An automatic algorithm for finding racing lines via computerized minimization of a measure of the curvature of a racing line is derived. Maximum sustainable speed of a car on a track is shown to be inversely proportional to the curvature of the line it is attempting to follow. Low curvature allows for higher speed given that a car has some maximum lateral traction when cornering. The racing line can also be constrained, or “pinned,” at arbitrary points on the track. Pinning may be randomly, deterministically, or manually and allows, for example, a line designer to pin the line at any chosen points on the track, such that when the automatic algorithm is run, it will produce the smoothest line that still passes through all the specified pins.