Research

Research at the Applied Geometry Group focuses on efficient representations and algorithms for digital 3D models with a particular emphasis on dynamic shapes, i.e., 3D objects that undergo frequent changes of shape or appearance. Dynamic shapes play an important role in many fields, such as protein folding simulation, 3D shape design and analysis for mechanical engineering, computer animation for games and feature films, or medical applications for diagnosis and surgery simulation. The goal of our research is to understand the principles of geometric computing and modeling, and to develop new algorithms and tools for efficient 3D model representation, shape analysis, simulation, and interaction. The menu on the left provides entry points to different projects of our group in this context. Please check out the Publications page for additional information. For a list of ongoing or announced student projects see Student Projects.

Current Projects

Symmetry Detection and Structure Discovery

Symmetry and structural regularity are essential concepts in many natural and man-made objects and play a crucial role in visual perception, biology and physics, design, engineering, and art. This project investigates computational methods to detect and enhance symmetries and regular structures in geometric models.

Shape Editing based on Geometric Optimization

This project focuses on tools based on nonlinear optimization for the manipulation of highly detailed surface representations, mesh animations, and particle simulations. Special attention is given to both generality and efficiency.

Scale-aware Stable Medial Axis

The medial axis of a shape is one of the fundamental geometric concepts in computational geometry, but its practical use is limited by its notorious instability under small perturbations of the shape. Our goal is to give a new definition of an approximate medial axis that is stable under a set of meaningful perturbations and at the same time respects the intrinsic scales of the data.

Architectural Geometry

The objective of this project is to investigate mathematical concepts, robust algorithms, scalable geometric optimization techniques, and flexible data structures to form a comprehensive toolset for architectural freeform surface design taking into account construction processes and rationalization.

Constraint-Based Surface Deformation

This project investigates constraint-based modeling by direct manipulation or preservation of positional, metric, and curvature constraints anywhere on the surface of a geometric model.

Physics-Based Computer Animation

This project investigates new physics-based approaches for the animation and control of deformable objects and fluids, as well as their interaction. The goal is to find numerical methods to solve the governing equations such that complex physical behaviors can be simulated in an efficient and stable manner, yielding visually plausible results. Furthermore, techniques are explored to enable an animator to control the fluid to achieve a desired behavior. Finally, a versatile and efficient surface model that is embedded into the physics representation needs to be explored.

Sample-Based Shape Analysis

This project investigates new methods for sample-based 3D shape analysis. The goal is to define new data structures and algorithms for efficient database retrieval, segmentation, feature extraction, and shape classification.