R rgl 3d log scale plot and Antenna pattern plots

first of all before my sharing my problem I want to share a bit of code that might be helpful for some people outside there. I have been looking quite some time code to plot in 3d antenna measurements but I could not find code that does that. The problem is that antenna measurements have polar coordinates and typical 3d plot functions use cartesian coordinates. So my code below does just that (I am not an advanced programmer so I am sure someone might be able to optimize it for its use). The code can be run directly and I added comments to make it easier readable.

require("rgl")
require("fields")
degreeToRadian<-function(degree){
  return   (0.01745329252*degree)
}

turnPolarToX<-function(Amplitude,Coordinate){
  return (Amplitude*cos(degreeToRadian(Coordinate)))
}

turnPolarToY<-function(Amplitude,Coordinate){
  return (Amplitude*sin(degreeToRadian(Coordinate)))
}


#  inputs for the code
test<-runif(359,min=-50,max=-20) # the 359 elements correspond to the polar coordinates of 1 to 359
test2<-runif(359,min=-50,max=-20)  # the 359 elements correspond to the polar coordinates of 1 to 359
test3<-runif(359,min=-50,max=-20)  # the 359 elements correspond to the polar coordinates of 1 to 359

# My three input vectors above are considered to be dBm values, typically unit for antenna or propagation measurements
# I want to plot those on three different 3d planes the XY, the YZ and the ZX. Since the rgl does not support
# polar coordinates I need to cast my polar coordinates to cartesian ones, using the three functions
# defined at the beginning. I also need to change my dBm values to their linear relative ones that are the mW


# Convert my dBm to linear ones
test<-10^(test/10)
test2<-10^(test2/10)
test3<-10^(test3/10) 

# Start preparing the data to be plotted in cartesian domain
X1<-turnPolarToX(test,1:359)
Y1<-turnPolarToY(test,1:359)
Z1<-rep(0,359)


X2<-turnPolarToX(test2,1:359)
Y2<-rep(0,359)
Z2<-turnPolarToY(test2,1:359) 

X3<-rep(0,359)
Y3<-turnPolarToX(test3,1:359)
Z3<-turnPolarToY(test3,1:359)


# Time for the plotting now

Min<-min(test,test2,test3)
Max<-max(test,test2,test3)

bgplot3d( suppressWarnings ( 
    image.plot( legend.only=TRUE, legend.args=list(text='dBm/100kHz'), zlim=c(Min,Max),col=plotrix::color.scale(seq(Min,Max,length.out=21),c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)))
    ) # zlim is the colorbar numbers
) 

# for below alternatively you can also use the lines3d to get values
points3d(X1,Y1,Z1,col=plotrix::color.scale(test,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)
points3d(X2,Y2,Z2,col=plotrix::color.scale(test2,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)
points3d(X3,Y3,Z3,col=plotrix::color.scale(test3,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)

The problem I have now is that my plotting ideally I would like to be on a log scale that the rgl packet does not support! If I try to use log on my X,Y,Z to compress them I get an error that log is not defined for negative numbers (of course that is correct). How would you think to solve that problem on compressing the axes values when log scale plotting is not supported?

I would like to thank you for your reply Regards Alex

Solution

It doesn't make sense to apply a log scale to X, Y and Z. Just apply it to your original data, and transform the logged values to polar coordinates.

Since your logged test values are negative, you probably will want to apply an offset; polar coordinates with negative radius values are pretty hard to interpret.

Once you have done that, you can use the axis3d() function to add an axis with arbitrary labels to the plot. For example, if you want the origin to correspond to -50 dBm, you'd skip the transformation to linear coordinates and just add 50. You need to undo this when calculating labels. Here's your example, modified:

require("rgl")
require("fields")
degreeToRadian<-function(degree){
  return   (0.01745329252*degree)
}

turnPolarToX<-function(Amplitude,Coordinate){
  return (Amplitude*cos(degreeToRadian(Coordinate)))
}

turnPolarToY<-function(Amplitude,Coordinate){
  return (Amplitude*sin(degreeToRadian(Coordinate)))
}


#  inputs for the code
test<-runif(359,min=-50,max=-20) # the 359 elements correspond to the polar coordinates of 1 to 359
test2<-runif(359,min=-50,max=-20)  # the 359 elements correspond to the polar coordinates of 1 to 359
test3<-runif(359,min=-50,max=-20)  # the 359 elements correspond to the polar coordinates of 1 to 359

# Add an offset of 50 to the values.

test <- test + 50
test2 <- test2 + 50
test3 <- test3 + 50

# Start preparing the data to be plotted in cartesian domain
X1<-turnPolarToX(test,1:359)
Y1<-turnPolarToY(test,1:359)
Z1<-rep(0,359)


X2<-turnPolarToX(test2,1:359)
Y2<-rep(0,359)
Z2<-turnPolarToY(test2,1:359) 

X3<-rep(0,359)
Y3<-turnPolarToX(test3,1:359)
Z3<-turnPolarToY(test3,1:359)


# Time for the plotting now

Min<-min(test,test2,test3)
Max<-max(test,test2,test3)

bgplot3d( suppressWarnings ( 
    image.plot( legend.only=TRUE, legend.args=list(text='dBm/100kHz'), zlim=c(Min,Max)-50,col=plotrix::color.scale(seq(Min-50,Max-50,length.out=21),c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)-50))
    ) # zlim is the colorbar numbers
) 

# for below alternatively you can also use the lines3d to get values
points3d(X1,Y1,Z1,col=plotrix::color.scale(test,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)
points3d(X2,Y2,Z2,col=plotrix::color.scale(test2,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)
points3d(X3,Y3,Z3,col=plotrix::color.scale(test3,c(0,1,1),c(0,1,0),0,xrange=c(Min,Max)),add=TRUE)

# Add axes

labels <- pretty(c(-50, -20))
axis3d("x", at = labels + 50, labels = labels, pos = c(NA, 0, 0) )
axis3d("y", at = labels + 50, labels = labels, pos = c(0, NA, 0) )
axis3d("z", at = labels + 50, labels = labels, pos = c(0, 0, NA) )

One my system it produces this display:

You might want to add circles to show how the scale continues around in each plane. This code would do it:

theta <- seq(0, 2*pi, len = 100)
for (i in seq_along(labels)) {
  x <- (labels[i] + 50)*cos(theta)
  y <- (labels[i] + 50)*sin(theta)
  lines3d(x, y, 0)
  lines3d(x, 0, y)
  lines3d(0, x, y)
}

I find the plot too busy with those added, but you can try it and decide for yourself.