Generation of Log-aesthetic curves using adaptive Runge-Kutta methods

Log aesthetic curve (LAC) has been explored extensively by many researchers since 2005. At first, Gaussian-Kronrod has been proposed to evaluate LAC as the formulation of LAC involves double integration. Recently, Incomplete Gamma Function (IGF) has been proposed to represent LAC analytically which decreases the computation time up to 13 times. This paper embarks on the representation of LAC using adaptive Runge-Kutta methods to decrease the LAC computation time. The famous adaptive methods such as Runge-Kutta Fehlberg, Dormand-Prince, Sarafyan and Kutta-Merson are employed to evaluate LAC so that a desired accuracy can be achieved. This paper ends with a detailed investigation on performance metric of IGF and adaptive RK methods to compute LAC. These methods will be compared in terms of computation time and truncation error. Numerical results indicate that the computation time of LAC can be greatly improved and at the same time preserving the LAC's family.