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rggplot2intersectioncurve

Point of intersection in ggplot2

I need to find the intersection points between two curves I have plotted in ggplot2.

This is my code:

ggplot(Table1, aes(x=10^H4,y=10^H5, colour = "blabla")) + 
  geom_line(size=1)  + coord_cartesian(xlim=c(100,1000000000))+
 coord_cartesian(ylim=c(0.000000000001,1)) +  xlab("blabla")+
 ylab("blabla")  + ggtitle("blabla")+
scale_y_log10(breaks=c(0.000000000001, 0.000000001, 0.000001, 0.001)
, labels = trans_format("log10", math_format(10^.x)))+
 scale_x_log10(breaks=c(100,1000,10000,100000,1000000,10000000,100000000,1000000000)   
 , labels = trans_format("log10", math_format(10^.x))) + 
  geom_line(data=Table1,aes(10^H4,10^H6, colour = "blabla1"))+ 
  scale_color_manual("", values =c("blabla"="blue", "blabla1" = "red")
, labels=c("blabla","blabla1"))

I have tried using the locator() which is useful but not precise as I would expect:

Desired point

The desired point is at 24600.

I also tried using the intercept(x,y):

a <- 10^A5
b <- 10^A6
intercept(a,b)
3.689776e-07 1.963360e-07 6.622165e-07

Which is not the case, I presume that it might be not considering the fact that this is a log-log scale.

My data :

structure(list(H4 = c(2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 
2.9, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 
4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5, 5.1, 5.2, 5.3, 5.4, 
5.5, 5.6, 5.7, 5.8, 5.9, 6, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 
6.8, 6.9, 7, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 8, 
8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9), H5 = c(-8.979, 
-8.927, -8.877, -8.829, -8.782, -8.736, -8.691, -8.648, -8.606, 
-8.565, -8.525, -8.485, -8.445, -8.405, -8.364, -8.323, -8.282, 
-8.241, -8.2, -8.159, -8.116, -8.064, -7.982, -7.826, -7.592, 
-7.333, -7.101, -6.91, -6.759, -6.64, -6.543, -6.461, -6.387, 
-6.321, -6.264, -6.218, -6.182, -6.155, -6.132, -6.117, -6.111, 
-6.12, -6.23, -6.433, -6.574, -6.664, -6.712, -6.726, -6.722, 
-6.707, -6.704, -6.748, -6.82, -6.864, -6.872, -6.859, -6.83, 
-6.796, -6.757, -6.717, -6.678, -6.636, -6.594, -6.549, -6.502, 
-6.454, -6.402, -6.349, -6.295, -6.238, -6.179), H6 = c(-5.116, 
-5.31, -5.495, -5.669, -5.823, -5.958, -6.075, -6.179, -6.271, 
-6.355, -6.433, -6.506, -6.575, -6.642, -6.707, -6.769, -6.829, 
-6.886, -6.941, -6.993, -7.044, -7.095, -7.144, -7.192, -7.237, 
-7.28, -7.321, -7.36, -7.398, -7.435, -7.47, -7.504, -7.536, 
-7.569, -7.602, -7.64, -7.684, -7.735, -7.789, -7.848, -7.917, 
-8.003, -8.131, -8.312, -8.494, -8.668, -8.823, -8.963, -9.095, 
-9.225, -9.365, -9.531, -9.711, -9.859, -9.965, -10.041, -10.098, 
-10.141, -10.175, -10.203, -10.236, -10.263, -10.285, -10.301, 
-10.314, -10.323, -10.33, -10.335, -10.339, -10.342, -10.344)), .Names = c("H4", 
"H5", "H6"), row.names = c(NA, -71L), class = "data.frame")
Solution

  • We could use the approxfun() function, which does linear interpolation. We use the difference between the two curves (or between the set of data points) and then find the approximate value in the x-axis that makes the difference or value in y equal to 0.

    #Finding the x value in the log10 scale

f1 <- approxfun(10^Table1$H5 - 10^Table1$H6,Table1$H4, rule=2)

f1(0)
[1] 4.516067

x11(); ggplot(Table1, aes(x=10^H4,y=10^H5, colour = "blabla")) + 
  geom_line(size=1)  + coord_cartesian(xlim=c(100,1000000000))+
 coord_cartesian(ylim=c(0.000000000001,1)) +  xlab("blabla")+
 ylab("blabla")  + ggtitle("blabla")+
scale_y_log10(breaks=c(0.000000000001, 0.000000001, 0.000001, 0.001)
, labels = trans_format("log10", math_format(10^.x)))+
 scale_x_log10(breaks=c(100,1000,10000,100000,1000000,10000000,100000000,1000000000)   
 , labels = trans_format("log10", math_format(10^.x))) + 
  geom_line(data=Table1,aes(10^H4,10^H6, colour = "blabla1"))+ 
  scale_color_manual("", values =c("blabla"="blue", "blabla1" = "red")
, labels=c("blabla","blabla1"))+
geom_vline(xintercept=10^ f1(0)) # adding the verical line

    enter image description here

    Data:

    structure(list(H4 = c(2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 
2.9, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 
4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5, 5.1, 5.2, 5.3, 5.4, 
5.5, 5.6, 5.7, 5.8, 5.9, 6, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 
6.8, 6.9, 7, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 8, 
8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9), H5 = c(-8.979, 
-8.927, -8.877, -8.829, -8.782, -8.736, -8.691, -8.648, -8.606, 
-8.565, -8.525, -8.485, -8.445, -8.405, -8.364, -8.323, -8.282, 
-8.241, -8.2, -8.159, -8.116, -8.064, -7.982, -7.826, -7.592, 
-7.333, -7.101, -6.91, -6.759, -6.64, -6.543, -6.461, -6.387, 
-6.321, -6.264, -6.218, -6.182, -6.155, -6.132, -6.117, -6.111, 
-6.12, -6.23, -6.433, -6.574, -6.664, -6.712, -6.726, -6.722, 
-6.707, -6.704, -6.748, -6.82, -6.864, -6.872, -6.859, -6.83, 
-6.796, -6.757, -6.717, -6.678, -6.636, -6.594, -6.549, -6.502, 
-6.454, -6.402, -6.349, -6.295, -6.238, -6.179), H6 = c(-5.116, 
-5.31, -5.495, -5.669, -5.823, -5.958, -6.075, -6.179, -6.271, 
-6.355, -6.433, -6.506, -6.575, -6.642, -6.707, -6.769, -6.829, 
-6.886, -6.941, -6.993, -7.044, -7.095, -7.144, -7.192, -7.237, 
-7.28, -7.321, -7.36, -7.398, -7.435, -7.47, -7.504, -7.536, 
-7.569, -7.602, -7.64, -7.684, -7.735, -7.789, -7.848, -7.917, 
-8.003, -8.131, -8.312, -8.494, -8.668, -8.823, -8.963, -9.095, 
-9.225, -9.365, -9.531, -9.711, -9.859, -9.965, -10.041, -10.098, 
-10.141, -10.175, -10.203, -10.236, -10.263, -10.285, -10.301, 
-10.314, -10.323, -10.33, -10.335, -10.339, -10.342, -10.344)), .Names = c("H4", 
"H5", "H6"), row.names = c(NA, -71L), class = "data.frame")