sectionProfiles: Construct section profiles
In unfoldr: Stereological Unfolding for Spheroidal Particles

Description Usage Arguments Details Value Author(s) Examples

Set up section profiles of spheroids for unfolding

1	sectionProfiles(size, alpha, type = c("prolate", "oblate"))

`size`	matrix of lengths of the semi-axes
`alpha`	angle of section profiles in the plane (see details)
`type`	name of the spheroid type, either "`prolate`" or "`oblate`" from which the section profiles are assumed to come from

The function aggregates the necessary information for trivariate unfolding of spheroids' joint size-shape orientation distribution of type either "prolate" or "oblate". The argument size is a numeric matrix of semi-axis lengths where the first column corresponds to the major semi-axis and the second one to minor semi-axis. The orientation of an ellipse is assumed to be measured as the angle between its major axis and vertical axis of the coordinate system in the intersection plane ('z' axis in 3D). For values in [0,2π] these angles are automatically transformed to [0,π/2] as required by the unfolding procedure.

The function returns a list which consists of either the longer or shorter semi-axis length named A of section profiles corresponding to the type of spheroids used before and whose joint joint distribution is to be estimated (by unfolding), the shape factor S of both semi-axes as the shape factor between (0,1] and the orientation angle alpha, either of class "prolate" or "oblate".

M. Baaske

 # load data set
 data(data15p)
 
 # matrix of semi-axes lengths (major,minor)
 AC <- data.matrix(data15p[c("A","C")])/1000	

 # selecting the minor semi-axis for prolate type of spheroids:
 # independent of nomenclature (always named \code{A})
 sp <- sectionProfiles(AC,unlist(data15p["alpha"]))

 summary(sp$A)			# here minor semi-axis because of prolate
 summary(sp$S)			# shape factor
 summary(sp$alpha)		# angle assumed to be w.r.t. (vertical) 'z' axis

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.000618 0.002138 0.003349 0.003666 0.004795 0.015055 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.09916 0.36097 0.47752 0.50427 0.62494 1.00000 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.1013  0.2429  0.3716  0.5236  1.5708