The window W will be decomposed into disjoint triangles.
  The result is a tessellation of W in which each tile is a
  triangle. All triangle vertices lie on the boundary
  of the original polygon.
  
The window is first converted to a polygonal window using
  as.polygonal. The vertices of the polygonal window
  are extracted, and the Delaunay triangulation of these vertices
  is computed using delaunay. Each Delaunay triangle
  is intersected with the window: if the result is not a triangle, 
  the triangulation procedure is applied recursively to this smaller polygon.