<p>A half-edge is an edge split along its length, and having a directional component, that is, a beginning vertex and an end vertex. Where two polygons share an edge, each polygon gets a single half-edge between the same two vertices, which will have opposite directions if the winding order is consistent. These half-edges will have references to one another as two halves of a pair.</p>

<p>The full half edge data structure stores for each half-edge:</p>

<ul>
<li>The polygon it belongs to</li>
<li>Previous and next half edges within the polygon</li>
<li>Its pair half-edge in a neighbouring polygon</li>
<li>Its origin vertex</li>
</ul>

<p>This structure allows you to extract all sorts of connectivity information from a mesh, such as which edges or polygons lie around a particular vertex, simply by traversing the half-edges. There's a good article explaining it <a href="http://kaba.hilvi.org/homepage/blog/halfedge/halfedge.htm" rel="noreferrer">here</a>.</p>

CC BY-SA 3.0
2017-12-12T23:46:58.187Z
Thank you for your answer, I think I was partly thrown by the dissimilarity between the "half-edges" that the library provided (simply an array of indices) and the more fully fledged structures which came up when searching for half-edges.
Mark A. Ropper
CC BY-SA 3.0
2017-12-12T04:09:35.353Z
2017-12-12T04:09:35.353Z
russ
<p>I ran into half-edges as part of the result of a Delaunay Triangulation library, but can't find an actual definition of what one is. </p>

<p>I understand vertices, edges and faces, but can't find a concrete definition of a half-edge.</p>

CC BY-SA 3.0
2017-12-12T00:54:59.300Z
as far as i know a half edge is a directed edge. That is, an edge with a defined begining and end rather than two points where order is irrelevant. I don't know how that would fit into a triangulation algorithm but i hope this helps.
Sebastián Mestre
CC BY-SA 3.0
2017-12-13T16:08:26.687Z
Here is a good practical introduction on the topic: https://fgiesen.wordpress.com/2012/02/21/half-edge-based-mesh-representations-theory/
Julien Guertault
<triangulation><data-structure>
What is the definition of a Half Edge?
Mark A. Ropper
# What is the definition of a Half Edge?

(Asked by: username_0 on 2017-12-12)

I ran into half-edges as part of the result of a Delaunay Triangulation library, but can't find an actual definition of what one is.

I understand vertices, edges and faces, but can't find a concrete definition of a half-edge.

**Tags:** triangulation, data-structure

> **Comments:**
> **username_1**: as far as i know a half edge is a directed edge. That is, an edge with a defined begining and end rather than two points where order is irrelevant. I don't know how that would fit into a triangulation algorithm but i hope this helps.  
> **username_2**: Here is a good practical introduction on the topic: https://fgiesen.wordpress.com/2012/02/21/half-edge-based-mesh-representations-theory/  

---

## 1 answers

### Answer by username_3 on 2017-12-12. Score: 13 | Accepted answer

A half-edge is an edge split along its length, and having a directional component, that is, a beginning vertex and an end vertex. Where two polygons share an edge, each polygon gets a single half-edge between the same two vertices, which will have opposite directions if the winding order is consistent. These half-edges will have references to one another as two halves of a pair.

The full half edge data structure stores for each half-edge:

* The polygon it belongs to
* Previous and next half edges within the polygon
* Its pair half-edge in a neighbouring polygon
* Its origin vertex

This structure allows you to extract all sorts of connectivity information from a mesh, such as which edges or polygons lie around a particular vertex, simply by traversing the half-edges. There's a good article explaining it [here](http://kaba.hilvi.org/homepage/blog/halfedge/halfedge.htm).

> **Comments:**
> **username_0**: Thank you for your answer, I think I was partly thrown by the dissimilarity between the "half-edges" that the library provided (simply an array of indices) and the more fully fledged structures which came up when searching for half-edges.  

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