Why polygon in R works with a full curve but not with a half curve?

问题

I'm wondering why polygon() works very well with a two-sided curve (bottom picture), but not working correctly with a half of that same curve (top picture)?

I appreciate a short explanation.

par(mfrow = c(2, 1))

gg = curve(dnorm(x), -4, 0) # Not working!
polygon(gg, col = 2)

gg = curve(dnorm(x), -4, 4) # Working!
polygon(gg, col = 2)

回答1:

One curve

Since polygon connects the start and the end of your curve, it creates some weird shape. From ?polygon we can see that

"It is assumed that the polygon is to be closed by joining the last point to the first point."

The first and last points are given by the from and to values in curve. In your first case these are -4 and 0.

Just add xlim and xaxs = "i" to curve()

gg = curve(dnorm(x), -4, 4, xlim = c(-4,0), xaxs = "i") # Working!
polygon(gg, col = 2)

Multiple curves in one plot

When you want to put multiple curves in one plot, you might face the problem that you can't limit your axes as shown above. Thus, we have to dig deeper into the structure of a curve object (here gg).

Let's first create two curves.

gg = curve(dnorm(x), -4, 4) ; 
polygon(gg, col = 2) ; 
gg = curve(dnorm(x), -4, 0, xlim = c(-4,0), xaxs = "i", add = T) ; 

Now we have a look at gg:

gg 
# $x
# [1] -4.00 -3.96 -3.92 -3.88 -3.84 -3.80 -3.76 -3.72 -3.68 -3.64 -3.60 -3.56 -3.52 -3.48 -3.44 -3.40 -3.36 -3.32 -3.28
# [20] -3.24 -3.20 -3.16 -3.12 -3.08 -3.04 -3.00 -2.96 -2.92 -2.88 -2.84 -2.80 -2.76 -2.72 -2.68 -2.64 -2.60 -2.56 -2.52
#  .....
# $y
# [1] 0.0001338302 0.0001569256 0.0001837125 0.0002147280 0.0002505784 0.0002919469 0.0003396012 0.0003944025 0.0004573148
# [10] 0.0005294147 0.0006119019 0.0007061107 0.0008135212 0.0009357722 0.0010746733 0.0012322192 0.0014106023 0.0016122275
#  .....

We see that gg is just a list of $x and $y coordinates. Thus, we can add one coordinate at 0, 0 to the second gg to simulate the end of the overlapping second curve. Afterwards both curves are plotted correctly.

gg$x <- c(gg$x, 0)
gg$y <- c(gg$y, 0)
polygon(gg, col = 4)

回答2:

Loki shows you how to fill the curve as you want but does not explain why the half curve fills as it does, which is important if you are looking to use this function moving forward.

Because you are giving polygon() a single curved line, it closes both ends by drawing a straight line to connect them. Then it fills in the spaces between the curve and the new line.

The full distribution rises and drops to the same point on the y-axis creating a nice pretty filled curve. By stopping at the top of the curve, the line is drawn through the changes in direction leaving open spaces between the curve and the line on both sides, which polygon() fills them both.

来源：https://stackoverflow.com/questions/45391205/why-polygon-in-r-works-with-a-full-curve-but-not-with-a-half-curve