  Using concepts from integral geometry, we propose a definition for a local
coarse-grained curvature tensor that is well-defined on polygonal surfaces.
This coarse-grained curvature tensor shows fast convergence to the curvature
tensor of smooth surfaces, capturing with accuracy not only the principal
curvatures but also the principal directions of curvature. Thanks to the
additivity of the integrated curvature tensor, coarse-graining procedures can
be implemented to compute it over arbitrary patches of polygons. When computed
for a closed surface, the integrated curvature tensor is identical to a rank-2
Minkowski tensor. We also provide an algorithm to extend an existing C++
package, that can be used to compute efficiently local curvature tensors on
triangulated surfaces.
