For designing, visualizing and utilizing various shapes in real and virtual environments, it is a basic requirement to work with appropriate digital representations. These must obey various requirements that significantly differ depending on the applications.
In this master’s thesis, I analyze a representation called Adaptive Distance Fields, or ADF. This is a hybrid representation with the essential feature that it organizes curve segments or surface patches into a hierarchical cell structure. These segments or patches are not limited to be linear approximations, but can be curved or doubly-curved. The cell functions are based on a distance-field - and optionally on a gradient-field, being defined in the space of the object to be approximated. The cell structure can adaptively be refined for representing more details.
The main focus of my work is the analysis of consecutive phases in ADF and the evaluation of different cell functions. The curve representations examined include (i) linear and (ii) bilinear functions, and (iii) Hermite and (iv) Double Quadratic interpolants. The surface representation used is a new, n-sided surface called Generalized Bézier patch.
I also describe special cases that frequently occur in the course of ADF, and compare the aforementioned cell functions to each other. It is shown that the application of cell functions with gradients can significantly improve the compactness of the representation. As explained, presumably the most crucial aspect of ADF is the distance metric applied.
I have implemented a software system in order to perform a comparative analysis and evaluate the various phases of ADF; its functionality is also detailed in the Thesis.