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1. Introduction
Hogarth curves were first proposed by a famous British Art Theorist, William Hogarth, after he carried out a series of research works on the beauty of curves in the mid-1800s (Ekaterina, 2009; Hogarth, 1753). Hogarth systematically analyzed the beauty of several common curves in our daily lives, under the guidance of six fundamental principles, i.e., fitness, variety, uniformity, simplicity, intricacy and quantity (Ekaterina, 2009; Hogarth, 1753). Based on these principles, Hogarth found that there were seven beautiful curves playing significant roles in the development of the formal aesthetics (Hogarth, 1753). Accordingly, he considered these seven curves as the most beautiful curves and defined these curves as Hogarth curves.
Seven Hogarth curves have different physical lengths and curvature, thus presenting the significantly different characteristic profiles with different beauty and attractions. When comparing with the simple straight lines, Hogarth curves can be varied in their lengths and curvature. These curves were, therefore, recognized to be more attractive and decorative than the simple straight lines. On the other hand, the combination of the curved and straight lines can produce the complicated curves, which could be more diverse and decorative than the curves themselves. Also, the combination of two curves in opposite directions can form the waving curves with beautiful and comfortable profiles. Moreover, torsion of one curve in different directions may produce the flexible and vivid serpentine curve (S-curve), which can significantly improve the beauty of the curve. Among these complicated curves, S-curve has attracted the most researchers, despite that it is built up only by one curve; this is due to the fact that there are various turning methods and abundant designing elements during the production of S-curve. It can therefore satisfy the different tastes from different people and guide them to pursue limitless diversity. Based on these aesthetics concepts of curves, Hogarth shed light on the beauty of his seven curves; he indicated that the first three curves were too gentle to show their beauty, whereas, the last three curves were so curved that leads to the over-complication of the curves. Hogarth therefore preferred the fourth curve as the most beautiful and attractive curve.
The theory of Hogarth curves has laid the foundation of the development of the European art and set up the...