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[cgal-discuss] Inserting a point into a regular triangulation so that it appears and no other vertex disappears


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  • From: Marc Alexa <>
  • To:
  • Subject: [cgal-discuss] Inserting a point into a regular triangulation so that it appears and no other vertex disappears
  • Date: Tue, 7 Jan 2020 19:18:05 +0100
  • Authentication-results: mail2-smtp-roc.national.inria.fr; spf=None ; spf=Pass ; spf=None
  • Ironport-phdr: 9a23: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
Dear all,

I want to insert a point p into a regular triangulation. The point has a
fixed coordinate. I am interested in the interval of weights so that the
point itself appears in the triangulation and none of the existing points
disappears. The upper bound (the point appears) is easy: find the cell the
contains p. The cell defines a hyperplane in the lift, and the lift for p
needs to be below the hyperplane. What methods are available in CGAL that
would help me finding the lower bound? Moreover, is there an easy way to walk
through all triangulations in this interval, perhaps parameterized by the
weight?

Thanks!
-Marc



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