# Blatt 6, Aufgabe 2 d)
########################
radius <- 0
maxRad = sqrt(2)

xcoords <- numeric(0)
ycoords <- numeric(0)

xcoords <- 0
ycoords <- 0

intersects <- numeric(0)
slopes <- numeric(0)

while(radius < maxRad) {
  radius <- radius + rexp(1, 10)
  angle <- runif(1, 0, 2*pi)

  x <- radius*cos(angle)
  y <- radius*sin(angle)

  xcoords <- c(xcoords, x)
  ycoords <- c(ycoords, y)

  intersects <- c(intersects, y + cos(angle) / sin(angle) * x)
  slopes <- c(slopes, -cos(angle) / sin(angle))
}

plot(xcoords, ycoords, xlim=c(-1,1), ylim=c(-1,1))
# plot(0,0, xlim=c(-1,1), ylim=c(-1,1))

for (i in 1:length(intersects)) {
  abline(intersects[i], slopes[i])
}