Math Geosci (2016) 48:419–437 DOI 10.1007/s11004-015-9602-1 ORGINAL RESEARCH Horizon Restoration by Best Fitting of Finite Elements and Rotation Constraints: Sensitivity to the Mesh Geometry and Pin-Element Location María José Ramón 1 · José Luis Briz 2 · Emilio L. Pueyo 1 · Oscar Fernández 3 Received: 28 May 2013 / Accepted: 22 May 2015 / Published online: 16 June 2015 © International Association for Mathematical Geosciences 2015 Abstract Restoration of geological structures helps understand and validate the reconstruction of subsurface structures. In many restoration algorithms, the surface is triangulated and then unfolded, starting from an undeformed location (pin-element). The aim of this paper is to assess the impact of the pin-element location and triangula- tion of the mesh (density and type) on restoration by best fitting of finite elements, with and without a rotation constraint. The deformation of complex structures is simulated at laboratory scale. First, a reference mesh is set on the undeformed models. Then, a deformation is applied to obtain the new mesh coordinates using photogrammetry. Finally, the mesh is restored and the deformation calculated on the restored model. Comparing the actual and computed deformation, it is found that dense meshes can help locate expected deformation areas, if a rotation constraint is used to reduce error propagation. Mesh type and density seem to play a secondary role in the final result for smooth surfaces, but become relevant for highly deformed surfaces. Pin-element location influences the restoration result, especially when no rotation constraint is considered. Overall, the results suggest that the accuracy and reliability of restoration methods based on triangular meshes can be significantly improved by using a rotation constraint. Keywords Unfolding · Restoration · Mesh-developable surfaces · Pin-element B María José Ramón mj.ramon.ortiga@gmail.com 1 Instituto Geológico y Minero de España (IGME), Unidad de Zaragoza. c/ Manuel Lasala 44, 9 ◦ , 50006 Saragossa, Spain 2 Depto. de Informática e Ingeniería de Sistemas e Instituto de Investigación en Ingeniería de Aragón (I3A), Universidad de Zaragoza, Saragossa, Spain 3 Repsol Exploración, Dirección de Geología, Madrid, Spain 123