Fiores and The Mathematics Of Style

Article From: 10/1/2005 Automotive Design & Production, , Contributing Editor

What's in a line?

What's in a line? In the geometric sense, two points. Adding a third point yields two connected lines, the first step toward a curve. What if a stylist wants that curve to invoke the feeling of acceleration or tension, sharpness or softness? What does it mean when a stylist wants a car to be a bit more edgy? What, then, are the properties of the lines that make up the curves, and ultimately the curves that make up a car's shape and emotional qualities?

Defining stylistic properties and then creating computer-aided styling (CAS) tools that can capture and produce those properties was the aim of two research projects funded by the European Commission, FIORES and FIORES-II ( Here's the problem: While computer-aided design (CAD) is very much a part of mechanical design, it is not in the styling of complex-shaped products, such as car hoods, consumer appliances, and toys. For those products, hand drawing and model building are routine. Moreover, without an "objective formal criteria for evaluating aesthetic shape properties," time, energy, and money are lost throughout the design process: from creating and modifying models, to the disconnects in concurrent aesthetic and engineering design, to the broken feedback loop from downstream design/engineering processes.

WHAT'S IN A STYLE? "Instead of playing with control points, such as those in NURBS, we work with intent," explains Alain Massabo, vice president of advanced R&D for think3, Inc. (Cincinnati, OH; "We want to [determine] how we can translate and record how emotions are conveyed by shape, and how stylists put those emotions into shape. We want stylists explaining what they want, and then have a system reach that goal."

Together, FIORES and FIORES-II mathematically formalized styling; that is, they mapped the emotional aspects of design to verbalized styling properties. It wasn't easy. For instance, marketing people and designers tend to speak different languages. The first speaks about emotion; the second, the "tension" of shape. Add to this that what looked "sporty" in the 1930s may not look sporty today. And what looks "sporty" to Europeans may not look so to American and Japanese car drivers. Using case-based reasoning (CBR) techniques across thousands of examples, the FIORES partners extracted correlations that determined what certain styling properties literally meant to the eye. The properties investigated included tension, acceleration, sharpness, softness, crispness, convexity (the opposite of "bump" or "crown"), concavity (a type of hollowness, also the opposite to convexity), and lead in. They next defined these properties mathematically. Explains Gerd Podehl, formerly of the Department of Mechanical and Process Engineering at the University of Kaiserslautern (Germany), and now working in the prototyping department at VW (Wolfsburg, Germany), a blending with a small radius can be called "sharp"; conversely, a blending with a big radius, "soft." The absolute values for "sharpness" or "softness" are not as important as identifying the difference in the two curves. So, making a radius "sharper" means to decrease the radius of the blend; making it "softer" means increasing the radius. Incidentally, "big" and "small" depend on the sizes and proportions of the curves to be blended.

The outcome of this work was not only a design vocabulary in absolute terms, it also created verbs and adjectives that could drive a CAS system. From there, it becomes a short leap to future CAD systems with styling capabilities, with slider bars for creating, say, an "edginess" from "one" to "ten."

DESIGNING WITH STYLE. Such a prototype exists in a beta version of thinkID, a CAD package from think3. One user is Paolo Bertoni, chief technology officer for Sketch to Surface S.r.l., the digital design department of Gruppo Vercarmodel (Orbassano, Italy). He explains that he can highlight a section of a design, such as a front bumper, and then "make it more flexible, more convex, more flat, more accelerated. When the section is okay, I can apply the ‘modifier' to the total surface." As required, Bertoni can "bump" a surface 1 cm 1 mm, or whatever exact measurement he wants. Or, he can bump the section "more" or "less." Using conventional CAD, Bertoni can spend 50 hours designing a front bumper. In two minutes with CAS, he can "tune the design to the ‘dream' of the designer."

FIORES-II algorithms and applications can help designers everywhere—wherever styling is important, and especially where styling is part of a brand name. Company-specific CBR-trained libraries of styles will be possible. Better, stylistic decisions based on "emotion" will be a thing of the past. Now, that emotion will be something to draw, modify, and quantify right on the CAD screen.