Instantiation of shapes for products by shape formation rules based on the vague discrete interval model

Abstract

The aim of designers in conceptual design is to generate a large number of alternatives for the shape of the developed product in a minimum amount of time. The alternatives may be different in the form of the global shape or in the local shape features, or in both. To overcome the limitations of conventional freeform geometric modelling systems, which support the modelling of one specific instance shape at a time, this paper proposes a method that allows us to instantiate multiple global and local shapes. Utilizing the opportunities offered by vague discrete interval modelling, the proposed method starts out from an interval shape and allows us to derive specific instances by a composition of shape formation rules, obeying linguistically formulated shape formation principles. The latter, on the one hand, express the concept (or paradigm) of a shape; on the other hand, they capture the intent of the designer. That is, they govern on a cognitive level how to derive instances from a shape interval. They are mapped onto shape formation rules, which make it possible for the designer to set the morphological characteristics and features of the shape accordingly. Mathematically, the shape formation rules are described in a declarative form, which makes it possible to convert them to computable mathematical functions, called effect functions. Shape instantiation based on an interval shape model means: (i) forming a concept for the instance shape, (ii) selecting and combining relevant shape formation rules, (iii) setting appropriate numerical values for the coefficients of the effect functions, (iv) computing and displaying the instance shapes, and (v) merging the instance shapes into one single shape with the necessary fairing. The paper explains the theoretical background of the shape formation rules-based shape instantiation, and presents examples for the application of this method to conceptual shape design of a vacuum cleaner.