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Amphi 2 : triangulations de Delaunay (I) Steve Oudot INF562 G eom - PowerPoint PPT Presentation

Aug 25, 2022 •178 likes •1.31k views

INF562 G eom etrie Algorithmique et Applications Amphi 2 : triangulations de Delaunay (I) Steve Oudot INF562 G eom etrie Algorithmique et Applications Amphi 2 : triangulations de Delaunay (I) Steve Oudot (certains slides

  1. Why (and how) it works Property 1 : the conflict zone is connected → compute conflict zone by dfs in dual graph Property 2 : conflict zone is starred with respect to p → re-triangulating the conflict zone w.r.t. p gives a triangulation Property 3 : every new Delaunay triangle is incident to p → re-triangulating the conflict zone w.r.t. p gives a Delaunay tr.

  2. The Guibas/Stolfi variant • Locate point in triangulation

  3. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle

  4. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle • Apply flipping algo.

  5. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle • Apply flipping algo.

  6. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle • Apply flipping algo.

  7. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle • Apply flipping algo.

  8. The Guibas/Stolfi variant • Locate point in triangulation • Star triangle → implemented in the Jcg library • Apply flipping algo.

  9. Delaunay triangulation with constraints

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