# Emulate Eye tracking data and remove all that is x pixels away from the centre
set.seed(007)

# Assume screen of 1920 by 1080 pixels
xmax <- 1920
ymax <- 1080
ymid <- ymax/2
xmid <- xmax/2

# Simulate some data that truly fixes on the centre screen
sims <- 10000 # How many simulations
xT <- rnorm(sims,xmid,20)
yT <- rnorm(sims,ymid,20)

# Add noise where people fixed at random points of screen
xN <- runif(sims/5,0,xmax)
yN <- runif(sims/5,0,ymax)

# Merge together
x <- c(xT,xN)
y <- c(yT,yN)
results <- data.frame(x,y)

# Plot all simulations
plot(results, xlim=c(0,xmax), ylim=c(0,ymax))

# Try to subset part of data that is within radius of centre
threshold <- 40 # Threshold set aggressive to clarify issue
resultsSub <- results[results$x <= xmid+threshold & results$x >= xmid-threshold & results$y <= ymid+threshold & results$y >= ymid-threshold,]

# Plot obviously wrong solulution. Now a square is left rather than a circle
plot(resultsSub, xlim=c(0,xmax), ylim=c(0,ymax))

# Potential way forward?
# Centre as 0.0
resultsC <- results
resultsC$x <-  resultsC$x-xmid
resultsC$y <-  resultsC$y-ymid

# Create circle with radius of threshold
objects <- 100
th = seq(0,(2*pi),2*pi/objects)
thred =  th[seq(1,100,1)]

### Default
xposd = cos(thred)*40
yposd = sin(thred)*40

# Somehow compare defined circle against data
plot(resultsC)
points(xposd,yposd, col="red")