The Monuments Board of the Slovak Republic

Abstract Although fertile soil is rare in central Slovakia, the region is rich in raw minerals, a resource exploited since the Palaeolithic. Maintaining trade through a reliable network of safe routes across the mountainous landscape was of vital importance, and the remains of roads that connected this mining area to the rest of the world can still be found. Furthermore, the south–north route connecting these resources with the Carpathian Basin in the south and the Vistula River Basin in the north may have played an important role as a possible bypass to the well-known Amber Road. By combining walkthrough surveys and high-resolution LiDAR data, the paths of single roads can be reconstructed and analysed in relation to the main routes. Furthermore, by applying the geographic information system-based spatial context of settlement structures, analyses can be performed on whether routes passing through certain areas caused the establishment of settlements or whether the routes were built to connect the established sites with the rest of the road network. Finally, defining ancient route planning strategies can help answer the question of how the main routes affect settlement patterns.

Abstract A novel approach to a three-dimensional (3D) model creation from data sets obtained by laser scanning or photogrammetry is presented, including a description of the method and efficient numerical algorithms for 3D model creation for surveying applications. The presented method solves the fundamental problem of surface reconstruction by constructing models using differential geometry and partial differential equations. The time-relaxed eikonal equation was used to obtain the distance function from the cloud of points, and the 3D model was then created by the evolution of an initial guess by the advection equation regularized by curvature, where the advective velocity is given by the gradient of the computed distance function. The partial differential equations were discretized by the finite-difference schemes, and the results of the 3D model creation are presented and discussed.