# Questions tagged [doubly-connected-edge-list]

A doubly-connected edge list (DCEL) is an edge-centered data structure capable of maintaining incidence information of vertices, edges and faces, for example for planar maps.

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### When Triangulating monotone polygons, how can diagonals be added to a DCEL in constant time?

I am working on the polygon triangulation algorithms from "Computational Geometry - Algorithms and applications 3rd ed", chapter 4. I've managed to turn polygons into y-monotone polygons ...
• 11
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### Sort half-edges around common vertex in 3d

I'm trying to figure out this problem for very long time and am no getting nowhere. I'm working on a simple 3d modeler that uses half-edge data structure. Say I have non-manifold geometry where two ...
• 177
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### Given a DCEL, how do you identify the unbounded face

I have constructed a DCEL using the procedure described in How do I construct a doubly connected edge list given a set of line segments?. This correctly identifies all faces, however I'm struggling ...
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### DCEL with dynamic graph

Is doubly-connected edge list a good data-structure for planar graph which vertices can be moved freely? I experienced DCEL as a very good structure when it comes to add/delete some vertex or edge. ...
• 131
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### DCEL operations on quad-edges, Twin, Next, and Prev

Suppose I have a quad-edge data-structure, and I want to be able to perform the operations of DCEL (twin, next, ...
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### How do I visit all edges incident to a vertex in a DCEL data structure?

In a doubly-connected edge list (DCEL) data structure, each vertex v stores a pointer to one arbitrary half-edge, v.inc, which ...
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### How do you find out if the polygon lies to the right of a regular vertex?

In section 3.2 of the book Computational Geometry: Algorithms and Applications (by Berg et al.), the authors describe a procedure to make a polygon y-monotone. The algorithm distinguishes vertices ...
For a given planar graph $G(V,E)$ embedded in the plane, defined by a set of line segments $E= \left \{ e_1,...,e_m \right \}$, each segment $e_i$ is represented by its endpoints \$\left \{ L_i,R_i \...