


Shape Geometry and Aestheticsby Franca Giannini and Marina Monti FIORESII is a research project of the European Commission that aims at investigating and identifying the links between emotional shape perception and geometry, in order to facilitate communication between designers and CAD operators and to create more user friendly tools for aesthetic design. The market success of industrial products strongly depends on their aesthetic character, ie the emotional reaction that the product is able to evoke. To achieve their aim designers have to act on specific shape properties, but at present they are not directly supported in this by existing digital tools for model definition and manipulation, mainly because of the still missing mathematical formalisation of the properties themselves. The European project FIORESII (GRD1199910785Character Preservation and Modelling in Aesthetic and Engineering Design), started in April 2000, aims at investigating and identifying the links between emotional shape perception and geometry and to create, through their mathematical formalization, more user friendly tools for aesthetic design Relationships Between a Physical Form and its Emotional Message Starting from the above considerations, major attention has been given to mathematically formalising the most used terms of the Language of the Trade (ie Acceleration, Tension, Convexity, Concavity, Lead in, Crispness, Sharpness, Softness, Crown), with the objective to develop modelling tools which are fundamental for:
The development of these tools implies the solution of the following problems for each term:
As an example, to illustrate how the above points have been mathematically solved, the convexity property is briefly described. Traditionally a curve is convex/concave, if the curvature (ie the second derivative) along the curve has the same sign. In our case, it has a more specific meaning. Interviews with the endusers reveal that judging a curve as more or less convex depends on several factors: symmetry, roundness, curvature variation…. Many of these factors depend in turn on mathematical properties that can be calculated on the curve and have to be combined to define a suitable measure criterion, which has to be continuous and differentiable. We took into account the aspects that are implicitly judged by the users, as well as mathematical properties such as curve length, area enclosed by the curve, coordinates of the gravity centre, momentum of inertia of the lamina with respect to the axes of the local coordinate system along the curve, etc. The combination of these properties (by means of the Minkowsky measure and with the adoption of weights for better calibration) provided a measuring criterion corresponding to the user feedback in a quite satisfying way. The theoretical specification of the tools is almost complete and the implementation of a software prototype is currently under development. It has not been easy to acquire a full understanding of how designers perceive shape and then to translate this into mathematical formalism. Even if some of the terms used have a direct mathematical counterpart, the meaning is not always the same. For example, not all curves in which the second order derivative increases are necessarily perceived as accelerating curves. Moreover, different shapes may be perceived as having the same property value. This means that several variables contribute to a single property, thus requiring a further level of interpretation to give a formal description of their interdependencies. The preliminary results confirm the validity of the approach not only from the point of view of user interest but also from a scientific perspective, linking different disciplines such as mathematics and perceptual psychology. Link: Please contact: 