There is a widespread opinion in different sources, ranging from popular to scientific, that the project of the Petrovaradin Fortress was conceived under the influence of the most important European military engineer and innovator of the time, Sebastien de Vauban. By examining the historical context as well as by comparing Vauban’s geometrical methods for determination of the fortification master line (la ligne magistrale) with Austrian plans and the actual state of the Petrovaradin fortress, especially its Wasserstadt part, we have examined how well-founded this claim is.

In the middle of the 15th century, the fortification system of medieval European cities underwent a transformation into a bastion fortification system. This system will dominate until the mid-19th century, experiencing its zenith by the late 17th century with the improvements of the French military engineer Vauban. A defining feature of this system is the distinct contour of the magistral line in the ground plan, with its geometry progressing from simplicity in the early stages, to comprehensive solutions that addresses dimensions of all elements within bastion fortifications, in the final ones. Our research encompasses the geometric principles used by four selected military engineers from this period (Marolois, de Ville, Pagan, Vauban) with the aim to identify the development of geometric procedures in the design of the magistral line. We explore the specifics and differences in their approaches and methodologies. Conducting a comparative analysis of the geometric principles employed by different builders, using the example of star fortresses, we follow the progression of theoretical framework and design aspirations underlying the key elements of the magistral line. We consequently consider whether the “Vauban style” is a spontaneous creation of a single genius, or an outcome that emerged from the collective contributions of numerous predecessors across Europe. This paper spotlights the principles of bastion fortress design based on geometry, offering a way to identify markers of influence in observed examples, and also to complement non-invasive methods of cultural heritage preservation with adapted 17th-century geometric procedures, making them more compatible with modern approaches.

We are facing a number of applications for altering portrait photographs using the help of artificial intelligence. Apart from the entertainment purposes, modern computer technologies can also help us get dynamic effects from static images, an example of which is the subject of this study. Dealing with the change of lighting in portraits photographs through real-time rendering, this paper provides a method of obtaining an image with variable light source that affects the facial features generated on the basis of the face tracking data acquired from the existing static photograph. Thus, we get a portrait with altered light, as if such a source was present at the actual moment of photographing. This method aims to improve or even change the visual experience when viewing the image, so that its further application corresponds to the given context.

The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of the CeP II segments (C̅P II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments C̅P II-10-A, as well as of C̅P II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner.