Fast and exact Geodesics on meshes, Backtracking confusion
The solution I found to this problem is to ALWAYS intersect the edge. In other words the distance to the geodesic source $v$ from a point $p$ is $||v-p'|| + ||p - p'||$ where $p'$ is the intersection of the line $\overline{vp}$ with the current edge. In cases where $p'$ is &quot;behind&quot; $p$ with respect to $v$ we set the distance to the edge to be infinity.
The above seems to work in the simple tests I have generated at minimum.