I have created the below example plot using ggplot2.
The plot area is divided into various zones (SD, TC, CC, CCS) between the gray lines. I know the equations of each of these gray lines. I have also plotted my data What I would like to do is to find the zone where each data point is plotted, so I can divide them into categories and e.g. give them different colors for each zone. Does anyone have any idea? Thanks a lot in advance.
EDIT I added code to reproduce a simple example.
# load libraries
library(tidyverse)
# sample data
sample_data <- 
    tibble(
        x = c(8, 8, 8, 8, 8, 0),
        y = c(5, 10, 20, 50, 100, 100)
    )
# names of zones
zoning_data <-
  tibble(
    x = c(
      18,
      18,
      0,
      18
    ),
    y = c(
      70,
      25,
      600,
      600
    ),
    label = c(
      "CC",
      "CCS",
      "SD",
      "TC"
    )
  )
# plot
ggplot(
  data = sample_data,
  aes(
    x,
    y
  )
) +
  # points
  geom_point() +
  scale_x_continuous(
    expand = c(0, 0),
    minor_breaks = NULL,
    breaks = c(
      seq(-2, 20, by = 2)
    )
  ) +
  scale_y_continuous(
    trans = "log10",
    expand = c(0, 0),
    minor = c(
      seq(1, 10, by = 1),
      seq(10, 100, by = 10),
      seq(100, 1000, by = 100)
    )
  ) +
  coord_cartesian(
    xlim = c(-2, 20),
    ylim = c(1, 1000),
    expand = c(0, 0)
  ) +
  # equations for zoning lines
  geom_function(
    fun = function(x) ((x - 1.05) * 5)^1.0526,
    xlim = c(1.31, 20)
  ) +
  geom_function(
    fun = function(x) ((x - 1.1) * 1.5)^1.0989,
    xlim = c(2.82, 20)
  ) +
  geom_function(
    fun = function(x) x,
    xlim = c(-2, 20)
  ) +
  # zoning names
  geom_text(
    data = zoning_data,
    aes(
      x = x,
      y = y,
      label = label
    )
  ) +
  # theme
  theme(aspect.ratio = 1)
 
    

