This paper introduces our qualitative shape representation formalism that is devised to overcome, as we have argued, the class abstraction problems created by numeric schemes. The numeric shape representation method used in conventional geometric modeling systems reveals difficulties in several aspects of architectural designing. Firstly, numeric schemes strongly require complete and detailed information for any simple task of object modeling. This requirement of information completeness makes it hard to apply numeric schemes to shapes in sketch level drawings that are characteristically ambiguous and have non-specific limitations on shape descriptions. Secondly, Cartesian coordinate-based quantitative shape representation schemes show restrictions in the task of shape comparison and classification that are inevitably involved in abstract concepts related to shape characteristics. One of the reasons why quantitative schemes are difficult to apply to the abstraction of individual shape information into its classes and categories is the uniqueness property, meaning that an individual description in a quantitative scheme should refer to only one object in the domain of representation. A class representation, however, should be able to indicate not only one but also a group of objects sharing common characteristics. Thirdly, it is difficult or inefficient to apply numeric shape representation schemes based on the Cartesian coordinate system to preliminary shape analysis and modeling tasks because of their emphasis on issues, such as detail, completeness, uniqueness and individuality, which can only be accessed in the final stages of designing. Therefore, we face the need for alternative shape representation schemes that can handle class representation of objects in order to manage the shapes in the early stages of designing. We consider shape as a boundary description consisting of a set of connected and closed lines. Moreover, we need to consider non-numeric approaches to overcome the problems caused by quantitative representation approaches.This paper introduces a qualitative approach to shape representation that is contrasted to conventional numeric techniques. This research is motivated by ideas and methodologies from related studies such as in qualitative formalism ([4], [6], [19], [13], [31]), qualitative abstraction [16], qualitative vector algebra ([7], [32]), qualitative shapes ([18], [23], [21]), and coding theory ([20], [25], [26], [1], [2], [3], [22]). We develop a qualitative shape representation scheme by adopting propitious aspects of the above techniques to suit the need for our shape comparison and analysis tasks. The qualitative shape-encoding scheme converts shapes into systematically constructed qualitative symbols called Q-codes. This paper explains how the Q-code scheme is developed and applied.
Dependence of Model Energy Spectra on Vertical Resolution