G²Continuous Generalized Log-Aesthetic Curves

Abstract

Log-Aesthetic (LA) curve has been claimed as one of a most promising curve for design purpose. However, LA curve has no shape variable which can be used to control its end curvatures directly. Generalized Log-Aesthetic Curve (GLAC) which is the family of LA curve has ability to control its curvature with an extra shape parameter. This paper highlights on designing two segments of GLACs in the form of C-and S-shapes with curvature continuity using interior point method. Designers will be able to design S-shapes and C-shapes by inputting control points, its direction of travel and estimated end curvatures.

Log-Aesthetic Curves for Shape Completion Problem

“…Moreover, the resulting LAC segments are satisfying 1 continuity where the curve segments interpolate both endpoints in the specified tangent directions. In case the user wants a 2 LAC solution, one may plug in the technique proposed by Miura et al [15] or employ 2 GLAC [17] in which we may use shape parameter V in GLAC to satisfy the desired curvatures. Table 3: The value of parameters obtained in LAC algorithm for S-shaped gap.…”