Aesthetic Curve Design with Linear Gradients of Logarithmic Curvature/Torsion Graphs

R. U. Gobithaasan, Kenjiro T. Miura, L. P. Yee, A. F. Wahab


The quality of a curve for industrial design and computer graphics can be interrogated using Logarithmic Curvature Graph (LCG) and Logarithmic Torsion Graph (LTG). A curve is said to be aesthetic if it depicts linear LCG and LTG function. The Log-aesthetic curve (LAC) was developed bearing this notion and it was later extended to a Generalized Log-aesthetic curve (GLAC) using the -shift and -shift approach. This paper reformulates GLAC by representing the Logarithmic Curvature and Torsion graph’s gradient function as a nonlinear ordinary differential equation (ODE) with boundary conditions. The outputs of solving the ODEs result in a well defined Cesaro equation in the form of curvature function that is able to produce both planar as well as spatial curves with promising entities for industrial product design, computer graphics and more.

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