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Since I have a vacation this time I decided to implement some entertaining graphics. I have chosen to animate a Cassini oval.Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
The task is can be accomplished using polar equation:
library(animation)< o:p>
xy <- function(angle, a, b) {< o:p>
ca <- cos(2 * angle)< o:p>
r2 <- a ^ 2 * ca + sqrt(a ^ 4 * ca ^ 2 – (a ^ 4 – b ^ 4))< o:p>
c(sqrt(r2) * cos(angle), sqrt(r2) * sin(angle))< o:p>
}< o:p>
go <- function() {< o:p>
angle <- seq(0, 2 * pi, len = 1000)< o:p>
par(mar = rep(0,4))< o:p>
b <- 1 + 0.5 * seq(0, 1, len = 31) ^ 3< o:p>
b <- c(b, 1.5, rev(b))< o:p>
for (i in b) {< o:p>
coord <- t(sapply(angle, xy, a = 1, b = i))< o:p>
plot(coord, type = “l”, < o:p>
xlim = c(-2, 2), ylim = c(-1.25, 1.25))< o:p>
polygon(coord, col = “gray”)< o:p>
}< o:p>
}< o:p>
ani.options(interval = 0.1)< o:p>
saveGIF(go())< o:p>
Parameter a is fixed to 1 and b changes from 1 to 1.5. In order to achieve smooth animation the sequence defining changes of b is not uniform but is more dense near 1.
And here is the result:
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