Converting triangulation to convex polygons?

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I need to convert a triangulation to a set of convex polygons. A good result would have a large average polygon size and a small average deviation from the average polygon size. Is anyone aware of papers/articles/algorithms to do this?

A related question, given the criteria mentioned above, should I expect better results when using a constrained delaunay triangulation vs a mere constrained triangulation as input?

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