Modification of Cubic Bézier Spirals for Curvature Linearity

We propose the extended Bézier spiral in this paper. The spiral is useful for both design purposes and improved aesthetics. This is because the spiral is one of the Bézier curves, which play an important role in interactive curve design, and because the assessment of the curve is based on the human reception of the curve. For the latter purpose we utilize the logarithmic distribution graph that quantifies the designers’ preferences. This paper contributes the unification of the two different curve design objectives (the interactive operation and so called “eye pleasing” result generation); which have been independently investigated so far. key words: spirals, curvature variation, clothoid, Bézier curve, volume of a curve, transition curve