Design Of Log-aesthetic Curves Based On Quintic Polynomial Approximate

This family of log-aesthetic curves(LACs for short)is defined in terms of linear logarithmic curvature graphs and thus possesses monotonic curvature.LACs have been widely used to describe visually fair shapes in conputer graphics,computer aided design and computer arts.The fitting approximation of LAC has become a hot research topic in curve modeling.However,LACs are generally represented in non-polynomial form and are thus not compatible with current CAD systems.In traditional methods,most researchers approximate LAC segments by minimizing the deviation in positions.In this paper,we represent the quintic G2 curve using four variables and propose quintic G2 polynormial approximation of LAC segments.This greatly increases the flexibility of the ability of.curve modeling.Based on quintic G2 Hermite interpolation,it enables to describe visually fair shapes and modify the curves freely.In this paper,we advocate a curve construction method based on curvature editing.For a given LAC segment,a quintic G2 interpolating B(?)zier curve is obtained by minimizing a curvature-based error metric,with the advantage of being more likely to preserve the monotonic curvature property.Numerical experiments demonstrate that our method can usually generate better results than the previous methods in terms of the deviation in positions and curvatures.Compared with the traditional methods,the new algorithm not only approximates the shape of the curve closer to the target curve,but also can be applied to the curve construction for geometric modeling.