标题： $pκ$-曲线：曲率近似抛物线的插值曲线 显示英文标题

标题： $pκ$-Curves: Interpolatory curves with curvature approximating a parabola

摘要： 本文介绍了一类新颖的公平且插值的曲线，称为$p\kappa$曲线。这些曲线由平滑拼接的贝塞尔曲线段组成，每个曲线段的曲率分布被设计为与抛物线非常相似，从而形成美观的形状。此外，每个曲线段在抛物线具有极值的参数处通过一个插值点，促使插值点与曲率极值对齐。为了实现这些特性，我们定制了一个能量函数，引导优化过程以获得所需的曲线特性。此外，我们开发了一个高效的算法和初始化方法，使得无需全局优化即可进行$p\kappa$曲线的交互式建模。我们提供了各种示例，并与现有最先进的方法进行了比较，以展示$p\kappa$曲线的曲线建模能力和视觉吸引力。 显示英文摘要

摘要： This paper introduces a novel class of fair and interpolatory curves called $p\kappa$-curves. These curves are comprised of smoothly stitched B\'ezier curve segments, where the curvature distribution of each segment is made to closely resemble a parabola, resulting in an aesthetically pleasing shape. Moreover, each segment passes through an interpolated point at a parameter where the parabola has an extremum, encouraging the alignment of interpolated points with curvature extrema. To achieve these properties, we tailor an energy function that guides the optimization process to obtain the desired curve characteristics. Additionally, we develop an efficient algorithm and an initialization method, enabling interactive modeling of the $p\kappa$-curves without the need for global optimization. We provide various examples and comparisons with existing state-of-the-art methods to demonstrate the curve modeling capabilities and visually pleasing appearance of $p\kappa$-curves.