third-degree curves

 

Del Coates, Watches tell more than time, ????

third-degree curves (WTMTT)

p.183

On average, however, studies show that most people prefer the gently undulating lines and surfaces of third-degree geometry――in other words, curves that are complex but not too complex. In one study, engineering students tended to prefer more highly organized second-degree curves, where as music students tended to prefer more complex fourth-degree curves.

     p.205

     [...]

Generally, then, objective concinnity is greatest when curves and surface are constructed of third-degree curves. Traditionally, designers have accomplished this with drawing templates called ‘French curves’ that maintain sufficient levels of continuity throughout curves of ever-changing radius.

     [...]

     CAD systems ... software ... nonuniform rational B-splines (NURBs)

     [...]

     p.206

     ...However, aesthetics was not the issue. They were concerned about aerodynamics. Aircraft manufacturers and NASA  had long since determined that bodies with the lowest air drag were characterized by third- or fourth-degree surfaces.

     So they devised a wind tunnel test to find out just how serious the compromise of using second-degree surfaces would be. They built two all but identical models of a car design, one composed of second-degree surfaces and the other composed of third-degree surfaces. To no one's surprise, the third-degree model yielded the best results; a real car based on this design would have been more fuel efficient than other. What did surprise them was that, eerily, the third-degree model somehow had a different character visually. It also ‘looked’ better――even though the models seemed identical without careful examination. The eye seemed to be more disturbed by the subtle discontinuities of the second-degree model, just as the air was as it swept over the surface. The results provided yet another vidication of the classic aesthetic maxim that “form follows function.”

   (‘Watches tell more than time : product design, information, and the quest for elegance’, written by Del Coates, publisher McGraw-Hill, p.183, p.205, p.206)