Traffic rules violations and accidents on road are major issues now-a-days. Identification of vehicles violating traffic rules and manual monitoring of vehicles is difficult, due to traffic congestion on freeways. A novel mathematical model is proposed to generalize detection of a number of traffic violations on highways. The model, using image processing techniques translates lanes on the road as equation of lines. A tracking algorithm generates a vehicle trace which is modelled as equations. A piecewise linearity is used for the modelling and ease of computation of traffic violation. The model then solves a number of equations for finding intersection of traces with the traffic lanes to identify the violations. This novel modelling approach can help machine based identification of a number of traffic violations and proposed system need not to be installed in vehicles and all along road for violation detection. To cover larger length of the road, camera handoff algorithm is also designed. This technique keeps track of all vehicles along with their traces on Google maps.