Qualitative sketch optimization

Abstract

AbstractThe “sketch” drawn by a human designer represents a shape class of wider variability than can be captured by traditional CAD models; these typically work with parametrizations based on a nearly finished shape. Traditional Qualitative Reasoning is also unable to model this degree of ambiguity in shape. Cognitively, shapes are often represented in terms of an axial model. In defining 2D contours, such an axial representation is called the Medial Axis Transform or MAT. By perturbing the parameters of the MAT—length, link angle, and the node radius—one can define a shape class. Unlike the contour-to-MAT transform, which is well-known to be unstable, the MAT-to-contour process is an integrative process and is very stable. The variation in these parameters can be controlled by defining a suitable discretization over the parameter space. This leads to a broad class of similar shapes from which an optimized shape can be obtained for a given set of criteria. The optimizing criteria may involve the boundary description for each shape; the axial model is only used for generating the shape class. This Qualitative MAT model has been tested in several design optimization contexts, using Genetic Algorithms, and we show results for Automobile contours, IC engine parts, building profiles, etc.