## The goal is to reproduce this Bid-Rent graph in R:

**The challenge is to draw the projected circles. So far I got:**

The 2D part is created by the R code below with the traditional graphic system in base R:

```
#Distance
X <- seq(0,7,1)
#Bid Rent Curves: Commercial, Industrial, Residential
com <- -5*X + 10
ind <- -2*X + 7
res <- -0.75*X + 4
graph <- plot(X, com, type="l", col="green", ylim=c(0,10), xlab="", ylab="", axes=FALSE)
lines(X, ind, col="red")
lines(X, res, col="blue")
abline(v=0, h=0)
segments(1,0, 1,5, lty=2)
segments(2.5,0, 2.5,2, lty=2)
title(main="Bid Rent Curves", sub="Alonso Model",
xlab="Distance from CBD", ylab="Rent per m2")
text(2.5,7.5, "Commercial", col="green")
text(3.5,4, "Industrial", col="red")
text(5.5,2, "Residential", col="blue")
```

- (Detail: Why the curves do not respect the ylim = 0 ?)
- How make the projection and draw the semi-circles?

It is not exactly a 3D plot. I have looked into plot3D and rgl. I am not sure which packages or strategy to use from here.

# Best How To :

I'm taking you at your word that you want circles, so you need to push the plot area into the upper right corner:

```
outHalfCirc <- function(r,colr) {opar=par(xpd=TRUE, new=TRUE) #plot ouside plot area
polygon(x=seq(r,-r,by=-0.1),
y= -sqrt(r^2 - seq(r,-r,by=-0.1)^2) , # solve r^2 = x^2 +y^2 for y
xlim =c(0,7 ), ylim=c(0,10), col=colr, # need xlim and ylim to match base plot ranges
yaxs="i", yaxt="n", xaxs="i") # yaxis off; x and y axes meet at origin
par(opar)}
```

Then push plot up and to the right: This will draw a colored half-circles (largest first so they overlap) below the y=0 line.

```
png() # send to image file; not needed for testing
opar <- par(mar=c(15, 15, 2,2) ) # default units are in widths of text-"line".
# the margins start at lower, then clockwise
# run your code
outHalfCirc(5.5, "blue")
outHalfCirc(2.5, "red")
outHalfCirc(1, "green")
dev.off() # complete image production
par(opar) # different than the 'opar' inside the function
```

Voila! Although not really circles because the aspect ratio is not 1. That can be fixed (or you could set the xlim and ylim to be equal.