Are coronal loops projection effects?

We report results of an in-depth numerical investigation of three-dimensional projection effects which could influence the observed loop-like structures in an optically thin solar corona. Several archetypal emitting geometries are tested, including collections of luminous structures with circular cross-sections of fixed and random size, light-emitting structures with highly anisotropic cross-sections, as well as two-dimensional stochastic current density structures generated by fully-developed magnetohydrodynamic (MHD) turbulence. A comprehensive set of statistical signatures is used to compare the line of sight -integrated emission signals predicted by the constructed numerical models with the loop profiles observed by the extreme ultraviolet telescope onboard the flight 2.1 of the High-Resolution Coronal Imager (Hi-C). The results suggest that typical cross-sectional emission envelopes of the Hi-C loops are unlikely to have high eccentricity, and that the observed loops cannot be attributed to randomly oriented quasi-two dimensional emitting structures, some of which would produce anomalously strong optical signatures due to an accidental line-of-sight alignment expected in the coronal veil scenario \citep{malanushenko2022}. The possibility of apparent loop-like projections of very small (close to the resolution limit) or very large (comparable with the size of an active region) light-emitting sheets remains open, but the intermediate range of scales commonly associated with observed loop systems is most likely filled with true quasi-one dimensional (roughly axisymmetric) structures embedded into the three-dimensional coronal volume.