Classify XY points on scatter plot by sectors and euclidian distance?-CodePudding

I wish to show on my scatter plot :

how far away are values from the plot origin [0,0], and
are they closer to the center, X, Y axis, both XY, or far away? In terms of spliting the plot into sectors by 2 lines (at 33 degrees) and cirle-like sections.

To estimate how far are the points from the origin [0,0], I can easily calculate the Euclidian distace.

But I am not sure how to classify my points based to their distance to the origin [0,0], and to the X, or Y axis or both? I think my issue here is that I can't simply set the classification rule s as:

Center = if X < 0.5 & Y < 0.5, as this represents a square. Rather, my values should follow the euclidian distance here? e.g Center = X < 0.5 & Y < 0.5 & Euclid_dist < 0.5

But how to get the classification for the 'X', 'Y', 'XY' and their 'far' alternatives, considering at the same time both lines and circles as sectors? It is likely a simple trigonometric question, but I can't figure it out.

Here is my ideal case:

And my dummy example:

dd <- data.frame(x = runif(10, min=0, max=2),
                 y = runif(10, min=0, max=2))

# Get euclidean distance
euclidean <- function(a, b) sqrt(sum((a - b)^2))

dd <- dd %>% 
  mutate(euclid_dist = euclidean(x, y))

dd %>% 
  ggplot(aes(x = x,
             y = y))  
  geom_point()  
  theme_bw()  
  theme_update(aspect.ratio=1)

CodePudding user response：

This is probably not the most efficient way to do it, but it's a start.

set.seed(4242)
dd <- data.frame(x = runif(20, min=0, max=2),
                 y = runif(20, min=0, max=2))

# I changed your euclidean distance function to return distance of each point from the origin
euclidean <- function(a, b) {
  sqrt((dd$x)^2   (dd$y)^2)
}

# Define the slopes of the lines that divide the area into x, y, xy
slope1 <- 0.5
slope2 <- 2

# Define the radii of the circles that define the origin,?, far areas,
# which I've called near, mid, far
r1 <- 0.5
r2 <- 1.5

dd2 <- dd %>% 
  mutate(
    euclid_dist = euclidean(x, y),
    computed_y1 = x * slope1,
    computed_y2 = x * slope2,
    dist = cut(euclid_dist, breaks=c(0, r1, r2, 5), label=c('near', 'mid', 'far'))
    )

# There's presumably a way to do this within the above mutate function using case_when()
dd2$pos <- 'xy'
dd2$pos[dd2$y < dd2$computed_y1] <- 'x'
dd2$pos[dd2$y > dd2$computed_y2] <- 'y'
dd2$pos <- as.factor(dd2$pos)

ggplot(dd2)  
  geom_point(aes(x = x, y = y, col=dist, shape=pos), size=3)  
  
  annotate("path",
           x = r1*cos(seq(0,2*pi,length.out=100)),
           y = r1*sin(seq(0,2*pi,length.out=100))
  )  
  annotate("path",
           x = r2*cos(seq(0,2*pi,length.out=100)),
           y = r2*sin(seq(0,2*pi,length.out=100))
  )  
  
  geom_abline(intercept = 0, slope=0.5, col='red')  
  geom_abline(intercept = 0, slope=2, col='blue')  
  scale_x_continuous(expand = c(0, 0), limits = c(0, 2))  
  scale_y_continuous(expand = c(0, 0), limits = c(0, 2))  
  theme_classic()

CodePudding user response：

library(tidyverse)
library(ggthemes)
set.seed(123)
dd <- data.frame(x = runif(200, min=0, max=2),
                 y = runif(200, min=0, max=2))

slope = 33 #degrees

dd %>% 
  #calculate dfistance from origin
  mutate(orig_dist = sqrt(x^2   y^2)) %>%
  #calculate position (origin, far, etc..)
  mutate(position = case_when(orig_dist < 0.5 ~ "origin",
                              orig_dist >= 1 ~ "-far",
                              TRUE ~ "")) %>%
  #calculate XY label
  mutate(labelXY = case_when((180*atan(x / y) / pi) < slope ~ "Y",
                             (180*atan(x / y) / pi) > (90 - slope) ~ "X", 
                             TRUE ~ "XY")) %>%
  #create group category
  mutate(group = ifelse(position == "origin", 
                        position, 
                        paste0(labelXY, position))) %>%
  #plot
  ggplot(aes(x = x, y = y, color = group))   geom_point()  
  ggthemes::scale_color_colorblind()  
  theme_bw()   theme_update(aspect.ratio=1)