plot Ellipse bounding a percentage of points

Question

I am using ellipsoidhull() function to derive an ellipse that bounds all the points in x,y coordinates. I then use point.in.polygon() function to predict if a new set of X,Y co-

Answer 1

Presumably you were using cluster::ellipsoidhull. In a different package the car::dataEllipse function calculates a center, shape and radius value and passes to ellipse. For the "presumed Normal" situation, which it seems you might be assuming, the relevant code is:

library(car)
dataEllipse
function(x,y, ....
...
else {
        shape <- var(cbind(x, y))
        center <- c(mean(x), mean(y))
    }
    for (level in levels) {
        radius <- sqrt(dfn * qf(level, dfn, dfd)

Then 'ellipse' calculates its individual points which get passed to lines. The code to do that final calculation is

ellipse <-
function (center, shape, radius, ....)
....
 angles <- (0:segments) * 2 * pi/segments
    unit.circle <- cbind(cos(angles), sin(angles))
    ellipse <- t(center + radius * t(unit.circle %*% chol(shape)))
    colnames(ellipse) <- c("x", "y")

So the combination of these two functions works with your data:

getEparams <-function(x,y, level) { dfn <- 2
        dfd <- length(x) - 1
        shape <- var(cbind(x, y))
        center <- c(mean(x), mean(y))
        radius <- sqrt(dfn * qf(level, dfn, dfd))
        return(list(center=center, shape=shape, radius=radius) ) }

ellcalc <- function (center, shape, radius, segments=51){segments=segments
    angles <- (0:segments) * 2 * pi/segments
    unit.circle <- cbind(cos(angles), sin(angles))
    ellipse <- t(center + radius * t(unit.circle %*% chol(shape)))
    colnames(ellipse) <- c("x", "y")
    return(ellipse)}

evals <- getEparams(Query$X, Query$Y, 0.80)
plot(ellcalc(evals[["center"]], evals[["shape"]], evals[["radius"]]))
title(main='Output of plot(ellcalc(evals[["center"]], evals[["shape"]], 
                           evals[["radius"]]))\nStackOverflow Demonstration')
 points(Query$X, Query$Y, cex=0.3, col="red")

You could obviously save or pass the results of the ellcalc call to any object you wanted