Interactive Modelling of Dynamics 3D Surfaces

The interdisciplinary research area of Geometry Processing combines concepts from computer science, applied mathematics, and engineering for the efficient acquisition, reconstruction, optimization, editing, and simulation of geometric objects. Applications of geometry processing algorithms can be found in a wide range of areas, including computer graphics, computer aided design, geography, and scientific computing. Moreover, this research field enjoys a significant economic impact asit delivers essential ingredients for the production of cars, airplanes, movies, and computer games, for example.Most of the research so far has concentrated on the efficient processing of static 3D surfaces (in particular, triangle meshes), and a number of well-established algorithms exist for interactively editing, compressing, smoothing, or subdividing this kind of data. However, some applications (e.g., animation or simulation) are intrinsically based on the concept of dynamic 3D surfaces, that is, surfaces with a time-varying geometry or even topology. Currently, such surfaces are often treated in a discrete way, as a finite set of static 3D surfaces, and hence they are usually processed independently of each other with any of the aforementioned algorithms.The main idea of this project is to rather consider dynamic 3D surfaces as an entire and continuous 4D object and to gain advantages from this point of view. Hence, the goal of the project is to develop effective strategies and efficient algorithms for processing this kind of data. In particular, we are interested in methods for interactively modelling and editing dynamic 3D surfaces. This poses a number of interesting problems that need to be addressed and solved, ranging from the reconstruction of dynamic 3D surfaces from a discrete set of static surfaces, the design of novel data structures for representing and storing them, to the efficient visualization of this kind of data.