Why does the line function close the path in R?

Question

Purpose: Given the two points, find the coordinates of the arc that connects them, and build it. Implementation: One function for finding arc points ( circleFun ) and another for constructing it ( plottest ). Colors indicate the direction of the path, from red to green.

 circleFun <- function(x,y) { center <- c((x[1]+y[1])/2,(x[2]+y[2])/2) diameter <- as.numeric(dist(rbind(x,y))) r <- diameter / 2 tt <- seq(0,2*pi,length.out=1000) xx <- center[1] + r * cos(tt) yy <- center[2] + r * sin(tt) res <- data.frame(x = xx, y = yy) if((x[1]<y[1] & x[2]>y[2]) | (x[1]>y[1] & x[2]<y[2])){ res <- res[which(res$x>min(c(x[1],y[1])) & res$y>min(c(x[2],y[2]))),] } else { res <- res[which(res$x<max(c(x[1],y[1])) & res$y>min(c(x[2],y[2]))),] } return(res) } plottest <- function(x1,y1) { plot(c(x1[1],y1[1]),c(x1[2],y1[2]), xlim=c(-2,2),ylim=c(-2,2),col=2:3,pch=20,cex=2,asp=1) lines(circleFun(x1,y1)) } par(mfrow=c(2,2)) plottest(c( 1,-1),c(-1, 1)) plottest(c(-1, 1),c( 1,-1)) plottest(c(-1,-1),c( 1, 1)) plottest(c( 1, 1),c(-1,-1)) 

Result:

Question: I cannot understand why the lines function closes the path in figures [1,1] and [1,2], while this is not for figures [2,1] and [2,2]. The expected result should be all the figures, as in the second row.

Thanks!

Answer 1

Like the others. This, as they say, is a much simpler version of your function with the expected result.

 circleFun <- function(x, y) { center <- (x + y) / 2 radius <- sqrt(sum((x - y)^2)) / 2 angle <- atan2((y - x)[2], (y - x)[1]) direc <- ifelse(abs(angle) > pi / 2, -1, 1) tt <- seq(0, direc * pi, length.out = 1000) return(data.frame(x = center[1] + radius * cos(angle + tt), y = center[2] + radius * sin(angle + tt))) } 

where the direc variable determines whether to draw a semicircle clockwise or counterclockwise.

Answer 2

I can answer your question about the lines function, but I will leave it to you to figure out how to fix your circleFun to get the expected behavior:

lines() connects the points in the order in which they appear in the data. In addition, the path is closed only when the first point is included again at the end of the data. The following figure shows this behavior.

 par(mfrow=c(1, 2)) plot(x=c(-1, 0, 1), y=c(-1, 1, -1), xlim=c(-2, 2), ylim=c(-2, 2), type="l", asp=1) points(x=c(-1, 1), y=c(-1, -1)) plot(x=c(-1, 0, 1, -1), y=c(-1, 1, -1, -1), xlim=c(-2, 2), ylim=c(-2, 2), type="l", asp=1) points(x=c(-1, 1), y=c(-1, -1))