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.

翻译：本文提出了一类新型的公平插值曲线，称为$p\kappa$-曲线。这类曲线由光滑拼接的贝塞尔曲线段构成，其中每一段的曲率分布被设计为近似抛物线形状，从而产生美观的几何形态。此外，每个曲线段在抛物线取极值的参数位置处通过一个插值点，这促使插值点与曲率极值点对齐。为实现这些特性，我们定制了一个能量函数，通过优化过程引导获得期望的曲线特征。同时，我们开发了一种高效算法及初始化方法，无需全局优化即可实现$p\kappa$-曲线的交互式建模。通过多种实例及与现有顶尖方法的对比，我们展示了$p\kappa$-曲线的建模能力及令人愉悦的视觉效果。