Geometry

The geometry of the track to be modeled became quite complicated, as it was desired to maintain curvature continuity throughout. This resulted in the use of the clothoid, which was very useful due to its linearly varying curvature. Four primary element types were used: straight elements, curves, loops, and corkscrews. Joint elements were used to connect elements such that curvature continuity was maintained. Once each element was created in local coordinates, its global coordinates were calculated, and it was added to the end of the track in such a manner as to guarantee position, slope, and curvature continuity.