gistfile1.txt

## DJV 1 target, see http://imgur.com/LHiZFeG
## unit x y -> cm
## points on outer polygon (ring 1)
djv1 <- read.table(file=textConnection("x y
                                        25.4 67.9
                                        21.2 59.3
                                        27.5 49.4
                                        36.7 46.2
                                        50.4 46.2
                                        57.2 47.3
                                        58.9 55.7
                                        56.6 65.1
                                        40.2 65.7
                                        30.9 66.3"), header=TRUE)

## assumed shot distribution
## bivariate normal centered at ring 10 + bias c(2, 3) cm
## about sdX=1.5 MOA sdY=2 MOA -> sdX=9 and sdY=12 cm
## correlation = 0.2
ctr10 <- c(40.2, 55.7)     # target center coords
mu    <- ctr10 + c(2, 3)   # systematic accuracy bias
sdX   <- 9
sdY   <- 12
corXY <- 0.2
covXY <- sdX*sdY*corXY
sigma <- cbind(c(sdX^2, covXY), c(covXY, sdY^2))   # covariance matrix

## define polygonal integration region covering DJV 1 ring 1
## install.packages(c("shotGroups", "polyCub"))
## install.packages("gpclib", type="source")
library(polyCub)  # for polyCub.exact.Gauss()
library(gpclib)   # for as.gpc.poly()
djv1Pts  <- data.matrix(subset(djv1, select=c(x, y)))  # just x, y coords
djv1Poly <- as(djv1Pts[chull(djv1Pts), ], "gpc.poly")  # convert to gpc polygon
gpclibPermit()    # necessary for running polyCub.exact.Gauss()
## integrate shot distribution over polygon = DVJ 1 ring 1
polyCub.exact.Gauss(djv1Poly, mean=mu, Sigma=sigma, plot=FALSE)
# 0.5431248

## approximate DJV 1 ring 1 polygon with elliptical integration region
S <- cbind(c(18^2, 0), c(0, 10^2))
e <- solve(S)
## integrate shot distribution over ellipse
library(shotGroups) # for pmvnEll(), drawEllipse()
pmvnEll(r=1, sigma=sigma, mu=mu, e=e, x0=ctr10)
# 0.4977843