arc {doolkit}

Average-Relative Curvature (ARC)

Description

Compute a scale-free estimate of mean curvature.

Usage

arc(mesh, range = c(0.01, 0.99))

Arguments

mesh

object of class mesh3d

range

a numeric vector of the form c('minrange', 'maxrange') indicating the set limits for extreme values, beyond which arc values will be truncated. If 'minrange' and 'maxrange' are comprised between 0 and 1, they are used as arc percentages. If 'minrange' and 'maxrange' are not comprised between 0 and 1, they are used as raw arc values

Details

Area-relative curvature (ARC) is obtained by dividing the mean curvature of each triangle by the mean curvature of an hemisphere, the surface area of which is the same as the surface area of the total mesh object. Coincidentally, the surface area of a hemisphere is linked to its mean curvature by the following function: 2.4481 * 1 / square root(surface area) As a result, ARC is a scale-free estimate of surface curvature. It can be used to estimate the sharpness of a mesh.

Value

A numeric vector of area-relative curvature values for all the polygons of the mesh.

Examples

curvature <- arc(dkmodel$complex)
summary(curvature)

#There is a default truncature of extreme values below 1% or above 99%.
#Without truncature:
curvature <- arc(dkmodel$complex, range = c(0, 1))
summary(curvature)

#mean positive ARC:
parc <- mean(curvature[curvature >= 0])
#mean negative ARC:
narc <- mean(curvature[curvature < 0])

#render on a map:
dkmap(dkmodel$complex, curvature, col = "arc",
min.range = -20, max.range = 20)
#absolute truncature of the values above 20 or below -20:
dkmap(dkmodel$complex, curvature, col = "arc", min.range = -20, max.range = 20)