[R] Filled region on graph

[Ross Ihaka]

On Thu, Nov 02, 2000 at 07:27:14PM -0500, Yves Gauvreau wrote:
> Hi,
> 
> Say I'd like to fill in color or by hashing the region above 0.5 and
> below -0.5 in the following situation.
> 
> > x <- seq(0,2*pi, length=100)
> > plot(x, sin(x), type="l")
> > # Now fill the top part and the bottom part

Like many other problems there is no high level solution and you have
to create your own.  The function "polygon" can be used to draw filled
polygons and it can be used to fill a polygon approximation to the area
you want filled.  (Hashing is on my TODO list, but its not close to
the top).

To start, we need the points where the line y==0.5 cuts the curve.
In the case you mention, it is easy to see that these points are

    lower <- asin(0.5)
    upper <- pi - asin(0.5).

More generally, you could determine the intersection points by root finding

    lower <- uniroot(function(x) sin(x)-0.5, lower=0, upper=pi/2)$root
    upper <- uniroot(function(x) sin(x)-0.5, lower=pi/2, upper=pi)$root

Now we just compute the appoximating polygon

    x <- seq(lower, upper, length=100)
    y <- sin(x)

and draw it

    polygon(x, y, col = "hotpink")

So here a the full solution.

    x <- seq(0,2*pi, length=100)
    plot(x, sin(x), type="l")
    lower <- uniroot(function(x) sin(x)-0.5, lower=0, upper=pi/2)$root
    upper <- uniroot(function(x) sin(x)-0.5, lower=pi/2, upper=pi)$root
    x <- seq(lower, upper, length=100)
    y <- sin(x)
    polygon(x,y,col="hotpink")
    lower <- uniroot(function(x) sin(x)+0.5, lower=pi, upper=3*pi/2)$root
    upper <- uniroot(function(x) sin(x)+0.5, lower=3*pi/2, upper=2*pi)$root
    x <- seq(lower, upper, length = 100)
    y <- sin(x)
    polygon(x, y, col = "limegreen")

	Ross
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