Drawing spherical wedges with rgl

Posted on February 22, 2018 by Stéphane Laurent

Tags: R, graphics, rgl

This post provides some code to draw a spherical wedge with the R library rgl.

As a helper function, I use spherical2cartesian to convert from spherical coordinates to Cartesian coordinates:

spherical2cartesian <- function(rthetaphi){
  r <- rthetaphi[1]
  theta <- rthetaphi[2]
  phi <- rthetaphi[3]
  c(x=r*cos(theta)*sin(phi), y=r*sin(theta)*sin(phi), z=r*cos(phi))
}

Now, here is the main function:

sphereWedge <- function(theta1, theta2, radius=1, nm=30, np=30, col="blue"){
  thetas <- seq(theta1, theta2, length.out=nm)
  phis <- pi * 1:(np-1)/np
  meridians <- sapply(phis, 
                      function(phi) sapply(thetas, 
                                           function(theta) c(radius,theta,phi)), 
                      simplify=FALSE)
  for(i in 1:(np-2)){
    x1 <- plyr::aaply(meridians[[i]], 2, spherical2cartesian)
    x2 <- plyr::aaply(meridians[[i+1]], 2, spherical2cartesian)
    for(j in 1:(nm-1)){
      quads3d(rbind(x1[j:(j+1),],x2[(j+1):j,]), color=col)
      triangles3d(rbind(c(0,0,radius), spherical2cartesian(meridians[[1]][,j]), 
                        spherical2cartesian(meridians[[1]][,j+1])), color=col)
      triangles3d(rbind(c(0,0,-radius), spherical2cartesian(meridians[[np-1]][,j]), 
                        spherical2cartesian(meridians[[np-1]][,j+1])), color=col)
    }
  }
}

A simple example:

sphereWedge(0, pi/3, col="purple")

Now let’s draw a tricolor sphere:

sphereWedge(0, 2*pi/3, col="red")
sphereWedge(2*pi/3, 4*pi/3, col="green")
sphereWedge(4*pi/3, 2*pi, col="blue")

As you can see, I use 2*pi and not 0 for the blue wedge. That should be equivalent. However, and I don’t know why, using 0 instead of 2*pi colors the interior of the two other wedges:

sphereWedge(0, 2*pi/3, col="red")
sphereWedge(2*pi/3, 4*pi/3, col="green")
sphereWedge(4*pi/3, 0, col="blue")

Spherical triangles with rgl

I also did a code which draws spherical triangles for rgl. I won’t reproduce it here. If you are interested, it is available in this gist.