Rectangle

This is a simple box consisting of ra/dec (or lat/lon) limits. lines of equal declination (latitude) are (generally) small circles parallel to the equator. The equal lines of right ascension (longitude) are meridiens, which are great circles. The four halfspaces defined by these circles are oriented so that they "trap" the rectangular region of interest. This is nothing more than the intersection of four halfspaces, therefore it can be represented as a single convex.

The white band is created by the intersection of the two halfspaces each of which is bigger than a hemisphere. Those are the ones with D < 0 (red and blue). The other two hemispheres' intersection creates the lune. The intersection of the band and the lune yield the white rectangle.

Figure 3. 4 halfspaces that define a rectangle

SPECIFICATION

REGION CONVEX
    0.0  0.0  1.0 -0.08 
    0.0  0.0 -1.0 -0.15
   -0.1 -0.9  0.0  0.0
    0.7  0.6  0.0  0.0

NORMAL FORM

REGION
  CONVEX
  0 0 1 -0.08
  0 0 -1 -0.15
  -0.11043152607484655 -0.9938837346736189 0 0
  0.75925660236529657 0.6507913734559686 0 0

The normal form is a bit different from the specification because all vectors are normalized

C# Code snippet

using Spherical;
/* .... */
namespace MySpace {
    public class MyApp {
        public void MyFunc(){
            Region r = new Region();
            Convex c = new Convex();
            c.Add(new Halfspace( 0.0,  0.0,  1.0, -0.08)); 
            c.Add(new Halfspace( 0.0,  0.0, -1.0, -0.15)); 
            c.Add(new Halfspace(-0.1, -0.9,  0.0,  0.0)); 
            c.Add(new Halfspace( 0.7,  0.6,  0.0,  0.0)); 
            r.Add(c);
	    /* ... */
        }
    }
}