Department of Geometry


Budapest University of Technology and Economics


JAVA Applets

Visualization of a user-defined truncated pyramid in axonometric view and in the Monge-projections. (M. Szilvási-Nagy)

Construction of a composition of truncated pyramids. The actual user-defined model can be positioned by rotation and translation and merged to the collection. The result is shown in the Monge-projections or in axonometric view.
The stand alone program (compoly.jar) writes the data of the composition in obj format for javaview. [download] (M. Szilvási-Nagy)

The 17 crystallographic groups of the Euclidean plane. The program allowes of  visualizing the orbit of a point, drawing patterns and constructing DV-cell tilings randomly or by user input. (I. Prok)

A large collection of three dimensional regular and semiregular polyhedra is shown allowing of moving and colouring them. (I. Prok)

A large collection of four dimensional convex uniform polytopes. The program can visualize also the incidence structure of verteces, edges, 2D-faces and 3D-faces.  (I. Prok)

Convex hull of maximal 200 points given by their Chartesian coordinates in three dimensional Euclidean space.
The applet does not read or writes data files, but offers few examples and the possibility to type input data points. The program computes edges and faces of the convex hull of the specified points and shows the result in Monge-projections and in axonometric view. You may look at the polyhedron from different directions and scale and translate the projections.
The stand alone program (convexhull.jar) reads data files (three coordinates in each line) and also writes the data of the convex hull in obj format for javaview. [download] You may [download] also a data collection of semi symmetric polyhedra and the vertices of a Dirichlet cell with the most facets known until now computed by I. Prok. (M. Szilvási-Nagy)

Geometry teaching

Three geometry coarses are presented in this linked file (a series of dias  in Microsoft PowerPoint file):
1. Classical descriptive geometry for first year mechanical engineering students
2. Descriptive geometry with computer aided geometric modeling for first year engineering designer students
3. Constructive geometry with computer, using a professional modeling system (CadKey) for second year mathematician and engineering students. A collection of works of our students are shown in the web-site: The model files can be downloaded and visualized with the Viewer of KubotekSpectrum (free download from
A Maple worksheet for defining and visualizing surfaces and their lines of intersection. [download] This worksheet helps in teaching differential geometry. (M. Szilvási-Nagy)

Developements with Javaview

Three works of our students represented with Javaview