Discrete Domain Representation for Shape Conceptualization

This paper presents a solution for discrete domain representations of 3D geometric models, and techniques for shape instance extraction from a distribution domain. The discrete domain representation captures modality, impreciseness and uncertainty. It facilitates both shape conceptualization and computer processing. We model the elements of the shape by particle clouds, which are generated from regular and dense enough point-set(s) obtained from specific input devices e.g. hand movement detector, 3D scanner. A particle cloud contains a finite number of particles. A particle is a weakly defined 3D point specified by its reference vector, metric occurrence, mass, and velocity. The metric occurrence of the particle represents the geometric uncertainty of the shape. It is defined as the range of distribution between the primary and secondary covering of the domain of variance. Technically, the metric occurrences are handled by the so-called connectivity bushes between primary and secondary covering of a particle cloud. Instance generation operators make it possible to obtain arbitrary number of shape instances of the same type. The paper also presents an application example.