Znanstveno-stručni časopis
Hrvatskog druątva za geometriju i grafiku

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

Vladimir Benić, Sonja Gorjanc (benic@grad.hr, sgorjanc@grad.hr)

(1,n) Congruences

The first order algebraic congruences are classified into two basic classes which depend on their directing curves. By the method of synthetic geometry, we investigated the basic properties for each of these classes: the construction of rays, singularities, decomposition into developable surfaces, focal properties and the types of rays. The paper ends with a short analytical approach, which enables the visualizations of these congruences in the program Mathematica. Some examples are shown.

Keywords: congruence, decomposition on developable surfaces, focal lines, singularities, visualization

Article in PDF.

Márta Szilvási-Nagy (szilvasi@math.bme.hu)

About Curvatures on Triangle Meshes

A face-based curvature estimation on triangle meshes is presented in this paper. A flexible disk is laid on the mesh around a given triangle. Such a bent disk is used as a geodesic neighborhood of the face for approximating normal and principal curvatures. The radius of the disk is free input data in the algorithm. Its influence on the curvature values and the stability of estimated principal directions are investigated in the examples.

Keywords: triangle mesh, curvature

Article in PDF.

László Vörös (vorosl@witch.pmmf.hu)

Two- and Three-dimensional Tilings Based on a Model of the Six-dimensional Cube

A central-symmetric three-dimensional model of the six-dimensional cube can give us the idea of filling the space with mosaics of zonotopes. This model yields also plane tilings by its intersections. Using the parts of the model the mosaic and the tiling can further be dissected by projections, associations and Boolean operations. Further constructions are also indicated in the paper.

Keywords: 3-dimensional models of the hypercube, plane-tiling, space-filling

Article in PDF.

Attila Bölcskei, Brigitta Szilágyi (bolcskei.attila@ymmfk.szie.hu)

Visualization of Curves and Spheres in Sol Geometry

The paper makes an attempt to visualize one of the homogeneous geometries, the Sol geometry, by illustrating first the geodesic curves and spheres then the so-called translation curves and spheres. We've collected their basic properties, too.

Keywords: visualization of Thurston's geometries

Article in PDF.

Özcan Gelişgen, Rustem Kaya (gelisgen@ogu.edu.tr)

Generalization of a-distance to n-dimensional Space

In this study, we generalize the concept of a- distance which contains both of Taxicab distance and Chinese Checker distance as special cases to n-dimensional space.

Keywords: Taxicab distance, CC-distance, a-distance, metric, non-Euclidean geometry

Article in PDF.

Günter Wallner (gw@autoteles.org)

Geometry of Real Time Shadows

Shadows provide important visual hints about the spatial relationship between objects. Shadow volumes are one way to generate sophisticated shadows for use in real time environments. This paper focuses on the geometric aspects which are involved in the creation of the shadow volume. Speed up techniques like shaders and dual space approaches for silhouette determination are discussed. Finally the application of the described methods in a software for shadow profile calculation is explained.

Keywords: Shadow volumes, Dual space, Silhouette determination, Shader, Real time

Article in PDF.

Matija Herceg, Drago ©poljarić (mherceg@geof.hr)

Application of webMathematica and LiveGraphics3D in Spherical Astronomy

This paper describes development of interactive web application designed for coordinate’s recalculation within the celestial coordinate systems. Furthermore, this application is also a simple tool for the graphical display of the celestial objects location (coordinates). Recalculation of coordinates and visualization of the celestial coordinate systems capable of magnification, rotation and perspective change makes this interactive application suitable for e-learning.

Keywords: celestial coordinate systems, recalculation of coordinates, visualization, webMathematica, LiveGraphics3D, e-learning.

Article in PDF.