---
title: "Drawing spherical wedges with rgl"
author: "Stéphane Laurent"
date: "2018-02-22"
tags: R, graphics, rgl
rbloggers: yes
output:
  md_document:
    variant: markdown
    preserve_yaml: true
  html_document:
    highlight: kate
    keep_md: no
highlighter: pandoc-solarized
---


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:

```r
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:

```r
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:

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

![](figures/wedge1.png)


Now let's draw a tricolor sphere:

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

![](figures/wedge2.png)

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:

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

![](figures/wedge3.png)


## 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](https://gist.github.com/stla/1cd2c0b3c4db4898f7132003e2ed2766).

![](figures/triangulatedSphere.png)