Another look at 3D road surface modelling

A new algorithm is presented that constructs three-dimensional track surface models from a mesh of measured data. The track surface models described here are parametrised 3D surfaces described in curvilinear coordinates. It is not assumed that the track can be represent by a ribbon thereby enforcing lateral flatness. The underlying model is a parametrised Monge patch, with the parametric variables found by solving an optimal control problem; Euler angles play no part. The algorithm provides all the information required to conduct vehicle dynamics studies on curved surfaces–the first and second fundamental forms. The algorithm was tested on measured Lidar data for the Darlington and Charlotte speedways and was found to be fast to compute, accurate and reliable.