Home | english  | Impressum | Sitemap | KIT

Offene Bachelor-/Masterarbeiten

Haben Sie Interesse an einer Bachelor- oder Masterarbeit im Bereich Angewandte Geometrie an unserem Institut?

Kontaktieren Sie uns oder kommen Sie vorbei und sprechen Sie einen unserer Mitarbeiter an!

Aktuelle Themen finden Sie ebenfalls am Aushang vor der Informatikbibliothek und im 1. OG im Gebäude 50.34.  Unten gibt es Beispiele von möglichen Arbeiten an unserem Institut.

Decomposing Surfaces of Arbitrary Genus into Pants

A pair of pants is a surface of genus zero and three boundaries. Any closed surface of genus g ≥ 2 can be decomposed into 2(g − 1) pairs of pants. This set of pants becomes an important building block in many graphical applications, including surface parametrization, shape matching, and surface morphing.

The purpose of the thesis is to study the mathematical foundations behind pants decompositions and/or to experiment with pants decompositions in a software application. Depending on your interests, the thesis can be of more theoretical or practical nature.

Feel free to come by Room 127 (50.34) to discuss the details or send an email to

Pawel Herman (pherman∂ira.uka.de).

 

References:

Parameterizing Surfaces of Arbitrary Topology

Taking a piece of paper, joining two opposite edges to form a cylinder, and then joining the ends of the cylinder creates a torus. Based on this construction, you can easily see that a torus admits an affine parametrization. Unfortunately, surfaces with no holes or with more than one hole cannot be parameterized over the affine plane. However, they can be parameterized over the hyperbolic plane.

The purpose of the thesis is to become acquainted with the hyperbolic plane and then to study whether and how various known parametrization techniques developed for the affine plane can be applied to parameterizations over the hyperbolic plane. Depending on your interests, the thesis can be of more theoretical or practical nature.

Feel free to come by Room 127 (50.34) to discuss the details or send an email to

Pawel Herman (pherman∂ira.uka.de).

 

References:

Shadow Art Sculptures

Are you interested in a 3D printing project? How about printing shadow art sculptures?

The purpose of the thesis is to design an algorithm that takes a target shadow and a set of geometries as input and outputs a model that arranges these geometries so that their shadow coincides with the shadow in the input. Examples of such shadow art sculptures can be printed on our 3D printer.

Feel free to come by Room 127 (50.34) to discuss the details or send an email to

Pawel Herman (pherman∂ira.uka.de).

 

References:

Constructing Internal Support Structures by Volumetric Subdivision

Most 3D prints need an internal support structure so that they do not collapse on themselves when standing or when they are held in one's hands. The challenge is to produce a strong structure while minimizing the amount of material needed to print it.

One novel approach to constructing internal support structures is to represent a given model with a tetrahedral mesh and then to subdivide this mesh reasonably. The purpose of the thesis is to study these volumetric subdivision techniques and apply them to generating robust 3D prints. The models produced by a successful implementation can be printed on our 3D printer.

Feel free to come by Room 127 (50.34) to discuss the details or send an email to

Pawel Herman (pherman∂ira.uka.de).

 

References:

3D Puzzles

If a model of a given size does not fit into the print space of a 3D printer, then the model must be decomposed into smaller parts that are printed individually and then assembled together. Obvious challenges include deciding how to decompose a model and how to design robust joints. These algorithms can also be used to create 3D puzzles.

The purpose of the thesis is to study methods for decomposing models into interlocking parts, design several 3D puzzles, and then print them on our 3D printer.

Feel free to come by Room 127 (50.34) to discuss the details or send an email to

Pawel Herman (pherman∂ira.uka.de).

 

References: