| dc.description.abstract | Accurately describing the geometry of objects in a digital environment, i.e. computers, isan essential ingredient in many of nowadays applications. Often it is desired to forecastthe behavior of real phenomena which depend on the geometry of objects by performinga simulation of, e.g. , a car crash, the ow around the wing of a plane, the stability of abuilding or the quality of the mobile phone network in a city to name just a few. Suchsimulations are indispensable in situations where an experiment cannot be performed asfor instance the task of inspecting the stability of a building in case of an earthquake.However, even in cases where an experiment could potentially be performed, e.g. in thedevelopment of a new product, it often makes sense to run a simulation instead of thereal-world experiment in order to reduce development cost and/or time.Another ongoing trend is the virtualization of environments as can be seen for examplein the area of navigation or internet shopping. A digital geometry representation enablesthe user to thoroughly explore a possibly faraway object not only from pre-chosen viewsbut in its full variety. Moreover a digitalized environment oers the powerful possibilityof interactively visualizing additional data which is designed to support the desired applicationas for instance overblended signs in a navigation software.One step further, instead of replicating and enriching the real world in a digital environment,designers, artists or engineers are able to utilize the enormous potential oftoday's 3D modeling environments to create new complex objects or sometimes even completely artificial worlds as for example in animation movies.Motivated by the huge amount of applications there is a long history of different digitalgeometry representations which were used in the past. Some applications require asolid (volumetric) representation of the object while for others it is sufficient to solelyrepresent its boundary, i.e. the surface of the object. In this thesis we will focus onsurface representations while an outlook on the analog volumetric problem will be given | en_US |
