Extract (count) the points within a certain region of a ggplot-CodePudding

I have the following data.


x_plus <- c(1.3660254, 1.1123724, 1.0000000, 0.9330127, 0.8872983,
            0.8535534, 0.8273268, 0.8061862, 0.7886751, 0.7738613,
            0.6936492, 0.6581139, 0.6369306, 0.6224745, 0.6118034,
            0.5968246, 0.5866025, 0.5707107, 0.5612372, 0.5500000,
            0.5433013, 0.5387298, 0.5353553, 0.5306186, 0.5273861, 
            0.5193649, 0.5158114, 0.5122474, 0.5103510, 0.5086603,
            0.5050000, 0.5027386, 0.5008660)


x_minus <- c(-0.3660254, -0.1123724,  0.0000000,  0.0669873,  0.1127017,
             0.1464466,  0.1726732,  0.1938138,  0.2113249, 0.2261387,  
             0.3063508,  0.3418861,  0.3630694,  0.3775255,  0.3881966,
             0.4031754,  0.4133975,  0.4292893, 0.4387628,  0.4500000,
             0.4566987,  0.4612702,  0.4646447,  0.4693814,  0.4726139,
             0.4806351,  0.4841886, 0.4877526,  0.4896490,  0.4913397,
             0.4950000,  0.4972614,  0.4991340)


y <- c(1.50, 3.00, 4.50, 6.00, 7.50, 9.00, 1.05e 01, 1.20e 01, 1.35e 01,
       1.50e 01, 3.00e 01, 4.50e 01, 6.00e 01, 7.50e 01, 9.00e 01, 1.20e 02,
       1.50e 02, 2.25e 02, 3.00e 02, 4.50e 02, 6.00e 02, 7.50e 02, 9.00e 02,
       1.20e 03, 1.50e 03, 3.00e 03, 4.50e 03, 7.50e 03, 1.05e 04, 1.50e 04,
       4.50e 04, 1.50e 05, 1.50e 06)


df <- data.frame(cbind(x_plus, x_minus, y))

x_points <- c(.5, .6, .43, .1, 1, .52, .6)
y_points <- c(50, 100, 5000, 300, 500, 700, 10)

which I use to produce the following plot.

library(ggplot2)

ggplot() 
  geom_point(aes(x = x_points, y = y_points)) 
  geom_path(data = df, aes(x = x_plus, y = y)) 
  geom_path(aes(x = x_minus, y = y)) 
  scale_y_log10() 
  coord_cartesian(ylim = c(10, 1e4))

How would one go about mathematically determining how many points fall between the two geom_path() lines? For my actual application there may be thousands of points on this plot. Any advice is greatly appreciated!

CodePudding user response：

You can use approxfun() to create a function which interpolates the point on the curve and tells you the y coordinate of the curve for any x. Then you just compare these values with the y coordinates of your points:

# rearrange the data into just two columns of x and y
df <- data.frame(x=c(df$x_minus, df$x_plus), y=df$y)
df <- df[order(df$x), ]

# function for linear interpolation of points
interp_fun <- approxfun(df)
# which points are below the curve
points_below <- interp_fun(x_points) > y_points

ggplot() 
  geom_point(aes(x = x_points, y = y_points, color=points_below)) 
  geom_path(data = df, aes(x=x, y=y)) 
  scale_y_log10() 
  coord_cartesian(ylim = c(10, 1e4))

The number of points below the curve can be obtained with sum(points_below).