Fig. 1. Right and left angles (θ_r and θ_l resp.) in a curve. and .

Fig. 2. Inserting the point A in S as a mesh vertex: it belongs to the interior of a face (a) and to an edge (b).

Fig. 3. First approximation Γ₀: Dijkstra's Algorithm (a) and FMM (b).

Fig. 4. Correcting the vertex position on an edge. Intersection inside the edge (a), and outside (b). Corrected polygonal vertices are marked with a .

Fig. 5. Elimination of a vertex inside S_k.

Fig. 6. Correcting a vertex coinciding with a mesh vertex. Convex star (a) and non-convex star (b). The resulting path before the additional correction in the non-convex vertex is shown as a dotted line.

Fig. 7. Geodesics touching the boundary.

Fig. 8. Geodesics over the Stanford bunny. The first approximations (a), the computed geodesics (b), and both (c).

Fig. 9. Some geodesics over Costa's Surface, all sharing a common extreme (a), and a zoom close to the common extreme (b).

Fig. 10. Some geodesics over a Face model, all sharing a common extreme (a), and a zoom close to the common extreme (b).

Fig. 11. Using our algorithm to solve single source problem.

Run time and number of vertex corrections for the originally proposed method and the alternative method using a heap