Find the exact coordinates of a contour on a surface and plot it manually in R plotly

Question

I am drawing a surface plot and would like to "manually" draw a contour line using plotly. In the code below I:

• simulate the data for drawing the surface plot
• calculate the coordinates of the contour line at a specific z level using the contoureR package
• draw the surface plot and contour line

# Load packages
library(plotly) # for interactive visualizations
library(contoureR) # for calculating contour coordinates

# Simulate the data for plotting
x <- y <- seq(from = 0, to = 100, by = 1)
z1 <- outer(X = x, Y = y, FUN = function(x, y) x^0.2 * y^0.3) # data for surface plot

# Obtain coordinates of contour for z = 5
z_level <- 5
r <- contourLines(x = x, y = y, z = z1, levels = z_level)

plot_ly(
  type = "surface",
  x = x,
  y = y,
  z = z1,
) %>%
  add_trace(
    type = "scatter3d",
    x = r[[1]]$x,
    y = r[[1]]$y,
    z = z_level
  )

I am aware that these are all approximations, so I also tried to pass the x and y coordinates produced by contourLines() to the formula used to create z1above and use the corresponding values to plot my contour line (instead of using z_level = 5, but I still do not obtain the desired result:

plot_ly(
  x = x,
  y = y,
  z = z1,
  type = "surface"
) %>%
  add_trace(
    type = "scatter3d",
    x = r[[1]]$x,
    y = r[[1]]$y,
    z = r[[1]]$x^0.2*r[[1]]$y^0.3
  )

I alo know that plotly enables me to draw specific contour lines (see my question and answer here: Add a permanent contour line to a surface plot in R plotly). However, I would like to draw my contour line myself (after getting their coordinates) so it can "pull" by cursor and show me the tooltip info whenever I hover over it. Ideally, if there was a way to obtain the contour lines coordinates as computed by plotly itself, that would be great.

Thank you for your help.

Answer 1

I was able to find two solutions to this problem.

Solution 1: transpose the z1 matrix

The first solution was given me by @nirgrahamuk and it consists in transposing the z1 matrix:

library(plotly) # for interactive visualizations

# Simulate the data for plotting
x <- y <- seq(from = 0, to = 100, by = 1)
z1 <- outer(X = x, Y = y, FUN = function(x, y) x^0.2 * y^0.3) # data for surface plot

# Obtain coordinates of contour for z = 5
z_level <- 6
r <- contourLines(x = x, 
                  y = y, 
                  z = z1, 
                  levels = z_level)

plot_ly(
  type = "surface",
  z = t(z1), # *** WE TRANSPOSE THE MATRIX HERE! ***
) %>%
  add_trace(
    type = "scatter3d",
    x = r[[1]]$x,
    y = r[[1]]$y,
    z = z_level
  )

Solution 2: use the isoband package

The second solution is to compute the contour lines coordinates with the isoband::isolines() function:

library(plotly) # for interactive visualizations
library(isoband) # for find contour lines coordinates

# Simulate the data for plotting
x <- y <- seq(from = 0, to = 100, by = 1)
z1 <- outer(X = x, Y = y, FUN = function(x, y) x^0.2 * y^0.3) # data for surface plot

# Obtain coordinates of contour for z = 5
z_level <- 6
r <- isolines(x = x, # *** WE USE THE isolines() FUNCTION HERE ***
              y = y, 
              z = z1, 
              levels = z_level)

plot_ly(
  type = "surface",
  z = z1, 
) %>%
  add_trace(
    type = "scatter3d",
    x = r[[1]]$x,
    y = r[[1]]$y,
    z = z_level
  )