Znanstvenostručni
časopis Hrvatskog društva za geometriju i grafiku Scientific and Professional Journal 
Marija Šimić HorvathIn Memoriam

 Angéla Vránics, Jenő Szirmaí (angilord@gmail.com, szirmai@math.bme.hu)
Lattice Coverings by Congruent Translation Balls Using Translationlike Bisector Surfaces in Nil GeometryIn this paper we study the Nil geometry that is one of the
eight homogeneous Thurston 3geometries. 
Georg Glaeser (georg.glaeser@uniak.ac.at)
Focus Stacking from a Purely Geometrical Point of ViewIn order to create extremely sharp photographs, focus stacking has become a widely used method nowadays, mainly in macro or micro photography. Whereas the aspect of computationally detecting sharp regions of an image has been dealt with in many publications, there is only little published about the geometric background. This paper analyzes the process from a purely geometrical point of view, revealing some nontrivial aspects that may potentially also lead to improvements in a variety of applications such as the 3D scanning of small objects. It is shown that  under calibrated conditions and with certain restrictions  focus stacking of a scene leads to arbitrarily many geometrically correct perspective images of this scene, even including normal projections. The reason for this is that the process of photography never leads to purely twodimensional images, but collinearly distorted spatial images.

 Vladimir Volenec, Ema Jurkin, Marija Šimić Horvath (volenec@math.hr, ema.jurkin@rgn.hr, msimic@arhitekt.hr)
Covertex Inscribed Triangles of Parabola in Isotropic PlaneIn the paper the concept of a covertex inscribed triangle
of a parabola in an isotropic plane is introduced. It is a
triangle inscribed to the parabola that has the centroid
on the axis of parabola, i.e. whose circumcircle passes
through the vertex of the parabola. We determine the coordinates of the triangle centers, and the equations of the
lines, circles and conics related to the triangle. 
 Ružica KolarŠuper (rkolar@foozos.hr)
Bouvaist Cubic of a Triangle in an Isotropic PlaneThe cubic in an isotropic plane which passes through the intersections of the sides of an orthic triangle with the sides of a complementary triangle of a given triangle, and through the point which is complementary to the Steiner point of triangle is studied in this paper. It is proved that its nonisotropic asymptote is parallel to Lemoine line of a given triangle. 
 Simone Porro, Luigi Cocchiarella (simone1.porro@mail.polimi.it, luigi.cocchiarella@polimi.it)
Use of a Game Engine Artificial Intelligence to Represent People Flows in Architectural Spaces via Geometry and GraphicsThe digital and the related technological evolution in recent years have shifted to words such as Virtual Reality and Artificial Intelligence. The wider use of these and other technologies in architecture has been far limited by a lack of IT tools with which architects could interface since they have been made available in the last few years only. The evolution of the tools used by the architect can be condensed and simplified into a sequence of three stages: Drawing Board, CAD systems, Game Engines. The frames of this sequence, in addition to indicating instruments, are representative of the historical context in which they have been or are still being used. This study, based on a Master thesis recently discussed at the Politecnico di Milano [14], examines the role that Game Engines can play in the graphic representation and design processes. More specifically, it takes a closer look at the Unreal Engine as a tool for creating a realtime design environment and using Artificial Intelligence (AI) technologies to represent user flows in the space as valuable support and a relevant part of the design strategies aiming at implementing and evaluating design options. For this purpose, various simulations have been carried out both considering users' flows based on assigned spaces, and generating spaces based on the users' flows. 