| Interactive three-dimensional modelling is the procedure of measuring and reconstructing the surface of an object in real-time. The main obstacle toward creating a real-time, interactive modelling system is the computational complexity of modelling algorithms; in order to insure the non-degrading performance of the modelling system, the computational complexity has to be linear with respect to the quantity of measured data. We propose a 3D modelling framework that allows all modelling algorithms with linear complexity in all modelling steps.;Adopting a novel representation of the surface implies that all modelling algorithms have to be developed anew in order to exploit the vector fields. For that reason, we propose surface reconstruction algorithms that allow model reconstruction from any type of range data: surface patches (range images), surface curves, clouds of points or their combination. Furthermore, registration, compression and visualization algorithms are proposed as well. All algorithms are of linear computational complexity and are based uniquely on vector fields without using any other intermediate representation.;The main proposition of this thesis is that solving modelling problems, including computational complexity, requires an adequate representation of the data (surface) rather than novel algorithms alone. In particular, the closest point search problem---that appears in one form or another throughout the modelling chair---is identified as the main source of non-linear computational complexity. As a solution for this problem, a vector field surface representation is proposed. Being defined on a regular 3D grid and by explicitly encoding the closest surface points, that is tangent planes, vector fields provide direct access to the closest points thus avoiding all searches and rendering the computational complexity linear with respect to the quantity of measured data. |
