How many vertices does a triangle fan use opengl

Question

I am learning openGL, and i have come across triangle fans using vertex buffer objects. If given an array of vertices to render, how does openGL decide how many of those vertices must be used to construct a triangle fan. It seems like an arbitray number of the vertices could be used.

Answer 1

This can easily be explained by comparing Triangle Strips with Triangle Fans.

Triangle Strip

As you probably know, a Triangle Strip is a set connected triangles which share vertices, this allows for more efficient memory usage. (We save memory because we don't store all duplicated vertices)

Example of a Triangle Strip

Triangle Fan

On the other hand we have a Triangle Fan, this is also a set of connected triangles. Though all these triangles have one vertex in common, which is the central vertex. (The first vertex is always the center)

With that said we can take the same image above and change the order of the vertices. When that done the Triangle Fan would look like this. (Where A, is the first and central vertex)

Example of a Triangle Fan

In the image above the Triangle Fan will only work in the colored area, because of how the vertices need to be arranged according to be a Triangle Fan.

Answer 2

Visually, this is how a triangle fan works:

Each triangle shares the central vertex A, and re-uses the last vertex addressed. Thus after defining ABC each following triangle only requires 1 point (e.g. D, E, F).

Indices:     A,B,C,D,E,F     [Count: 6]
Triangles:  (A,B,C)
            (A) (C,D)
            (A)   (D,E)
            (A)     (E,F)    [N=4]  -->  4+2 = 6

Another way of thinking about this is that each triangle shares an edge radiating from a central vertex with the prior triangle; literally like a folding a paper fan.

      

You need N+2 vertices, where N is the number of triangles in your fan.