# [R] Quantifying widths of polygons

Alexander Shenkin ashenkin at ufl.edu
Fri Sep 25 16:20:15 CEST 2015

```Hello all,

I am working with data on tree crowns, and this data describes points
(verticies) around the polyhedron of the crown volume (think of the
crown as a single volume with vertices and faces).  I can calculate
maximum z distance between any 2 points (maximum depth) and maximum x/y
distance (maximum width).  These are useful metrics.  I would also like
to quantify an "average" width of the polygon in 2D space (x/y only), as
well as a metric that would describe the "eccentricity" of the polygon.
But, I'm not sure how to go about doing that.

In general, I've made the polyhedrons and polygons into convex shapes.

I have considered getting a centroid, intersecting lines every 10
degrees (for example) going through the centroid with the x/y polygon
owin in spatstat, and then analyzing those line lengths.  But, I'm not
sure that's the right way to go, and maybe there are already tools out
there to do this.  Any thoughts anyone might have would be very welcome!

Thanks,
Allie

library(rgl)
library(spatstat)
library(geometry)

x =
c(1.9,-1.4,1.5,1.8,2.2,0.2,0.6,-0.9,-3.7,1.3,-1.9,-3.4,3.7,2.1,-2.0,-1.9)
y =
c(-3.1,3.0,1.1,-1.3,1.0,0.0,1.4,1.6,2.3,-3.6,-1.5,-1.3,0.3,-2.1,0.2,-0.3)
z = c(5.5,4.5,4.3,4.8,6.7,5.8,7.4,6.2,3.5,2.9,4.0,3.7,3.2,3.0,3.1,8.4)
depth = max(z) - min(z)
width_max = max(dist(matrix(c(x,y),ncol=2)))

xy_win = owin(poly=list(x=x,y=y))
conv_win = convexhull(xy_win)
# from here, maybe draw lines every 10 degrees through a centroid?
# avg_width = ??
# eccentricity = ??

# 3D plot of crown polyhedron (convex)
ps = data.frame(x=x,y=y,z=z)
crown.surf = t(convhulln(matrix(c(x,y,z),ncol=3)))
open3d()
rgl.triangles(ps[crown.surf,1],ps[crown.surf,2],ps[crown.surf,3],col=heat.colors(nrow(ps)),alpha=.2)
axes3d()

```