In the field of aesthetic design, log-aesthetic curves have a significant role to meet the high industrial requirements. In this paper, we propose a new interactive $G^1$ Hermite interpolation method based on the algorithm of Yoshida et al. with a minor boundary condition. In this novel approach, we compute an extended log-aesthetic curve segment that may include inflection point (S-shaped curve) or cusp. The curve segment is defined by its endpoints, a tangent vector at the first point, and a tangent direction at the second point. The algorithm also determines the shape parameter of the log-aesthetic curve based on the length of the first tangent that provides control over the curvature of the first point and makes the method capable of joining log-aesthetic curve segments with $G^2$ continuity.

翻译：在美学设计领域,对数曲线在满足高工业要求方面起着重要作用。在本文中,我们根据Yoshida等人的算法提出一个新的互动的1G$1美元Hermite内插法,该方法具有次要的边界条件。在这种新的方法中,我们计算了一个延伸的对数曲线段,其中可能包括穿透点(S-形曲线)或角。曲线段由终点、初点的切线矢量和第二点的正切方向来定义。算法还根据第一个对第一个点的曲线长度来决定对数曲线的形状参数,从而能够以$G_2的连续性加入对数曲线段。