Creating Surface 3D Plot of 3 Numeric variables in R

Question

> plot_data
      cs    w          u
1     0  0.0 1.00000000
2   125  0.5 1.23818786
3   250  1.0 4.15500984
4   375  1.5 1.41931096
5   500  2.0 0.51660657
6   625  2.5 0.29800493
7   750  3.0 0.20846944
8   875  3.5 0.16441816
9  1000  4.0 0.14116564
10 1125  4.5 0.12890978

#Scatter PLot 
 p <- plot_ly(x=plot_data$cs,y=plot_data$w,z=plot_data$u)
 p

plot_data is data frame with three variables .. using plot_ly function 3d scatter plot can be obtain .. how to do surface plot for same variables as surface plot looks for matrix and how to create that matrix .

Answer 1

TL;DR There are many options. Three are explained below, including one with plotly as requested by the OP. plotly is probably not the best. Some data preparation may be required as is the case in the example data given by both the OP and the answer by @rar .

Disclaimer: Unfortunately 3d surface plots are a bit of a pain in R. Python is a possible alternative; I find python-matplotlib is extremely easy, straightforward, and intuitive compared to all of the many options in R.

Data preparation 1: You should actually have 3d data

Plotting 2d data as 3d is a common mistake. The data in the OP, for instance, forms nearly linear curve in 3d. While it may be possible to treat these points as independent observations of z-axis values in particular locations in the xy-plain and to interpolate a 3d-surface from that, I doubt that the resulting surface plot would be very useful or informative.

In any case for plotting of 3d-surfaces, you will almost always need a grid of observations over the xy-plain. To interpolate values necessary for such a grid in R, you may use akima::interp like so

library(akima)
df <- data.frame(matrix(rnorm(60), nrow=20))
plot_data <- interp(df$X1,df$X2,df$X3)

However, akima::interp is rather fragile and will crash your R interpreter shell in certain cases (eg for the example of the data_grid variable below).

On the plus side, it creates a data structure with tow vectors and a matrix for you, the way all (?) 3d surface plotting functions in R expect the data.

Data preparation 2: You cannot have data in long format

Say, you have data for 9 points in a 3x3 grid (to keep this example simple):

data_grid <- data.frame(data_col = c(45.62151, 60.30996, 66.01667, 45.48701, 
                                     60.39519, 65.42441, 45.48208, 60.39041, 65.52165), 
               axis_one=c(10000, 10000, 10000, 1000000, 1000000, 1000000, 100000000, 
                          100000000, 100000000), 
               axis_two=c(1, 100, 10000,1, 100, 10000,1, 100, 10000))
data_grid
#  data_col axis_one axis_two
#1 45.62151    1e+04        1
#2 60.30996    1e+04      100
#3 66.01667    1e+04    10000
#4 45.48701    1e+06        1
#5 60.39519    1e+06      100
#6 65.42441    1e+06    10000
#7 45.48208    1e+08        1
#8 60.39041    1e+08      100
#9 65.52165    1e+08    10000

I was not able to find any 3d-plotting package or function in R that would accept a data structure like this. Most replies regarding 3d plotting in R on stackoverflow assume this, probably because in most cases it is assumed that this is not empirical data but values pulled from a 3d function. Examples here and here and here or the (for 3d plotting examples) frequently used volcano data set included in base R.

So what do these packages expect? They want two vectors (for the grid coordinates in the base plane) and a matrix with entries corresponding to the meshgrid created by these two vectors for the z axis. In other words you need to rearrange any long format data to wide format, ie a matrix with the x and y coordinates as row and column indices/labels.

This can be done with reshape2::acast :

library(reshape2)
plot_matrix <- t(acast(data_grid, axis_one~axis_two, value.var="data_col"))
plot_matrix
#         10000    1e+06    1e+08
#1     45.62151 45.48701 45.48208
#100   60.30996 60.39519 60.39041
#10000 66.01667 65.42441 65.52165

If you have data in wide format already: brilliant, you don't have to do this.

Note that the other answer by @rar seems to uses example data structured in long format but plots it the wrong way, such that R interprets columns cs and w not as base plain coordinates but as additional observations. It is difficult to tell if this is indeed a mistake or if the answer intended it that way; unfortunately it includes very little text.

Plotting option 1: Plotting it with persp

Plotting is straightforward enough. Unfortunately, we have modified the x and y data as well now. So we have to pull these back out of the column and row names of the matrix. There may be other ways to save these before transforming the data to a wide format matrix but this may be a source of errors if data for different axes is taken from different objects.

persp(x = as.numeric(colnames(plot_matrix)), 
  y = as.numeric(rownames(plot_matrix)), 
  z = plot_matrix,
  xlab = "Axis one",
  ylab = "Axis two",
  zlab = "Data",
  ticktype ='detailed',
  theta = 310, 
  phi = 20,
  col = "green", shade = 0.5)

A major drawback of persp is that it does not seem to be able to have log scale axes. This is inconvenient; so we have to do it manually.

persp(x = log(as.numeric(colnames(plot_matrix))), 
  y = log(as.numeric(rownames(plot_matrix))), 
  z = plot_matrix,
  xlab = "log Axis one",
  ylab = "log Axis two",
  zlab = "Data",
  ticktype ='detailed',
  theta = 310, 
  phi = 20,
  col = "green", shade = 0.5)

We save the plot as usual (albeit quite counterintuitive compared to, say, Python)

pdf(file="out.pdf", width=5, height=5)
persp(x = log(as.numeric(colnames(plot_matrix))), 
  y = log(as.numeric(rownames(plot_matrix))), 
  z = plot_matrix,
  xlab = "log Axis one",
  ylab = "log Axis two",
  zlab = "Data",
  ticktype ='detailed',
  theta = 310, 
  phi = 20,
  col = "green", shade = 0.5)
dev.off()

...or equivalently for png etc. etc.

Plotting option 2: Plotting it with plotly

The OP asked about plotly instead. So here we go:

Plotly has more functionality and looks nicer, but retains some of the same drawbacks (requires wide format).

library(plotly)
plot_ly(
      x = as.numeric(colnames(plot_matrix)), 
      y = as.numeric(rownames(plot_matrix)), 
      z = plot_matrix
    ) %>% 
  add_surface() %>%
  layout(
    title = "",
    scene = list(
      xaxis = list(type = "log", title = "Total observations"),
      yaxis = list(type = "log", title = "Firm size"),
      zaxis = list(title = "Median"),
      camera = list(eye = list(x = 1.95, y = -1.25, z = 1.25))
    ))

What may be near impossible with plotly, however, is saving the figure. In the past, plotly seems to have required subscription to a paid service to create a figure online on their server with plotly::export . Today it recommends using a package called orca which has to be installed. The installation options are described on orca's github repository and invariably require you to hack your system by installing either untrusted third party packages or a second package manager conda which may also want root access or an entire second Python distribution.

If you are using their tool stack already, eg, if you have an Anaconda distribution for Python or so, you may be able to install orca without compromising your system's integrity. Otherwise, don't bother. in this case, you can save the plot (apparently; I can't test it) by doing

plotly_figure <- plot_ly(
      x = as.numeric(colnames(plot_matrix)), 
      y = as.numeric(rownames(plot_matrix)), 
      z = plot_matrix
    ) %>% 
  add_surface() %>%
  layout(
    title = "",
    scene = list(
      xaxis = list(type = "log", title = "Total observations"),
      yaxis = list(type = "log", title = "Firm size"),
      zaxis = list(title = "Median"),
      camera = list(eye = list(x = 1.95, y = -1.25, z = 1.25))
    ))
orca(plotly_figure, file="out.pdf")

As a side note, their website's employment of third party scripts that will break browser add-ons (privacy enhancing ones in particular) is also a bit of a red flag. The figure is, of course more like a screenshot as it won't permit me to save anything. Plotting option 3+: Other packages

There are some more packages. Eg plot3D , which has some functions including plot3D::persp3D , the one here appropriate. Compared to persp , this looks a bit more fancy and adds colors highlighting surface elevation.

plot3D::persp3D(x = log(as.numeric(colnames(plot_matrix))), 
  y = log(as.numeric(rownames(plot_matrix))), 
  z = plot_matrix,
  xlab = "log Axis one",
  ylab = "log Axis two",
  zlab = "Data",
  ticktype ='detailed',
  theta = 310, 
  phi = 20)

It looks more interesting for more dense data like the data created above with akima::interp :

plot3D::persp3D(x = plot_data$x, 
  y = plot_data$y, 
  z = plot_data$z,
  xlab = "log Axis one",
  ylab = "log Axis two",
  zlab = "Data",
  ticktype ='detailed',
  theta = 310, 
  phi = 20)

Saving the figures should work like in persp above.

There is another one rgl:plot3d ; if I understand it correctly, this requires extremely dense data and otherwise falls back to a 3d scatter plot .

Answer 2

library(plotly)    
# df_sample could be your plot_data    
> df_sample 
         cs w     u
    1  21.0 6 160.0
    2  21.0 6 160.0
    3  22.8 4 108.0
    4  21.4 6 258.0
    5  18.7 8 360.0
    6  18.1 6 225.0
    7  14.3 8 360.0
    8  24.4 4 146.7
    9  22.8 4 140.8
    10 19.2 6 167.6
> df<-as.matrix(df_sample, rownames.force = NA)
> plot_ly(z=~df) %>% add_surface()

If you want to change the x,y and z axis. Then rearrange the columns as follows while plotting.

plot_ly(z=~df[,c(3,1,2)])%>%add_surface()