Abstract
This paper reports on the theretical fundamentals of a novel modeling approach that follows the singularity theory rather than the continuity theory. The singularity oriented modeling is very useful in Certain applications, e.g. in form-giving and styling, rapid prototyping and shape generation based on gestural devices. The authors refer to this novel description technique as natural shape representation (N-rep). The key modeling entities are shape singularities of various order, structures formed by their arrangements, and natural surfaces. A shape singularity is an observable discontinuity of the boundary of an object that is featured by specific tangency and curvature characteristics. Besides the formal definition of singularities, the paper deals with their structural properties. A natural surface has been defined as a compound geometric entity that, as a domain of a boundary, obeys some specific continuity and finiteness conditions. The N-rep data scheme extends the conventional B-rep scheme with higher level constructs. The paper describes an application of the theory for shape generation by gestural device.
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