Omri Azencot, Maks Ovsjanikov, Frédéric Chazal and Mirela Ben-Chen. Transactions on Graphics (TOG) 2015. Abstract Vector fields on surfaces are fundamental in various applications in computer graphics and geometry processing. In many cases, in addition to representing vector fields, the need arises to compute their derivatives, for example for solving partial differential equations on surfaces, or for designing vector fields with prescribed smoothness properties. In this work, we consider the problem of computing the Levi-Civita covariant derivative, i.e., the tangential component of the standard directional derivative, on triangle meshes. This problem is challenging since formally, tangent vector fields on polygonal…