Theoretical Fundamentals of Natural Representation of Shapes Generated with Gestural Devices

The use of gestural devices in shape generation is getting more and more accepted. The advantages of this approach are threefold: (a) it provides a highly interactive way of regeneration and modification of free from shape models, (b) it hides the mathematical details of parametric surface design from the user, and (c) this type of analogue input devices are more powerful in shape data generation than traditional discrete input devices. In order to use this means in the most efficient way, the gap between physical surface oriented generation and analytic (synthetic) surface oriented description of shape should be bridged. This paper presents a novel modeling scheme and an effective computer internal representation for the output of gesture devices. The key concepts are shape singularities and natural surfaces. A natural surface is a one-off generated geometric entity that obeys some specific continuity and finiteness conditions. A singularity is a shape discontinuity of specific tangency and curvature characteristics. The authors refer to this novel description technique as natural shape representation (N-rep) scheme. It incorporates new structural (topological) entities and specific relationship in order to harmonize the output of gesture devices with the external view of the scheme. Some constructs of conventional B-rep data schema are however maintained. The paper also describes the way of implementation.