overlap: Area of overlap between two estimated ellipses

In AndrewLJackson/siar: Stable Isotope Analysis in R

Description

Given the coordinates of two bivariate samples, this function calculates (computationally) the area of overlap between two standard ellipses. Note, be sure to use a sufficiently low step size when creating the ellipses (i.e. to ensure that there is no excessive discretising of the elliptical shape). As a result of this process, you will inevitably underestimate the true ellipse areas and hence their overlap (although this bias is likely to be inconsequential) if a suitable fine scale is chosen for the step size. There is no single rule for making this choice as it depends on the angle and shape of the ellipse but a step-size of 1 should be more than sufficient in most cases (N.B. the default steps=5). The ellipses calculated are the small sample size corrected standard ellipses.

Usage

overlap(x1,y1,x2,y2,steps = 5) 

Arguments

x1	A vector containing the x coordinates of the first data.
y1	A vector containing the y coordinates of the first data.
x2	A vector containing the x coordinates of the second data.
y2	A vector containing the y coordinates of the second data.
steps	The number of steps in degrees to estimate points on the curve.

Value

overlap	The area of overlap between the two standard ellipses.
area1	The area of the first ellipse.
area2	The area of the second ellipse.

Author(s)

Andrew Jackson

AndrewLJackson/siar documentation built on May 5, 2019, 5:59 a.m.