CG_DelaunayCh9 - Introduction Triangulations Delaunay...

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Unformatted text preview: Introduction Triangulations Delaunay Triangulations Delaunay Triangulations Computational Geometry Lecture 12: Delaunay Triangulations Computational Geometry Lecture 12: Delaunay Triangulations 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 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 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 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 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? 10 6 20 36 28 1000 980 990 1008 890 4 23 interpolated height = 985 q 10 6 20 36 28 1000 980 990 1008 890 4 23 interpolated height = 23 q Computational Geometry Lecture 12: Delaunay Triangulations 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 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 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....
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This note was uploaded on 05/27/2011 for the course CIS 4930 taught by Professor Staff during the Fall '08 term at University of Florida.

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CG_DelaunayCh9 - Introduction Triangulations Delaunay...

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