How can I perform a triangle inside test in polygon meshes? I have 3 vertices (V1, V2, V3) randomly selected on a regular triangle mesh. For these 3 vertices, I have computed the geodesic distance and the path (by using Dijkstra) among them and formed a triangle-like surface as in the above figure. 

Now, I have the vertices that lie in each path and can compute geodesic distances from a given vertex.

What I want to do is to get the vertices or triangles that lies in triangle-like area. How can I do this?
There is an alternative method that relies on flood filling. First arrange your edge data into a loop where the edges are forming a counterclockwise loop. Then start at an arbitrary point on the loop and pick edges joining that point. Use the outbound boundary edge and cross it with the other outbound edge, if it points in the direction of the face normal then it's an edge to be included, if not discard it. From this edge continue until you hit a boundary edge, at which point you terminate the fill. Continue at a yet to be visited boundary edge vertex.