Znanstveno-stručni časopis
Hrvatskog društva za geometriju i grafiku

Scientific and Professional Journal
of the Croatian Society for Geometry and Graphics

Ibrahim Günaltili (igunalti@ogu.edu.tr)

On the Projectively Extended Linear Spaces

In this article, we show that a linear space whose parameters are those of the complement of a subset in a finite projective plane π of order n such that no line is removed and a sufficient number of lines lost only one point, is projectively extended linear space.

Key words: linear space, projective plane, affine plane, semiextension, parallel class, projectively extended linear space

Article in PDF.

Ivanka Babić, Ana Sliepčević (ibabic@tvz.hr)

Regular Polygons in the Projectively Extended Hyperbolic Plane

Regular, semi-regular and polygons with right angles are constructed in Cayley-Klein's model of the projectively extended hyperbolic plane (H-plane). Some of the construction are analogous with the Euclidean ones. The ones for which there are not Euclidean analogues are carried out in original way characteristic for a H-plane. The construction of the defect of an equilateral triangle is of a special interest having the construction of the regular heptagon as its consequence.

Key words: hyperbolic plane, regular polygons, orthogon

Article in PDF.

Friedrich Manhart (manhart@geometrie.tuwien.ac.at)

Affine Geometry of Minkowski Minimal Surfaces in R13

On the one hand we give results concerning affine invarints of the focal surfaces of Minkowski minimal surfaces. Secondly we investigate the behaviour of affine invariants in case of association of Minkowski minimal surfaces.

Key words: Minkowski minimal surfaces, focal surfaces, associated surfaces

Article in PDF.

Radimir Viher (viher@master.grad.hr)

On the Multiple Roots of the 4th Degree Polynomial

In this article we investigate the connection between the multiple roots of the 4th degree polinomial P4(x) and its Descartes's cubic resolvent P3(x). The multiple roots of P4(x) are classified according to the position of all roots of the corresponding P3(x). Seven types are obtained.

Key words: 4th degree polynomial, Descartes's cubic resolvent, types of roots

Article in PDF.

Tatiana Olejníková (tatiana.olejnikova@tuke.sk)

Cyclical Surfaces Created by a Conical Helix

The paper describes cyclical surfaces created by revolution of a circle about an edge of the trihedron of a conical helix that is moving evenly along the helix. This Euclidean metric transformation is composed from revolution about one of the coordinate axes and transformation of the righthanded coordinate system to the right-handed system of the moving trihedron in every point of the conical helix. This transformation is analytically represented by a functional matrix of 4th order. These surfaces are determined at particular parameter values which have influence on the surface shape. The vector equation of surfaces and some illustrations of this group of surfaces are presented in the paper. The surfaces are illustrated and modelled in the programme Maple.

Key words: cyclical surface, conical helix, trihedron

Article in PDF.

Hans Günther Kopetzky, Hans Sachs (kopetzky@unileoben.ac.at)

Quadratic Cones and AutoCAD

Oblique circular cones and quadratic cones are discussed mainly with respect to implementations in Computer Algebra systems and CAD systems especially AutoCAD.

Key words: quadratic cones, oblique circular cones, elliptic cones

Article in PDF.

Daniela Velichová (daniela.velichova@stuba.sk)

Knotted Tori

Paper presents a family of surfaces called knotted tori, which can be regarded as special subset of two-axial surfaces of revolutions of Euler type. Analytic representation of surfaces and some of their specific geometric properties are derived, shaping parameters are discussed and several representatives of interesting shapes are illustrated.

Key words: knotted tori, Euler trajectory, two-axial surfaces of revolution

Article in PDF.

Željko Gjuranić (Zeljko.Gjuranic@t.ht.hr)

Terrain Modelling by Using Delaunay Triangulation

Delaunay triangulation is a terrain modelling procedure out of irregular set of points, such as geodetic survey. This article discusses one of the computation methods with computation theory and some practical uses. It also discusses some uses for Voronoi diagram as well as computation method.

Key words: Delaunay triangulation, Voronoi diagram, terrain modelling, geodetic survey

Article in PDF.