Aesthetics Vase Design with Transition Curves

Transition curves with monotone curvature profile are widely applied in fair curve design. Advantage of using transition curve is that it can avoid the undesirable curvature extrema. Demonstration of transition curve in designing surface of revolution, particular of vase design can be often seen in literature. For these demonstrations, authors mainly focused on the curvature control of the vase profile. To improve the quality of design, others beauty judgment should take into account. Referred to Birkhoff, in order to correlates the aesthetic measure with quality of elegance it is necessary to consider the symmetries and proportion. In the recent paper, we discussed the low energy transition curve. This paper demonstrates its application in aesthetic vase design. Specific location of curvature extremas is first evaluated base on the desirable symmetries and proportion. Whereby they are evaluate through considering the meet points of horizontal and vertical tangents line at the curvature extrema. Low energy transition curve satisfying the curvature distribution is then computed to form the vase profile. The symmetries and proportion of resulting vase profile is then compared against the idea vase given by Birkhoff.