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Proceedings of CAD'16, 2016, 23-28
Quadratic Log-Aesthetic Curves
Abstract. This paper proposes quadratic log-aesthetic curves, which are curves whose logarithmic curvature graphs are quadratic. In previous work, generalized log-aesthetic curves have been proposed by Miura and Gobithaasan. Generalized log-aesthetic curves are derived by shifting either the curvature or the radius of curvature of log-aesthetic curves. Quadratic log-aesthetic curves are another generalization of log-aesthetic curves by making logarithmic curvature graphs quadratic. We derive the equations of quadratic log-aesthetic curves and clarify their characteristics. One notable difference from generalized log-aesthetic curves is that quadratic log-aesthetic curves include curves with finite arc lengths and their curvature varying from 0 to infinity. We show that such curves can be obtained if the quadratic coefficient Gamma in the logarithmic curvature graph is negative. For drawing quadratic log-aesthetic curves, we need to compute the inverses of the error and imaginary error functions. We present a method for computing these inverses and confirm that the curves can be generated in real time.
Keywords. Quadratic log-aesthetic curve, Logarithmic curvature graph, Error and imaginary error functions