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Triangular meshes are the most popular representations of 3D objects, butmany mesh surfaces contain topological singularities that represent a challengefor displaying or further processing them properly. One such singularity is theself-intersections that may be present in mesh surfaces that have been createdby a scanning procedure or by a deformation transformation, such asoff-setting.  Mesh foldings comprise a special case of mesh surface self-intersections,where the faces of the 3D model intersect and become reversed, with respect tothe unfolded part of the mesh surface. A novel method for the recognition andrepair of mesh surface foldings is presented, which exploits the structuralcharacteristics of the foldings in order to efficiently detect the foldedregions. Following detection, the foldings are removed and any gaps so createdare filled based on the geometry of the 3D model. The proposed method isdirectly applicable to simple mesh surface representations while it does notperform any embedding of the 3D mesh (i.e. voxelization, projection). Target ofthe proposed method is to facilitate mesh degradation procedures in a fashionthat retains the original structure, given the operator, in the most efficientmanner.

FoR$^2$M: Recognition and Repair of Foldings in Mesh Surfaces. Application to 3D Object Degradation