the batman equation

require(ggplot2)

f1 <- function(x) {
    y1 <- 3*sqrt(1-(x/7)^2)
    y2 <- -3*sqrt(1-(x/7)^2)
    y <- c(y1,y2)
    d <- data.frame(x=x,y=y)
    d <- d[d$y > -3*sqrt(33)/7,]
    return(d)
}

x1 <- c(seq(3, 7, 0.001), seq(-7, -3, 0.001))
d1 <- f1(x1)
p1 <- ggplot(d1,aes(x,y)) + geom_point(color="red")

x2 <- seq(-4,4, 0.001)
y2 <- abs(x2/2)-(3*sqrt(33)-7)*x2^2/112-3 + sqrt(1-(abs(abs(x2)-2)-1)^2)

#only work with ggplot2 <= 0.8.9
#p2 <- p1 + geom_point(aes(x=x2,y=y2), color="yellow") 

# in ggplot2 0.9.0, should be:
d2 <- data.frame(x2=x2, y2=y2)
p2 <- p1 + geom_point(data=d2, aes(x=x2,y=y2), color="yellow")



x3 <- c(seq(0.75,1,0.001), seq(-1,-0.75,0.001))
y3 <- 9-8*abs(x3)
#p3 <- p2+geom_point(aes(x=x3,y=y3), color="green")
d3 <- data.frame(x3=x3, y3=y3)
p3 <- p2+geom_point(data=d3, aes(x=x3,y=y3), color="green")


x4 <- c(seq(0.5,0.75,0.001), seq(-0.75,-0.5,0.001))
y4 <- 3*abs(x4)+0.75
#p4 <- p3+geom_point(aes(x=x4,y=y4), color="steelblue")
d4 <- data.frame(x4=x4,y4=y4)
p4 <- p3+geom_point(data=d4, aes(x=x4,y=y4), color="steelblue")


x5 <- seq(-0.5,0.5,0.001)
y5 <- rep(2.25,length(x5))
#p5 <- p4+geom_point(aes(x=x5,y=y5))
d5 <- data.frame(x5=x5,y5=y5)
p5 <- p4+geom_point(data=d5, aes(x=x5,y=y5))

x6 <- c(seq(-3,-1,0.001), seq(1,3,0.001))
y6 <- 6 * sqrt(10)/7 +
    (1.5 - 0.5 * abs(x6)) * sqrt(abs(abs(x6)-1)/(abs(x6)-1)) -
    6 * sqrt(10) * sqrt(4-(abs(x6)-1)^2)/14
#p6 <- p5+geom_point(aes(x=x6,y=y6), colour="blue")
d6 <- data.frame(x6=x6,y6=y6)
p6 <- p5+geom_point(data=d6,aes(x=x6,y=y6), colour="blue")

p <- p6+theme_bw()
print(p)