Calculation of the area of ​​the confidence ellipse in a certain area of ​​space

Question

I was wondering if anyone had an idea on how to calculate the blue shaded area inside my trust ellipse. Any suggestions or places to search are greatly appreciated. In addition, I hope to find a general formula, since the ellipse does not have to lie in this area in the application (i.e. the ellipse could be larger). Here is my code for my image, if that helps:

library(car) x = c(7,4,1) y = c(4,6,7) plot(x,y,xlim=c(0,10),ylim=c(0,10)) rect(x,y,max(x)+100000,max(y)+100000,col="lightblue",border=NA) points(x,y,col="red",pch=19) ellipse(center=c(3.5,5),shape=matrix(c(1,.5,.5,2),nrow=2),radius=3,col="green") 

Answer 1

If you can convert the ellipse and the blue region to SpatialPolygons , then this is cinch, using the functions from the rgeos package to calculate their area, the area of ​​their intersection and all other kinds of interesting quantities.

Unfortunately, getting the objects in proper shape requires a bit of heavy lifting:

 library(car) library(sp) library(rgeos) ## Function for creating a SpatialPolygons object from data.frame of coords xy2SP <- function(xy, ID=NULL) { if(is.null(ID)) ID <- sample(1e12, size=1) SpatialPolygons(list(Polygons(list(Polygon(xy)), ID=ID)), proj4string=CRS("+proj=merc")) } ## Ellipse coordinates plot.new() # Needed by ellipse() ell <- ellipse(center=c(3.5,5),shape=matrix(c(1,.5,.5,2),nrow=2),radius=3) dev.off() # Cleaning up after plot.new() ## Three rectangles' coordinates in a length-3 list x <- c(7,4,1) y <- c(4,6,7) mx <- max(x) + 1e6 my <- max(y) + 1e6 rr <- lapply(1:3, function(i) { data.frame(x = c(x[i], x[i], mx, mx, x[i]), y = c(y[i], my, my, y[i], y[i])) }) ## Make two SpatialPolygons objects from ellipse and merged rectangles ell <- xy2SP(ell) rrr <- gUnionCascaded(do.call(rbind, lapply(rr, xy2SP))) ## Find area of their intersection gArea(gIntersection(ell, rrr)) # [1] 10.36296