys Anthropol 145:247-261 doi: 10.1002 ajpa.21489

Usage

DNE(plyFile, outliers = 0.1, kappa = 0, BoundaryDiscard = "Vertex", oex = "c")

Arguments

plyFile

An object of classes 'mesh3d' and 'shape3d' with calculated normals

outliers

The percentile of Dirichlet energy density values to be excluded defaults to top 0.1 percent

kappa

An integer value of mean curvature to define concave vs convex faces

BoundaryDiscard

String indicating how to handle the exclusion of boundary faces. Default of Vertex excludes faces which have at least 1 vertex on the boundary

oex

String indicating outlier exclusion principle. Defaults to 'c', which combines all convex and concave faces and removes the percentage of outliers defined by outliers. See details.

Details

The function requires an object created by reading in a ply file.

Dirichlet normal energy is calculated on meshes that represent specimen surfaces and have already been simplified and pre-smoothed in a 3D data editing program.

In the default settings, the function seeks to discard boundary faces. This can be changed by adjusting the BoundaryDiscard argument to 'None' which will not discard any faces on the boundary. Further, there are two ways of excluding boundary faces. Either if they have a leg on the boundary by setting BoundaryDiscard='Leg' or by excluding any face which has a vertex on the boundary with BoundaryDiscard='Vertex'. The function defaults to remove the top 0.1 percent of calculated energy densities as outliers. Mesh orientation does not affect this calculation.

Faces are labeled as concave or convex on the basis of the kappa value, which defaults to 0. Each face is assigned a kappa value, which describes the the localized degree of convergence or divergence among the three vertex normals on each face. Faces with positive kappa values have vertex normals that are divergent. Faces with negative kappa values possess vertex normals that are convergent. Users can adjust the kappa value to redefine areas of the tooth assigned to the convex or concave bin.

The mode of Outlier exclusion can be modified with the oex argument. The default, oex='c' considers the Dirichlet energy density values of all faces on the surface and removes those in the top percentile defined by outliers, regardless of the convexity or concavity bins. The alternative, oex='s', divides the surface into concave and convex portions, then removes the percentile defined by outliers from each of these subsets before calculating total surface DNE.

Examples

DNE_output <- DNE(Tooth)
summary(DNE_output)