CG_DelaunayCh9 - Introduction Triangulations Delaunay...

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Introduction Triangulations Delaunay Triangulations Delaunay Triangulations Computational Geometry Lecture 12: Delaunay Triangulations Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Motivation: Terrains a terrain is the graph of a function f : A R 2 R we know only height values for a set of measurement points how can we interpolate the height at other points? using a triangulation Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Motivation: Terrains a terrain is the graph of a function f : A R 2 R we know only height values for a set of measurement points how can we interpolate the height at other points? using a triangulation Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Motivation: Terrains a terrain is the graph of a function f : A R 2 R we know only height values for a set of measurement points how can we interpolate the height at other points? using a triangulation ? Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Motivation: Terrains a terrain is the graph of a function f : A R 2 R we know only height values for a set of measurement points how can we interpolate the height at other points? using a triangulation ? Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Motivation: Terrains a terrain is the graph of a function f : A R 2 R we know only height values for a set of measurement points how can we interpolate the height at other points? using a triangulation but which? 0 10 6 20 36 28 1000 980 990 1008 890 4 23 interpolated height = 985 q 0 10 6 20 36 28 1000 980 990 1008 890 4 23 interpolated height = 23 q Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Triangulation Let P = { p 1 ,..., p n } be a point set. A triangulation of P is a maximal planar subdivision with vertex set P . Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Triangulation Let P = { p 1 ,..., p n } be a point set. A triangulation of P is a maximal planar subdivision with vertex set P . Complexity: 2 n - 2 - k triangles 3 n - 3 - k edges where k is the number of points in P on the convex hull of P . Computational Geometry Lecture 12: Delaunay Triangulations
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Introduction Triangulations Delaunay Triangulations Angle Vector of a Triangulation Let T be a triangulation of P with m triangles and 3 m vertices. Its angle vector is A ( T ) = ( α 1 ,..., α 3 m ) where α 1 ,..., α 3 m are the angles of T sorted by increasing value. Let T be another triangulation of P .
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