随着北京冬奥会的成功举办， 冰雪运动在我国迎来了空前的发展机遇。雪车雪橇赛道作为冰雪运动场地的核心部分，其设计和建设尤为关键。赛道设计是场地建设的前提和基础，只有通过科学合理的设计，才能建设出满足标准、既安全又具有竞技挑战性的赛道。本研究旨在探索雪车雪橇赛道曲面的参数化表征和设计方法，实现雪车雪橇赛道的快速设计，并为未来赛道设计提供理论支持和技术参考。
本文采用参数化设计方法，对雪车雪橇赛道进行三维曲面解构，分析赛道中心线和横截面的设计要求与特点。提出了基于端点控制的多段式二阶连续中心线生成方法，以确保其水平和垂直方向上的连续性。同时，研究了基于半参数回归模型的横截面生成方法，通过拟合设计参数的参数方程，结合构建的参数方程系数的高斯过程回归模型，实现赛道横截面的连续生成。研究结果表明，本文提出的中心线生成方法能够同时满足入弯点和出弯点坐标、方向角和曲率信息的二阶连续光滑的赛道中心线生成，而建立的半参数回归模型能够实现各种长度和转弯半径的弯道横截面参数方程系数的推理，并结合中心线参数生成横截面，形成赛道曲面骨架。此外，通过案例分析，演示了雪车雪橇赛道设计流程，并成功生成了完整的赛道模型。
本文的研究成果为雪车雪橇赛道的参数化设计提供了新的思路和方法，对推动我国冰雪运动设施建设和提高赛道设计水平具有重要意义。未来的研究将进一步优化设计方法，探索更多赛道设计的可能性，以期达到更高的设计效率和更好的赛道性能。

关键词：雪车雪橇赛道；参数化设计；中心线生成 横截面生成；三维曲面生成

With the successful hosting of the Beijing Winter Olympics, winter sports have seen unprecedented development opportunities in China. The design and construction of the bobsleigh and skeleton track, as a core part of the winter sports venue, are particularly critical. Track design is the premise and foundation of venue construction. Only through scientific and reasonable design can we build a track that meets standards, is safe, and has competitive challenges. This study aims to explore the parametric representation and design methods of the bobsleigh and skeleton track surface to fill the design gap in this field in China and provide theoretical support and technical reference for future track design.
This paper adopts parametric design methods to deconstruct the three-dimensional surface of the bobsleigh and skeleton track, analyzing the design requirements and characteristics of the track centerline and cross-section. A multi-stage second-order continuous centerline generation method based on endpoint control is proposed to ensure its continuity in both horizontal and vertical directions. At the same time, the cross-section generation method based on semi-parametric regression model is studied. By fitting the parametric equation of the design parameters and combining the Gaussian process regression model with the coefficients of the parametric equation, the continuous generation of the track cross-section is realized. The research results show that the centerline generation method proposed in this paper can simultaneously satisfy the second-order continuous smooth track centerline generation with the coordinates, direction angles and curvature information of the entry and exit points, and the established semi-parametric regression model can realize the inference of the coefficients of the parametric equation of the curve cross-section of various lengths and turning radii, and generate the cross-section combined with the centerline parameters. In addition, through case analysis, the design process of the bobsleigh and skeleton track is demonstrated, and a complete track model is successfully generated.
The research results of this paper provide new ideas and methods for the parametric design of the bobsleigh and skeleton track, which is of great significance for promoting the construction of winter sports facilities in China and improving the level of track design. Future research will further optimize the design methods and explore more possibilities of track design to achieve higher design efficiency and better track performance.