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I am having trouble finding simple and complete explanations for algorithms on how to construct a Delaunay Triangulation given a set of points. Could anyone explain to me or redirect me to some resources that explain in a simple manner an algorithm?

Thanks

Dan Brenner
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    possible duplicate of [How does this code for delaunay triangulation work?](http://stackoverflow.com/questions/5825089/how-does-this-code-for-delaunay-triangulation-work) – Micromega Sep 10 '13 at 12:22
  • Wikipedia mentions four algorithms, for instance. Where exactly do you have troubles? – S. Huber Feb 05 '18 at 20:09

2 Answers2

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A delaunay triangulation subdivide the plane in triangles. The mesh can have big holes so the delaunay triangulation tries to keep the inner angles bigger. Hence the triangulation isn't unique and each vertex of the triangulation needs to be on the circumcircle of a triangle. Read here: How does this code for delaunay triangulation work?.

Community
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Micromega
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Steps to Construct Delauney's TIN from Scattered Points:

  1. Read Point Data (Xi,Yi,Zi), Store them in Points.
  2. Find Xmin,Xmax,Ymin,Ymax.
  3. Find a single Super Triangle (ABC) based on the extreme points found in step 2 above, that encloses all the given points well inside it.
  4. Take the First Point (P). Surely it lies within the super triangle ABC. Construct 3-triangles PAB,PBC and PCA. Store the Triangles and their Edges formed so far in two dynamic arrays, one for Triangles and one for Edges.
  5. Take the next point(Q). Find the existing Triangle (DEF) that encloses this point. Construct 3-triangles QDE, QEF and QFD. Delete Triangle DEF and its Edges. Add the newly created 3-New Triangles and their Edges.
  6. Check the surrounding Triangles in the vicinity of DEF for their validity. A triangle is said to be valid only if no other vertex lies within its circum-circle. Swap the diagonal of adjoining triangles to validate them. Update Triangles and Edges accordingly. Note that all edges must be in pair. No single-entry edge or no entry more than 2.
  7. Repeat step 5 and 6 for all Points in the data Points.
  8. Re-check Triangles Validity once for all Triangles.
  9. Finally Remove Super Triangle ABC. Find all the exterior sub-Triangles sharing the vertex A, B & C. The third side of these exterior sub-triangles will form the Boundary Edge of a convex hull. Draw the remaining interior Triangles and the Boundary.

Thats all!

Ratnakar
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