Suppose that I have a triangular mesh (discrete surface composed of triangles). Now, I have been given a vector field (one vector with each triangle, tangential, unit length, so can be represented by only one angle). I would like to compute the index of this vector field on every vertex. One of the definition of the index can be the number of full rotations experienced by a vector transported along a loop of triangles around the vertex.
I have some confusions because if only the vector of one triangle (among all triangles around the vertex) is changed, it seems that the index will not change. But the index will be definitely determined by the vectors of all triangles. What am I missing here?
