Optimization-based generation of 3D bobsleigh track centerlines from 2D data

Abstract

The centerline of a bobsleigh track defines its geometry and is fundamental for simulation modeling. However, publicly available centerline data are limited, and constructing training systems solely from two-dimensional (2D) centerlines is often imprecise. To address this issue, this study establishes a constrained optimization framework for three-dimensional (3D) bobsleigh track generation that explicitly incorporates geometric design constraints and Olympic safety rules, introduces a segment-wise height difference parameterization, and develops a track gradient based projected gradient descent solver validated on real tracks. Within the selected trajectories and parameter ranges considered in this study, the proposed algorithm generates 3D centerlines whose characteristic parameter trends closely follow those of the actual tracks, whether using real or scaled 2D data. Compared with the actual tracks, the maximum deviations in total length, height difference, and average gradient are 0.1%–1.1%, 1.0%–16.4%, and 0.8%–13.5%, respectively. Track sensitivity to segmentation and height difference weighting varies with the data type, and appropriate choices of these parameters effectively reduce deviations and enhance the geometric accuracy of the reconstructed centerlines. Overall, the proposed framework offers a flexible and efficient tool for supporting 3D bobsleigh track centerline generation.