Znanstvenostručni
časopis Hrvatskog druątva za geometriju i grafiku Scientific and Professional Journal 
 Barbora Pokorná, Pavel Chalmovianský (barbora.pokorna@fmph.uniba.sk, pavel.chalmoviansky@fmph.uniba.sk)
Collisionfree Piecewise Quadratic spline with Regular Quadratic ObstaclesWe classify mutual position of a quadratic Bézier curve
and a regular quadric in three dimensional Euclidean space.
For given first and last control point, we found the set of
all quadratic Bézier curves having no common point with
a regular quadric. This system of such quadratic Bézier
curves is represented by the set of their admissible middle
control points. The spatial problem is reduced to a planar
problem where the regular quadric is represented by a conic
section. Then, the set of all middle control points is found
for each type of conic section separately. The key issue is
to find the boundary of this set. It is formed from the middle control points of the Bézier curves touching the given
conic section. Our results are applicable in collisionfree
paths computation for virtual agents where the obstacles
are represented or bounded by regular quadrics. Another
application can be found in searching for pointwise spacelike curves in Minkowski space. 
 Zeynep Can, Özcan Gelișgen, Rüstem Kaya (zeynepcan@aksaray.edu.tr, gelisgen@ogu.edu.tr, rkaya@ogu.edu.tr)
On the Metrics Induced by Icosidodecahedron and Rhombic TriacontahedronThe theory of convex sets is a vibrant and classical field
of modern mathematics with rich applications. If every
points of a line segment that connects any two points
of the set are in the set, then it is convex. The more
geometric aspects of convex sets are developed introducing some notions, but primarily polyhedra. A polyhedra,
when it is convex, is an extremely important special solid
in R^n. Some examples of convex subsets of Euclidean
3dimensional space are Platonic Solids, Archimedean
Solids and Archimedean Duals or Catalan Solids. In this
study, we give two new metrics to be their spheres an
archimedean solid icosidodecahedron and its archimedean
dual rhombic triacontahedron. 
 Gunter Weiss (weissgunter@hotmail.com)
Elementary Constructions for Conics in Hyperbolic and Elliptic PlanesIn the Euclidean plane there are wellknown constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective affinities (de la Hire's construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the elementary geometric constructions for conics, such that they also hold for those (regular) nonEuclidean planes. Some of these modifications just replace Euclidean straight lines by non Euclidean circles. Furthermore we also study properties of Thales conics, which are generated by two pencils of (nonEuclidean) orthogonal lines.

Süleyman Yüksel, Münevver Özcan (suleymanyuksel@gazi.edu.tr, mozcan@ogu.edu.tr)
On Some Regular Polygons in the Taxicab 3SpaceIn this study, it has been researched which Euclidean regular polygons are also taxicab regular and which are not.
The existence of nonEuclidean taxicab regular polygons
in the taxicab 3space has also been investigated. 
Lászlo Németh (nemeth.laszlo@emk.nyme.hu)
Sectrix Curves on the SphereIn this paper we introduce a class of curves derived from a geometrical construction. These planar curves are the generalization of the lessknown sectrix of Ceva. We also present three variations of the sectrix curves on the sphere with using the geometrical construction on the sphere, with the stereographic projection and with a socalled \rolled" transformation. 
Blaľenka Divjak, Marcel Maretić (blazenka.divjak@foi.hr, marcel.maretic@foi.hr)
Geometry for Learning AnalyticsLearning analytics is focused on the educational challenge
of optimizing opportunities for meaningful learning.

Iva Kodrnja, Elizabeta ©amec (ikodrnja@grad.hr, elizabeta.samec@gmail.com)
Family of Surfaces HeltocatIn this paper the Heltocat family of surfaces is defined according to [5]. It is shown that the surfaces de ned by the family are minimal and form an isometric deformation from the helicoid to the catenoid. The visualizations and computations were made by using the programs Sage and Mathematica.

 Luigi Cocchiarella (blazenka.divjak@foi.hr, marcel.maretic@foi.hr)
When Image sets Reality Perspectival alchemy in Velázquez's Las MeninasThere are images in History of Art, Science, Technique,
Humanities, which are milestones. Las Meninas is one
of these. Several levels of reading and deepening have
been proposed by historians and theoreticians, and many
interpretations have been made. Yet the very sophisticated construction of this masterpiece seems to escape
any univocal hypothesis, making it as well astonishing as
enigmatic.
