# verticalSection: Vertical sections In unfoldr: Stereological Unfolding for Spheroidal Particles

## Description

Compute vertical section profiles of a spheroid system

## Usage

 `1` ```verticalSection(S, d, n = c(0, 1, 0), intern = FALSE) ```

## Arguments

 `S` list of spheroids, see `simPoissonSystem` `d` distance of the intersecting plane from the origin of the box `n` normal vector which defines the interecting vertical plane `intern` logical, `FALSE` (default), return all section profiles otherwise only those which have their centers inside the correspondig intersection window

## Details

The function intersects a spheroid system by a plane defined by the normal vector `n` either equal to `c(0,1,0)` (default) or `c(1,0,0)`, which is called a vertical section. Depending on the type of spheroid (either "`prolate` or "`oblate`") the returned semi-axis lengths are those corresponding to the minor semi-axis or, respectively, major semi-axis in the way these are required for unfolding.

## Value

list of sizes `A`, shape factors `S` and (vertical) angles `alpha` of section profiles in the plane w.r.t the 'z' axis between [0,π/2].

## Author(s)

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` box <- list("xrange"=c(0,5),"yrange"=c(0,5),"zrange"=c(0,5)) # (exact) bivariate size-shape (isotropic) orientation distribution (spheroids) theta <- list("size"=list("mx"=-2.5,"my"=0.5, "sdx"=0.35,"sdy"=0.25,"rho"=0.15), "orientation"=list("kappa"=1)) S <- simPoissonSystem(theta,lam=100,size="rbinorm",box=box, type="prolate",perfect=TRUE,pl=1) sp <- verticalSection(S,d=2.5,n=c(0,1,0),intern=TRUE) summary(sp\$alpha) ```