How can I merge 2 Delaunay triangulations / Voronoï diagrams?

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I am building a Voronoï diagram using both Delaunay triangulation and a divide and conquer paradigm but how can I merge multiple diagrams efficiently ?

As shown in this picture, I can make Voronoï diagrams but have yet to find a way to efficiently merge them :

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I have heard a lot about convex hulls but this would require me to :

  • be able to define the convex hull
  • be able to check if a Delaunay vertex is inside or outside the convex hull ( and reject the ones that are outside )
  • merge two or more convex hulls

I wish to know if this method can work or not ( am I missing an important point ? ) or if I should rather try an other method ?