REMARK: After publication, we reviewed the M.Sc. thesis "Tangent Vector Fields on Triangulated Surfaces - An Edge-Based Approach" by Alexandre Djerbetian, 2016, supervised by Mirela Ben-Chen, and now fully grasp its significant overlap with our paper. Djerbetian introduces essentially the same operator and demonstrates a similar suite of applications. The thesis is archived by the Technion Graduate School at https://www.graduate.technion.ac.il/Theses/Abstracts.asp?Id=30013