A two step analysis was performed to solve the tool path optimization problem. A computer program was initially created to estimate the tool path as a function of the orientation of cut. An analysis was performed using this program and graphical plots were obtained on different convex polygonal shapes. It was inferred from these plots that an optimization was possible. A detailed analytical model was hence created that allowed the nature of the relationship between the variables to be studied. This analytical function related the total path to orientation as an arithmetic progression of trigonometric functions based purely on object geometry and cutter diameter. The transformation orientations provided the optimal tool paths. The global minima of the length of cut function was obtained by orienting the cutter parallel to the longest edge. The present algorithm can be extended to include generic prismatic shapes in the future. Therefore the feasibility of analytical modelling as well as the results of tool path optimization are well verified.